1abel A B Bernanke B S Croushore D Macroeconomics Solutions M

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Answers to Textbook Problems

Review Questions 1. Both total output and output per worker have risen strongly over time in the United States. Output itself has grown by a factor of 100 in the last 133 years. Output per worker is now six times as great as it was in 1900. These changes have led to a much higher standard of living today. 2. The business cycle refers to the short-run movements (expansions and recessions) of economic activity. The unemployment rate rises in recessions and declines in expansions. The unemployment rate never reaches zero, even at the peak of an expansion. 3. A period of inflation is one in which prices (on average) are rising over time. Deflation occurs when prices are falling on average over time. Before World War II, prices tended to rise during war periods and fall after the wars ended; over the long run, the price level remained fairly constant. Since World War II, however, prices have risen fairly steadily. 4. The budget deficit is the annual excess of government spending over tax collections. The U.S. federal government has been most likely to run deficits during wars. From the early 1980s to the mid-1990s, deficits were very large, even without a major war. The U.S. government ran surpluses for several years, from 1998 to 2001. 5. The trade deficit is the amount by which imports exceed exports; the trade surplus is the amount by which exports exceed imports, so it is the negative of the trade deficit. In recent years the United States has had huge trade deficits. But from 1900 to 1970, the United States mostly had trade surpluses. 6. Macroeconomists engage in forecasting, macroeconomic analysis, macroeconomic research, and data development. Macroeconomic research can be useful in investigating forecasting models to improve forecasts, in providing more information on how the economy works to help macroeconomic analysts, and in telling data developers what types of data should be collected. Research provides the basis (results and ideas) for forecasting, analysis, and data development. 7. The steps in developing and testing an economic model or theory are: (1) state the research question; (2) make provisional assumptions that describe the economic setting and the behavior of the economic actors; (3) work out the implications of the theory; (4) conduct an empirical analysis to compare the implications of the theory with the data; and (5) evaluate the results of your comparisons. The criteria for a useful theory or model are that (1) it has reasonable and realistic assumptions; (2) it is understandable and manageable enough for studying real problems; (3) its implications can be tested empirically using real-world data; and (4) its implications are consistent with the data. 8. Yes, it is possible for economists to agree about the effects of a policy (that is, to agree on the positive analysis of the policy), but to disagree about the policy’s desirability (normative analysis). For example, suppose economists agreed that reducing inflation to zero within the next year would cause a recession (positive analysis). Some economists might argue that inflation should be reduced, because they prefer low inflation even at the cost of higher unemployment. Others would argue that inflation isn’t as harmful to people as unemployment is, and would oppose such a policy. This is normative analysis, as it involves a value judgment about what policy should be. 9. Classicals see wage and price adjustment occurring rapidly, while Keynesians think that wages and prices adjust only slowly when the economy is out of equilibrium. The classical theory implies that unemployment will not persist because wages and prices adjust to bring the economy rapidly back to equilibrium. But if Keynesian theory is correct, then the slow response of wages and prices means that unemployment may persist for long periods of time unless the government intervenes. ©2014 Pearson Education, Inc.

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

10. Stagflation was a combination of stagnation (high unemployment) and inflation in the 1970s. It changed economists’ views because the Keynesian approach couldn’t explain stagflation satisfactorily.

Numerical Problems 1. (a) Average labor productivity is output divided by employment: 2011: 12,000 tons of potatoes divided by 1000 workers = 12 tons of potatoes per worker 2012: 14,300 tons of potatoes divided by 1100 workers = 13 tons of potatoes per worker (b) The growth rate of average labor productivity is [(13/12) − 1] × 100% = 8.33%. (c) The unemployment rate is: 2011: (100 unemployed/1100 workers) × 100% = 9.1% 2012: (50 unemployed/1150 workers) × 100% = 4.3% (d) The inflation rate is [(2.5/2) − 1] × 100% = 25%. 2. The answers to this problem will vary depending on the current date. The answers here are based on the August 2012 release of the National Income and Product Accounts, Tables 1.1.5 and 3.2. Numbers are at annual rates in billions of dollars. 2010 GDP Exports Imports Federal Receipts Federal Expenditures a. Exports/GDP Imports/GDP Trade Imbalance/GDP b. Federal Receipts/GDP Federal Expenditures/GDP Deficit/GDP

2011

2012Q2

14,498.9 15,075.7 15,606.1 1,844.4 2,094.2 2,192.9 2,356.1 2,662.3 2,766.0 2,395.4 2,519.6 2,680.6 3,703.4 3,757.0 3,775.1 12.7% 16.3%

13.9% 17.7%

14.1% 17.7%

−3.5%

−3.8%

−3.7%

16.5% 25.5% 9.0%

16.7% 24.9% 8.2%

17.2% 24.2% 7.0%

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Chapter 1

Introduction to Macroeconomics

3

Analytical Problems 1. Yes, average labor productivity can fall even when total output is rising. Average labor productivity is total output divided by employment. So average labor productivity can fall if output and employment are both rising but employment is rising faster. Yes, the unemployment rate can also rise even though total output is rising. This can occur a number of different ways. For example, average labor productivity might be rising with employment constant, so that output is rising; but the labor force may be increasing as well, so that the unemployment rate is rising. Or average labor productivity might be constant, and both employment and unemployment could rise at the same time because of an increase in the labor force, with the number of unemployed rising by a greater percentage. 2. Just because prices were lower in 1890 than they were in 2012 does not mean that people were better off back then. People’s incomes have risen much faster than prices have risen over the last 100 years, so they are better off today in terms of real income. 3. There are many possible theories. One possibility is that people whose last names begin with the letters A through M vote Democratic, while those whose names begin with the letters N through Z vote Republican. You could test this theory by taking exit polls or checking the lists of registered voters by party. However, this theory fails the criterion of being reasonable, since there is no good reason to expect the first letters of people’s last names to matter for their political preferences. A better theory might be one based on income. For example, you might make the assumption that the Republican Party promotes business interests, while the Democratic Party is more interested in redistributing income. Then you might expect people with higher incomes to vote Republican and people with lower incomes to vote Democratic. Taking a survey of people as they left the polls could test this. In this case the assumptions of the theory seem reasonable and realistic, and the model is simple enough to understand and to apply. So it is potentially a useful model. 4. (a) Positive. This statement tells what will happen, not what should happen. (b) Positive. Even though it is about income-distribution issues, it is a statement of fact, not opinion. If the statement said “The payroll tax should be reduced because it . . . ,” then it would be a normative statement. (c) Normative. Saying taxes are too high suggests that they should be lower. (d) Positive. Says what will happen as a consequence of an action, not what should be done. (e) Normative. This is a statement of preference about policies. 5. A classical economist might argue that the economy would work more efficiently without the government trying to influence trade. The imposition of tariffs increases trade barriers, interfering with the invisible hand. The tariffs simply protect an industry that is failing to operate efficiently and is not competitive internationally. A Keynesian economist might be more sympathetic to concerns about the steel industry. Keynesians might argue that there may need to be a long-run adjustment in the steel industry, but would want to prevent workers in the steel industry from becoming unemployed in the short run.

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Answers to Textbook Problems

Review Questions 1. The three approaches to national income accounting are the product approach, the income approach, and the expenditure approach. They all give the same answer because they are designed that way; any entry based on one approach has an entry in the other approaches with the same value. Whenever output is produced and sold, its production is counted in the product approach, its sale is counted in the expenditure approach, and the funds received by the seller are counted in the income approach. 2. Goods are measured at market value in GDP accounting so that different types of goods and services can be added together. Using market prices allows us to count up the total dollar value of all the economy’s output. The problem with this approach is that not all goods and services are sold in markets, so we may not be able to count everything. Important examples are homemaking and environmental quality. 3. Intermediate goods and services are used up in producing other goods in the same period (year) in which they were produced, while final goods and services are those that are purchased by consumers or are capital goods that are used to produce future output. The distinction is important, because we want to count only the value of final goods produced in the economy, not the value of goods produced each step along the way. 4. GNP is the market value of final goods and services newly produced by domestic factors of production during the current period, whereas GDP is production taking place within a country. Thus, GNP differs from GDP when foreign factors are used to produce output in a country, or when domestic factors are used to produce output in another country. GDP = GNP − NFP, where NFP = net factor payments from abroad, which equals income paid to domestic factors of production by the rest of the world minus income paid to foreign factors of production by the domestic economy. A country that employs many foreign workers will likely have negative NFP, so GDP will be higher than GNP. 5.

The four components of spending are consumption, investment, government purchases, and net exports. Imports must be subtracted, because they are produced abroad and we want GDP to count only those goods and services produced within the country. For example, suppose a car built in Japan is imported into the United States. The car counts as consumption spending in U.S. GDP, but is subtracted as an import as well, so on net it does not affect U.S. GDP. However, it is counted in Japan’s GDP as an export.

6. Private saving is private disposable income minus consumption. Private disposable income is total output minus taxes paid plus transfers and interest received from the government. Private saving is used to finance investment spending, the government budget deficit, and the current account. National saving is private saving plus government saving. 7. National wealth is the total wealth of the residents of a country, and consists of its domestic physical assets and net foreign assets. Wealth is important because the long-run economic well-being of a country depends on it. National wealth is related to national saving because national saving is the flow of additions to the stock of national wealth. 8. Real GDP is the useful concept for figuring out a country’s growth performance. Nominal GDP may rise because of increases in prices rather than growth in real output.

9. The CPI is a price index that is calculated as the value of a fixed set of consumer goods and services at current prices divided by the value of the fixed set at base-year prices. CPI inflation is the growth

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Chapter 2

The Measurement and Structure of the National Economy

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rate of the CPI. CPI inflation overstates true inflation because it is hard to measure changes in quality, and because the price index doesn’t account for substitution away from goods that become relatively more expensive towards goods that become relatively cheaper. 10. The nominal interest rate is the rate at which the nominal (or dollar) value of an asset increases over time. The real interest rate is the rate at which the real value or purchasing power of an asset increases over time, and is equal to the nominal interest rate minus the inflation rate. The expected real interest rate is the rate at which the real value of an asset is expected to increase over time. It is equal to the nominal interest rate minus the expected inflation rate. The concept that is most important to borrowers and lenders is the expected real interest rate, because it affects their decisions to borrow or lend.

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

Numerical Problems 1.

GDP is the value of all final goods and services produced during the year. The final output of coconuts is 1000, which is worth 500 fish, because two coconuts are worth one fish. The final output of fish is 500 fish. So in terms of fish, GDP consists of 500 fish worth of coconuts plus 500 fish, with a total value of 1000 fish. To find consumption and investment, we must find out what happens to all the coconuts and fish. Gilligan consumes all his 200 coconuts (worth 100 fish) and 100 fish, so his consumption is worth 200 fish. The Professor stores 100 coconuts with a value of 50 fish. In an ideal accounting system, these stored coconuts would be treated as investment. However, in the national income accounts, because it is so difficult to tell when durable goods are consumed and when they are saved, they are counted as consumption. So the Professor’s consumption consists of 800 coconuts (value 400 fish) and 400 fish, for a total value of 800 fish. Thus the economy’s total consumption is valued at 1000 fish and investment is zero. In terms of income, Gilligan’s income is clearly worth 200 fish (100 fish plus 200 coconuts worth 100 fish). The Professor’s income is 800 coconuts (1000 coconuts minus the 200 coconuts paid to Gilligan) plus 400 fish (500 fish minus 100 fish paid to Gilligan). In terms of fish, the Professor’s income has a value of 800 fish. This question illustrates some of the nuances of national income accounting. Many difficult choices and measurement issues are involved in constructing the accounts. Here, for example, it is clear that what we call consumption really isn’t just the amount of goods consumers use up during the year, but also includes consumption goods that are purchased but saved for the future. Since there is no way to measure when goods are used after they are purchased, the accounts are unable to distinguish consumption from storage of goods.

2.

(a) Furniture made in North Carolina that is bought by consumers counts as consumption, so consumption increases by $6 billion, investment is unchanged, government purchases are unchanged, net exports are unchanged, and GDP increases by $6 billion. (b) Furniture made in Sweden that is bought by consumers counts as consumption and imports, so consumption increases by $6 billion, investment is unchanged, government purchases are unchanged, net exports fall by $6 billion, and GDP is unchanged. (c) Furniture made in North Carolina that is bought by businesses counts as investment, so consumption is unchanged, investment increases by $6 billion, government purchases are unchanged, net exports are unchanged, and GDP increases by $6 billion. (d) Furniture made in Sweden that is bought by businesses counts as investment and imports, so consumption is unchanged, investment increases by $6 billion, government purchases are unchanged, net exports decline by $6 billion, and GDP is unchanged.

3.

(a) ABC produces output valued at $2 million and has total expenses of $1.3 million ($1 million for labor, $0.1 million interest, $0.2 million taxes). So its profits are $0.7 million. XYZ produces output valued at $3.8 million ($3 million for the three computers that were sold, plus $0.8 million for the unsold computer in inventory) and has expenses of $3.2 million ($2 million for components, $0.8 million for labor, and $0.4 million for taxes). So its profits are $0.6 million. According to the product approach, the GDP contributions of these companies are $3.8 million, the value of the final product of XYZ. ABC’s production is of an intermediate good, used completely by XYZ, and so is not counted in GDP. According to the expenditure approach, the GDP contribution is also $3.8 million, with $3 million (of sold computers) adding to the capital stock (as investment spending), and $0.8 million (the unsold computer) as inventory investment.

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Chapter 2

The Measurement and Structure of the National Economy

15

The income approach yields the same GDP total contribution. The amounts are: ABC

XYZ

TOTAL

Labor

$1.0 million

$0.8 million

$1.8 million

Profit

$0.7 million

$0.6 million

$1.3 million

Taxes

$0.2 million

$0.4 million

$0.6 million

Interest

$0.1 million

$0.0 million

$0.1 million

Total of all incomes = $3.8 million (b) If ABC pays an additional $.5 million for computer chips from abroad, the results change slightly. The correct answer is easiest to see using the expenditure approach. As in part a, there is $3.8 million spent on final goods, but now there are also net exports of −$0.5 million. So the total expenditure on domestically produced goods is only $3.3 million. The product approach gets the same answer because the $0.5 million is a contribution to GDP of the country in which the chips were made, and so must be deducted from the GDP of the United States. The value added in the United States is only $3.3 million. Finally, the income approach gives the same answer as in part a, except that the cost of importing the chips reduces ABC’s profits by $0.5 million, so the sum of the incomes is only $3.3 million. 4.

(a) Product approach: $2 = gas station’s value added = $28 product minus $26 value of product produced in the previous year. Expenditure approach: $2 = $28 consumption spending plus inventory investment of −$26. Income approach: $2 paid to the factors of production at the gas station (wages of employees, interest, taxes, profits). (b) Product approach: $60,000 broker’s fee for providing brokerage services. Expenditure approach: $60,000 counts as residential investment made by the homebuyer. The important point here is that the transfer of an existing good, even at a higher value than that at which it was originally sold, does not add to GDP. Income approach: $60,000 income to the broker for wages, profits, etc. (c) Product approach: $40,000 salary plus $16,000 childcare equals $56,000. Note that there is a sense in which the childcare is an intermediate service and should not be counted, because without it the homemaker would not be able to work. But in practice there is no way to separate such intermediate services from final services, so they are all added to GDP. Expenditure approach: $56,000 ($16,000 consumption spending on child care services plus $40,000 in categories that depend on what the homemaker spends his or her income). Income approach: $56,000 ($40,000 compensation of homemaker plus $16,000 income to the factors producing the child care: employees’ wages, interest, taxes, profits). (d) Product approach: $100 million of a capital good. Since it is produced with local labor and materials, and assuming no payments go to Japanese factors of production, this is all added to U.S. GDP. Expenditure approach: $100 million net exports, since the plant is owned by the Japanese. (It is not part of gross domestic investment because the plant is not a capital good owned by U.S. residents.) Income approach: $100 million paid to U.S. factors of production. (e) Product approach: $0 because nothing is produced. Expenditure approach: $0 because this is a transfer, not a government purchase of goods or services. Income approach: $0, because this is not a payment to a factor of production, just a transfer. (f) Product approach: $5,000 worth of advertising services. Expenditure approach: $5,000 of government purchases. Income approach: $5,000 compensation of employees.

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

(g) Product approach: $120 million composed of $100 million of new cars produced plus $20 million of sales services provided by the consortium ($60 million sales price minus $40 million cost). Expenditure approach: $100 million by Hertz as investment plus $60 million by the public for consumption of the used cars minus $40 million of investment goods sold by Hertz, for a total of $120 million. Income approach: $100 million to the factors of production of GM plus $20 million in payments to the factors of production and profits for the consortium. 5.

Given data: I = 40, G = 30, GNP = 200, CA = −20 = NX + NFP, T = 60, TR = 25, INT = 15, NFP = 7 − 9 = −2. Since GDP = GNP − NFP, GDP = 200 − (−2) = 202 = Y. Since NX + NFP = CA, NX = CA − NFP = −20 − (−2) = −18. Since Y = C + I + G + NX, C = Y − (I + G + NX) = 202 − (40 + 30 + (−18)) = 150. Spvt = (Y + NFP − T + TR + INT) − C = (202 + (−2) − 60 + 25 + 15) −150 = 30. Sgovt = (T − TR − INT) − G = (60 − 25 − 15) − 30 = −10. S = Spvt + Sgovt = 30 + (−10) = 20. (a) (b) (c) (d) (e) (f) (g)

Consumption = 150 Net exports = −18 GDP = 202 Net factor payments from abroad = −2 Private saving = 30 Government saving = −10 National saving = 20

6. Base-Year Quantities at Current-Year Prices Apples

At Base-Year Prices

3000 × $3 = $ 9,000

3000 × $2 = $ 6,000

Bananas

6000 × $2 = $12,000

6000 × $3 = $18,000

Oranges

8000 × $5 = $40,000 $61,000

8000 × $4 = $32,000 $56,000

Total

Current-Year Quantities at Current-Year Prices

At Base-Year Prices

Apples

4,000 × $3 = $ 12,000

4,000 × $2 = $ 8,000

Bananas

14,000 × $2 = $ 28,000

14,000 × $3 = $ 42,000

Oranges

32,000 × $5 = $160,000

32,000 × $4 = $128,000

$200,000

$178,000

Total

(a) Nominal GDP is just the dollar value of production in a year at prices in that year. Nominal GDP is $56 thousand in the base year and $200 thousand in the current year. Nominal GDP grew 257% between the base year and the current year: [($200,000/$56,000) − 1] × 100% = 257%. (b) Real GDP is calculated by finding the value of production in each year at base-year prices. Thus, from the table above, real GDP is $56,000 in the base year and $178,000 in the current year. In percentage terms, real GDP increases from the base year to the current year by [($178,000/$56,000) − 1] × 100% = 218%.

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Chapter 2

The Measurement and Structure of the National Economy

17

(c) The GDP deflator is the ratio of nominal GDP to real GDP. In the base year, nominal GDP equals real GDP, so the GDP deflator is 1. In the current year, the GDP deflator is $200,000/$178,000 = 1.124. Thus the GDP deflator changes by [(1.124/1) − 1] × 100% = 12.4% from the base year to the current year. (d) Nominal GDP rose 257%, prices rose 12.4%, and real GDP rose 218%, so most of the increase in nominal GDP is because of the increase in real output, not prices. Notice that the quantity of oranges quadrupled and the quantity of bananas more than doubled. 7.

Calculating inflation rates: 1929–30: [(50.0/51.3) − 1] × 100% = −2.5% 1930–31: [(45.6/50.0) − 1] × 100% = −8.8% 1931–32: [(40.9/45.6) − 1] × 100% = −10.3% 1932–33: [(38.8/40.9) − 1] × 100% = −5.1% These all show deflation (prices are declining over time), whereas recently we have had nothing but inflation (prices rising over time).

8.

The nominal interest rate is [(545/500) − 1] × 100% = 9%. The inflation rate is [(214/200) − 1] × 100% = 7%. So the real interest rate is 2% (9% nominal rate − 7% inflation rate). Expected inflation was only [(210/200) − 1] × 100% = 5%, so the expected real interest rate was 4% (9% nominal rate − 5% expected inflation rate).

9.

(a) The annual rate of inflation from January 1, 2011, to January 1, 2013, is 10%. This can be found by calculating the constant rate of inflation that would raise the deflator from 200 to 242 in two years. This gives the equation (1 + π)(1 + π) = (242/200), which has the solution π = 10%. An easy way to think about this question is this. A constant inflation rate of π raises the deflator from 200 on January 1, 2011, to 200 × (1 + π) on January 1, 2012, and to 200 × (1 + π) × (1 + π) = 242 on January 1, 2013. So we need to solve the expression (1 + π)2 = 242/200. (b) By similar reasoning, the inflation rate over the three-year period is (1 + π)3 = 266.2/200, or π = 10%. (c) We can derive a general expression in the same way: 1 + π = P1/P0 1 + π = P2/P1 ⋅⋅⋅ ⋅⋅⋅ ⋅⋅⋅ 1 + π = Pn/Pn–1 Multiplying all these lines together, we get: (1 + π)n = (P1/P0) × (P2/P1) × ⋅⋅⋅ × (Pn/Pn – 1) = Pn/P0

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

Analytical Problems 1.

The key to this question is that real GDP is not the same thing as well-being. People may be better off even if real GDP is lower; for example, this may occur because the improvement in the health of workers is more valuable to society than the loss of GDP due to the regulation. Ideally, we would like to be able to compare the costs and benefits of such regulations; they should be put in place if the overall costs (the reduced GDP in this case) are valued less than the overall benefits (the workers’ health).

2.

National saving does not rise because of the switch to CheapCall because although consumption spending declines by $2 million, so have total expenditures (GDP), which equal total income. Since income and spending both declined by the same amount, national saving is unchanged.

3.

(a) The problem in a planned economy is that prices do not measure market value. When the price of an item is too low, then goods are really more expensive than their listed price suggests—we should include in their market value the value of time spent by consumers waiting to make purchases. Because the item’s value exceeds its cost, measured GDP is too low. When the price of an item is too high, goods stocked on the shelves may be valued too highly. This results in an overvaluation of firms’ inventories, so that measured GDP is too high. A possible strategy for dealing with this problem is to have GDP analysts estimate what the market price should be (perhaps by looking at prices of the same goods in market economies) and use this “shadow” price in the GDP calculations. (b) The goods and services that people produce at home are not counted in the GDP figures because they are not sold on the market, making their value difficult to measure. One way to do it might be to look at the standard of living relative to a market economy, and estimate what income it would take in a market economy to support that standard of living.

4.

Example from 2012:Q1 (amounts in billions of dollars): Gross saving = 1945.6, gross domestic investment = 2499.9, and current account balance = –553.6. So gross domestic investment + current account balance = 1946.3, which is 0.7 larger than gross saving. Capital account transactions = 0.5 and the statistical discrepancy is 1.1, so if we add the statistical discrepancy to gross saving and subtract capital account transactions, we get 1946.2, which is almost equal to gross domestic investment + current account balance; the very small difference occurs from rounding error.

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Answers to Textbook Problems

Review Questions 1. A production function shows how much output can be produced with a given amount of capital and labor. The production function can shift due to supply shocks, which affect overall productivity. Examples include changes in energy supplies, technological breakthroughs, and management practices. Besides knowing the production function, you must also know the quantities of capital and labor the economy has. 2. The upward slope of the production function means that any additional inputs of capital or labor produce more output. The fact that the slope declines as we move from left to right illustrates the idea of diminishing marginal productivity. For a fixed amount of capital, additional workers each add less additional output as the number of workers increases. For a fixed number of workers, additional capital adds less additional output as the amount of capital increases. 3. The marginal product of capital (MPK) is the output produced per unit of additional capital. The MPK can be shown graphically using the production function. For a fixed level of labor, plot the output provided by different levels of capital; this is the production function. The MPK is just the slope of the production function. 4. The marginal revenue product of labor represents the benefit to a firm of hiring an additional worker, while the nominal wage is the cost. Comparing the benefit to the cost, the firm will hire additional workers as long as the marginal revenue product of labor exceeds the nominal wage, since doing so increases profits. Profits will be at their highest when the marginal revenue product of labor just equals the nominal wage. The same condition can be expressed in real terms by dividing through by the price of the good. The marginal revenue product of labor equals the marginal product of labor times the price of the good. The nominal wage equals the real wage times the price of the good. Dividing each of these through by the price of the good means that an equivalent profit-maximizing condition is the marginal product of labor equals the real wage. 5. The MPN curve shows the marginal product of labor at each level of employment. It is related to the production function because the marginal product of labor is equal to the slope of the production function (where output is plotted against employment). The MPN curve is related to labor demand, because firms hire workers up to the point at which the real wage equals the marginal product of labor. So the labor demand curve is identical to the MPN curve, except that the vertical axis is the real wage instead of the marginal product of labor. 6. A temporary increase in the real wage increases the amount of labor supplied because the substitution effect is larger than the income effect. The substitution effect arises because a higher real wage raises the benefit of additional work for a worker. The income effect is small because the increase in the real wage is temporary, so it doesn’t change the worker’s income very much, thus the worker won’t reduce time spent working very much. A permanent increase in the real wage, however, has a much larger income effect, since a worker’s lifetime income is changed significantly. The income effect may be so large that it exceeds the substitution effect, causing the worker to reduce time spent working. 7. The aggregate labor supply curve relates labor supply and the real wage. The principal factors shifting the aggregate labor supply curve are wealth, the expected future real wage, the country’s working-age population, or changes in the social or legal environment that lead to changes in labor force

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Chapter 3 Productivity, Output, and Employment

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participation. Increases in wealth or the expected future real wage shift the aggregate labor supply curve to the left. Increases in the working-age population or in labor-force participation shift the aggregate labor supply curve to the right. 8. Full-employment output is the level of output that firms supply when wages and prices in the economy have fully adjusted; in the classical model of the labor market, this occurs when the labor market is in equilibrium. When labor supply increases, full-employment output increases, as there is now more labor available to produce output. When a beneficial supply shock occurs, then the same quantities of labor and capital produce more output, so full-employment output rises. Furthermore, a beneficial supply shock increases the demand for labor at each real wage and leads to an increase in the equilibrium level of employment, which also increases output. 9. The classical model of the labor market assumes that any worker who wants to work at the equilibrium real wage can find a job, so it is not very useful for studying unemployment. 10. The labor force consists of all employed and unemployed workers. The unemployment rate is the fraction of the labor force that is unemployed. The participation rate is the fraction of the adult population that is in the labor force. The employment ratio is the fraction of the adult population that is employed. 11. An unemployment spell is a period of time that a person is continuously unemployed. Duration is the length of time of an unemployment spell. Two seemingly contradictory facts are that most unemployment spells have a short duration and that most people who are unemployed at a particular time are experiencing spells with long durations. These can be reconciled by realizing that there may be a lot of people with short spells and a few people with long spells. On any given date, a survey finds a fairly long average duration for the unemployed, because of the people with long spells. For example, suppose that each week one person becomes unemployed for one week, so there are fiftytwo such short unemployment spells during the year. And suppose that there are four people who are unemployed all year, so there are four long unemployment spells during the year. In any given week five people are unemployed: one unemployed person has a spell of one week, while four have spells of a year. So most spells have a short duration (fifty-two short spells compared to four long spells), but most people who are unemployed at a given time are experiencing spells with long duration (one short spell compared to four long spells). 12. Frictional unemployment arises as workers and firms search to find matches. A certain amount of frictional unemployment is necessary, because it is not always possible to find the right match right away. For example, an unemployed banker may not want to take a job flipping hamburgers if he or she cannot find another banking job right away, because the match would be very poor. By remaining unemployed and continuing to search for a more suitable job, the banker is likely to make a better match. That will be better both for the banker (since the salary is likely to be higher) and for society as a whole (since the better match means greater productivity in the economy). 13. Structural unemployment occurs when people suffer long spells of unemployment or are chronically unemployed (with many spells of unemployment). Structural unemployment arises when the number of potential workers with low skill levels exceeds the number of jobs requiring low skill levels, or when the economy undergoes structural change, when workers who lose their jobs in shrinking industries may have difficulty finding new jobs. 14. The natural rate of unemployment is the rate of unemployment that prevails when output and employment are at their full-employment levels. The natural rate of unemployment is equal to the amount of frictional unemployment plus structural unemployment. Cyclical unemployment is the

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

difference between the actual rate of unemployment and the natural rate of unemployment. When cyclical unemployment is negative, output and employment exceed their full-employment levels. 15. Okun’s Law is a rule of thumb that tells how much output falls when the unemployment rate rises. It is written either in terms of the levels of output and unemployment, as in Eq. (3.5), ( Y − Y)/ Y = 2 (u − u ), or in terms of changes in output and unemployment, as in Eq. (3.6), ∆Y/Y = 3 − 2 ∆u. Since the Okun’s law coefficient is 2, a 2 percentage point increase in the unemployment rate causes output to decline by 4%.

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Numerical Problems 1. (a) To find the growth of total factor productivity, you must first calculate the value of A in the production function. This is given by A = Y/(K.3N.7). The growth rate of A can then be calculated as [(Ayear 2 − Ayear 1)/Ayear 1] × 100%. The result is: A 13.392 15.791 16.447 18.298 21.237 23.169

1960 1970 1980 1990 2000 2010

% Increase in A — 17.9% 4.2% 11.3% 16.1% 9.1%

(b) Calculate the marginal product of labor by seeing what happens to output when you add 1.0 to N; call this Y2, and the original level of output Y1. [A more precise method is to take the derivative of output with respect to N; dY/dN = 0.7A(K/N).3. The result is the same (rounded).]

1960 1970 1980 1990 2000 2007

Y1 Y2 2829 2859 4266 4304 5834 5875 8027 8074 11,216 11,273 13,063 13,129

MPN 30 38 41 47 57 66

2. (a) The MPK is 0.2, because for each additional unit of capital, output increases by 0.2 units. The slope of the production function line is 0.2. There is no diminishing marginal productivity of capital in this case, because the MPK is the same regardless of the level of K. This can be seen in Figure 3.8 because the production function is a straight line.

Figure 3.8 (b) When N is 100, output is Y = 0.2(100 + 100.5) = 22. When N is 110, Y is 22.0976. So the MPN for raising N from 100 to 110 is (22.0976 − 22)/10 = 0.00976. When N is 120, Y is 22.1909. So the MPN for raising N from 110 to 120 is (22.1909 − 22.0976)/10 = 0.00933. This shows diminishing

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

marginal productivity of labor because the MPN is falling as N increases. In Figure 3.9 this is shown as a decline in the slope of the production function as N increases.

Figure 3.9 3. (a) N 1 2 3 4 5 6

Y 8 15 21 26 30 33

MPN 8 7 6 5 4 3

MRPN (P = 5) 40 35 30 25 20 15

MRPN (P = 10) 80 70 60 50 40 30

(b) P = $5. (1) W = $38. Hire one worker, since MRPN ($40) is greater than W ($38) at N = 1. Do not hire two workers, since MRPN ($35) is less than W ($38) at N = 2. (2) W = $27. Hire three workers, since MRPN ($30) is greater than W ($27) at N = 3. Do not hire four workers, since MRPN ($25) is less than W ($27) at N = 4. (3) W = $22. Hire four workers, since MRPN ($25) is greater than W ($22) at N = 4. Do not hire five workers, since MRPN ($20) is less than W ($22) at N = 5. (c) Figure 3.10 plots the relationship between labor demand and the nominal wage. This graph is different from a labor demand curve because a labor demand curve shows the relationship between labor demand and the real wage. Figure 3.11 shows the labor demand curve.

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Chapter 3 Productivity, Output, and Employment

Figure 3.10

35

Figure 3.11

(d) P = $10. The table in part a shows the MRPN for each N. At W = $38, the firm should hire five workers. MRPN ($40) is greater than W ($38) at N = 5. The firm shouldn’t hire six workers, since MRPN ($30) is less than W ($38) at N = 6. With five workers, output is 30 widgets, compared to 8 widgets in part a when the firm hired only one worker. So the increase in the price of the product increases the firm’s labor demand and output. (e) If output doubles, MPN doubles, so MRPN doubles. The MRPN is the same as it was in part d when the price doubled. So labor demand is the same as it was in part d. But the output produced by five workers now doubles to 60 widgets. (f) Since MRPN = P × MPN, then a doubling of either P or MPN leads to a doubling of MRPN. Since labor demand is chosen by setting MRPN equal to W, the choice is the same, whether P doubles or MPN doubles.

4. MPN = A(100 − N) (a) A = 1. MPN = 100 − N. (1) W = $10. w = W/P = $10/$2 = 5. Setting w = MPN, 5 = 100 − N, so N = 95. (2) W = $20. w = W/P = $20/$2 = 10. Setting w = MPN, 10 = 100 − N, so N = 90. These two points are plotted as line NDa in Figure 3.12. If labor supply = 95, then the equilibrium real wage is 5.

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

Figure 3.12 (b) A = 2. MPN = 2(100 − N). (1) W = $10. w = W/P = $10/$2 = 5. Setting w = MPN, 5 = 2(100 − N), so 2N = 195, so N = 97.5. (2) W = $20. w = W/P = $20/$2 = 10. Setting w = MPN, 10 = 2(100 − N), so 2N = 190, so N = 95. These two points are plotted as line NDb in Figure 3.12. If labor supply = 95, then the equilibrium real wage is 10. 5. (a) If the lump-sum tax is increased, there’s an income effect on labor supply, not a substitution effect (since the real wage isn’t changed). An increase in the lump-sum tax reduces a worker’s wealth, so labor supply increases. (b) If T = 35, then NS = 22 + 12w + (2 × 35) = 92 + 12 w. Labor demand is given by w = MPN = 309 − 2N, or 2N = 309 − w, so N = 154.5 − w/2. Setting labor supply equal to labor demand gives 154.5 − w/2 = 92 + 12w, so 62.5 = 12.5w, thus w = 62.5/12.5 = 5. With w = 5, N = 92 + (12 × 5) = 152. (c) Since the equilibrium real wage is below the minimum wage, the minimum wage is binding. With w = 7, N = 154.5 − 7/2 = 151.0. Note that NS = 92 + (12 × 7) = 176, so NS > N and there is unemployment. 6. Since w = 4.5 K 0.5 N −0.5, N −0.5 = 4.5 K 0.5/w, so N = 20.25 K/w 2. When K = 25, N = 506.25/w 2. (a) If t = 0.0, then NS = 100w 2. Setting labor demand equal to labor supply gives 506.25/w 2 = 100w 2, so w 4 = 5.0625, or w = 1.5. Then NS = 100 (1.5)2 = 225. [Check: N = 506.25/1.52 = 225.] Y = 45N0.5 = 45(225)0.5 = 675. The total after-tax wage income of workers is (1 − t) w NS = 1.5 × 225 = 337.5. (b) If t = 0.6, then NS = 100 [(1 − 0.6) w] 2 = 16w 2. The marginal product of labor is MPN = 22.5/N 0.5, so N = 100 [(1 − 0.6) × 22.5/N 0.5] 2, so N 2 = 8100, so N = 90. Then Y = 45N 0.5 = 45(90) 0.5 = 426.91. Then w = 22.5/900.5 = 2.37. The total after-tax wage income of workers is (1 − t) w NS = 0.4 × 2.37 × 90 = 85.38. Note that there’s a big decline in output and income, although the wage is higher. (c) A minimum wage of 2 is binding if the tax rate is zero. Then N = 506.25/22 = 126.6, NS = 100 × 22 = 400. Unemployment is 273.4. Income of workers is wN = 2 × 126.6 = 253.2, which is lower than without a minimum wage, because employment has declined so much.

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Chapter 3 Productivity, Output, and Employment

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7. (a) At any date, 25 people are unemployed: 5 who have lost their jobs at the start of the month and 20 who have lost their jobs either on January 1 or July 1. The unemployment rate is 25/500 = 5%. (b) Each month, 5 people have one-month spells. Every six months, 20 people have six-month spells. The total number of spells during the year is (5 × 12) + (20 × 2) = 100. Sixty of the spells (60% of all spells) last one month, while 40 of the spells (40% of all spells) last six months. (c) The average duration of a spell is (0.60 × 1 month) + (0.40 × 6 months) = 3 months. (d) On any given date, there are 25 people unemployed. Twenty of them (80%) have long spells of unemployment, while 5 of them (20%) have short spells. 8. Number who become unemployed: From not in the labor force: 3% of 88.3 million = 2.649 million From employed: 2% of 142.2 million = 2.844 million Total = 5.493 million Number who become employed: From unemployed: 18% of 12.8 million = 2.304 million From not in the labor force: 4% of 88.3 million = 3.532 million Total = 5.836 million Number who become not in the labor force: From employed: 3% of 142.2 million = 4.266 million From unemployed: 21% of 12.8 million = 2.688 million Total = 6.954 million 9. Since ( Y − Y) /Y = 2(u − u ), this can be rewritten as Y − Y = 2(u − u ) Y or Y = [1 − 2(u − u )] Y , or Y = Y/[1 − 2(u − u )]. (a) Using the formula above, this table shows the value of Y , given values for u and Y. Year

u

Y

Y

1 2 3 4

0.08 0.06 0.07 0.05

950 1030 1033.5 1127.5

989.6 1030.0 1054.6 1105.4

b. The first calculation of ∆ Y/Y comes from calculating the percent change in Y from part a. The second calculation of Δ Y/Y comes from using Eq. (3.6): ∆Y/Y = ∆ Y/Y − 2 ∆u, so ∆ Y/Y = ∆Y/Y + 2 ∆u. Year

Y

∆ Y/Y

∆Y/Y

∆u

∆ Y/Y

1 2 3 4

989.6 1030.0 1054.6 1105.4

— 0.041 0.024 0.048

— 0.084 0.003 0.091

— −0.02 +0.01 −0.02

— 0.044 0.023 0.051

The two methods give fairly close answers.

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

10. (a) Total hours worked per week = 1900 workers × 40 hours per worker = 76,000 hours per week. Total output per week = 76,000 total hours per week × 10 units of output per hour = 760,000 units of output. The unemployment rate is 100 unemployed/2000 labor supply = 0.05, or 5%. (b) Employment falls 4% from 1900 to: (1 − 0.04) × 1900 = 1824. The labor force falls 0.2% from 2000 to: (1 − 0.002) × 2000 = 1996. With a labor force of 1996 and employment of 1824, unemployment is 1996 − 1824 = 172. The unemployment rate is 172/1996 = 0.086, or 8.6%. Hours worked per employed worker falls 2.5% from 40 to: (1 − 0.025) × 40 = 39. Total hours per week = 39 hours per worker × 1824 workers = 71,136. So total hours per week falls by (76,000 − 71,136)/76,000 = 0.064 = 6.4%. Total output per week falls 1.4% for every 1% drop in hours, so output falls by 6.4% × 1.4 = 8.96%. Since output was 760,000, it now falls to 760,000 × (1 − 0.0896) = 691,904. The Okun’s Law coefficient is the percent change in output divided by the increase in the unemployment rate = 0.0896/(0.086 − 0.05) = 2.49.

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Chapter 3 Productivity, Output, and Employment

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Analytical Problems 1.

(a) See Figures 3.13 and 3.14.

Figure 3.13

Figure 3.14

(b) In the initial situation, capital K1 and labor N1 produce output Y1; when productivity rises they produce output 1.1 Y1. Suppose that a small increase in capital to K2 with labor left at N1 produces output Y2 in the initial situation. Then it produces 1.1 Y2 when productivity rises by 10%. The marginal product of capital (MPK) in the initial situation is (Y2 − Y1)/(K2 − K1); when productivity rises the new MPK is (1.1 Y2 − 1.1 Y1)/(K2 − K1) = 1.1 (Y2 − Y1)/(K2 − K1). So the new MPK is 10% higher than the old MPK. This argument is completely symmetric, so it holds for MPN as well. If you substitute N for K everywhere and follow the same steps, you will show that the new MPN is 10% higher than the old MPN. (c) Yes, it is possible for a beneficial productivity shock to leave the MPK and MPN unchanged. This could happen only if the shock was additive—that is, if it shifted the whole production function upward, but did not affect its slope at any point. In Figures 3.15 and 3.16 this is shown as a shift up in the production function, leaving the slope unchanged.

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

Figure 3.15

Figure 3.16 2.

(a) An increase in the number of immigrants increases the labor force, increasing employment and increasing full-employment output. (b) If energy supplies become depleted, this is likely to reduce productivity, because energy is a factor of production. So the reduction in energy supplies reduces full-employment output. (c) Better education raises future productivity and output, but has no effect on current fullemployment output. (d) This reduction in the capital stock reduces full-employment output (although it may very well increase welfare).

3.

(a) As shown in Figure 3.17, when the real wage (w′) is above its market-clearing level, labor supply (NS′) exceeds labor demand (ND′). The difference is the amount of unemployment (U).

Figure 3.17

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Chapter 3 Productivity, Output, and Employment

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(b) Output is lower because of the real wage rigidity. With the real wage higher than the wage that clears the market at full employment, labor demand must be lower than it is at full employment, so employment and output are lower as well. 4.

(a) The increased value of Helena’s home increases her wealth. The rise in wealth leads to an income effect that leads Helena to reduce her labor supply. (b) The permanent rise in Helena’s real wage gives rise to offsetting income and substitution effects. The income effect of the higher wage reduces Helena’s labor supply, but the substitution effect increases it. So the result is theoretically ambiguous. Empirically, women tend to increase labor supply in response to a permanent increase in the real wage, and men tend to reduce labor supply in response to a permanent increase in the real wage. (c) The temporary income tax surcharge is equivalent to a temporary reduction in the real wage, which reduces current labor supply, assuming that the income effect is smaller than the substitution effect.

5.

The tax reduces the marginal product of labor by 6%, since that portion of output goes to the government rather than to the firm. Thus labor demand is reduced. With labor supply unchanged, the downward shift in labor demand reduces the real wage and employment, as shown in Figure 3.18.

Figure 3.18 6.

Yes, it is possible for the unemployment rate and the employment ratio to rise during the same month. For example, suppose the population falls, the labor force is constant, the number of unemployed rises, and the number of employed falls (but by less than the decline in population). Then the unemployment rate rises, since there are more unemployed but the same labor force, but the employment ratio rises, since population declines more than employment does. Yes, it is possible for the participation rate to fall at the same time that the employment ratio is rising. For example, suppose that population is constant, the labor force declines, employment rises, and unemployment falls. The participation rate falls, since there are fewer people in the labor force from the same population. The employment ratio is rising, since employment rises while population is constant.

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7.

Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

(a) Since Sally earns $150,000 per year, she is far above the cap, so the Social Security tax doesn’t affect her after-tax wage (so there’s no substitution effect)—the higher tax only affects her income—and thus has only an income effect. Since both proposals reduce Sally’s income by the same amount, she’ll increase her labor supply by the same amount under both proposals. (b) Under proposal A, Fred’s labor supply doesn’t change because his tax rate stays the same and he remains below the cap. So there’s neither an income effect nor a substitution effect. Under proposal B, the Social Security tax rate Fred faces would rise to 13% from 10.4%, so Fred’s after-tax wage rate declines and there’s both an income effect and a substitution effect. The income effect leads Fred to work more, since the higher tax leads to a reduction in Fred’s income. The substitution effect leads Fred to reduce his supply of labor, since the after-tax wage is lower, so there’s less reward to working. Whether Fred will supply more labor or less labor under proposal B thus depends on whether the substitution effect is stronger or weaker than the income effect.

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

Answers to Textbook Problems

Review Questions 1. Saving is current income minus consumption. For given income, any increase in consumption means an equal decrease in saving, so consumption and saving are inversely related. The basic motivation for saving is to provide for future consumption. 2. When a consumer gets an increase in current income, both current consumption and future consumption increase. Since current consumption rises, but by less than the increase in current income, saving increases. When the consumer gets an increase in expected future income, again both current and future consumption increase. Since current income does not increase, but current consumption does, saving decreases. When the consumer gets an increase in wealth, both current and future consumption again rise. Again, there has been no increase in current income, so saving decreases. At the aggregate level, these changes in consumption and saving made by individuals are decisions that change the aggregate level of desired consumption and saving. 3. The effect on desired saving of an increase in the expected real interest rate is potentially ambiguous. An increase in the real interest rate has two effects on desired saving: (1) the substitution effect increases saving, because the amount of future consumption that can be obtained in exchange for giving up a unit of current consumption rises; and (2) the income effect may increase or reduce saving. The income effect reduces saving for a lender, because a person who saves is better off as a result of having a higher real interest rate, so he or she increases current consumption. However, for a borrower, the income effect increases saving, because the borrower is worse off having to face a higher real interest rate, and so reduces current consumption. So the income effects work in different directions depending on whether a person is a lender or a borrower. For a borrower, then, both the income and substitution effects work in the same direction, and saving definitely increases. For a lender, however, the income and substitution effects work in opposite directions, so the result on desired saving is ambiguous. 4. The expected after-tax real interest rate is the after-tax nominal interest rate, (1 − t)i, minus the expected rate of inflation, π e, and represents the real return earned by a saver when a portion, t, of interest income must be paid as taxes. If the tax rate on interest income declines (that is, t declines), then 1 − t becomes larger, so the expected after-tax real interest rate increases. 5. When government purchases increase temporarily, consumers see that higher taxes will be required in the future to pay off the deficit. They reduce both current consumption and future consumption, but current consumption declines by less than the amount of the government purchases. Since national saving is output minus desired consumption minus government purchases, and government purchases have increased more than current desired consumption has decreased, national saving declines at a given real interest rate. In the case of a lump-sum tax increase, consumers have higher taxes today, but lower taxes in the future. If consumers take this into account, current desired consumption is unchanged, and since output and government purchases didn’t change, desired national saving is unchanged as well. This is the case of Ricardian equivalence, and is controversial because consumers may not understand that higher taxes today imply lower future taxes. As a result, they may reduce desired consumption today, increasing desired national saving.

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6. The two components of the user cost of capital are the interest cost and the depreciation cost. The depreciation cost is the value lost as the capital wears out during the period. The interest cost represents the opportunity cost of not using the funds that purchased the capital in some other way; an example would be if the money was invested in bonds rather than buying capital goods. 7. The desired capital stock is the amount of capital that allows the firm to earn the largest possible profit. The higher the expected future marginal product of capital, the higher the desired capital stock, since any given amount of capital will be more productive in the future. The higher the user cost of capital, the lower the desired capital stock, since a higher user cost yields lower profits on each unit of capital. The higher the effective tax rate, the lower the desired capital stock, again because the firm gets lower profits on each unit of capital. 8. Gross investment represents the total purchase or construction of new capital goods that takes place during a period. Net investment is gross investment minus the depreciation on existing capital. Thus net investment is the overall increase in the capital stock. Yes, it is possible for gross investment to be positive when net investment is negative. This occurs whenever gross investment is less than the amount of depreciation (and, in fact, happened in the United States during World War II). 9. Equilibrium in the goods market occurs when the aggregate supply of goods (Y) equals the aggregate demand for goods (Cd + Id + G). Since desired national saving (Sd ) is Y − C d − G, an equivalent condition is Sd = Id. Equilibrium is achieved by the adjustment of the real interest rate to make the desired level of saving equal to the desired level of investment, as shown in text Figure 4.6. 10. The saving curve slopes upward because saving is assumed to increase with an increase in the expected real interest rate. The investment curve slopes downward because investment is lower the higher is the expected real interest rate. The saving curve would be shifted to the right by an increase in current output, a decrease in expected future output, a decrease in wealth, a decrease in government purchases, and possibly by a rise in taxes. The investment curve would shift to the right by a decline in the effective tax rate or a rise in expected future marginal product of capital.

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Chapter 4

Consumption, Saving, and Investment

59

Numerical Problems 1.

First, a general formulation of the problem is useful. With income of Y1 in the first year and Y2 in the second year, the consumer saves Y1 − C in the first year and Y2 − C in the second year, where C is the consumption amount, which is the same in both years. Saving in the first year earns interest at rate r, where r is the real interest rate. And the consumer needs to accumulate just enough after two years to pay for college tuition, in the amount T. So the key equation is (Y1 − C)(1 + r) + (Y2 − C) = T. (a) Y1 = Y2 = $50,000, r = 10%, T = $12,600. The key equation gives ($50,000 − C)1.1 + ($50,000 − C) = $12,600. This can be simplified to $50,000 − C = $12,600/2.1 = $6000, which can be solved to get C = $44,000. Then S = Y − C = $50,000 − $44,000 = $6000. (b) Y1 = $54,200. The key equation is now ($54,200 − C)1.1 + ($50,000 − C) = $12,600. This can be simplified to ($54,200 × 1.1) + $50,000 − $12,600 = 2.1 C, or $97,020 = 2.1 C, so C = $46,200. Then S = Y1 − C = $54,200 − $46,200 = $8000. This illustrates that a rise in current income increases saving. (c) Y2 = $54,200. The key equation is now ($50,000 − C)1.1 + ($54,200 − C) = $12,600. This can be simplified to ($50,000 × 1.1) + $54,200 − $12,600 = 2.1 C, or $96,600 = 2.1 C, so C = $46,000. Then S = Y1 − C = $50,000 − $46,000 = $4000. This illustrates that a rise in future income decreases saving. (d) With the increase in wealth of W, the total amount invested for the second period is W + Y1 − C, so the key equation becomes ($1050 + $50,000 − C)1.1 + ($50,000 − C) = $12,600. This can be simplified to ($51,050 × 1.1) + $50,000 − $12,600 = 2.1 C, or $93,555 = 2.1 C, so C = $44,550. Then S = Y1 − C = $50,000 − $44,550 = $5450. This illustrates that a rise in wealth decreases saving. (e) T = $14,700. The key equation is now ($50,000 − C)1.1 + ($50,000 − C) = $14,700. This can be simplified to $50,000 − C = $14,700/2.1 = $7000, which can be solved to get C = $43,000. Then S = Y − C = $50,000 − $43,000 = $7000. The rise in targeted wealth needed in the future raises current saving. (f) r = 25%. The key equation is now ($50,000 − C)1.25 + ($50,000 − C) = $12,600. This can be simplified to $50,000 − C = $12,600/2.25 = $5600, which can be solved to get C = $44,400. Then S = Y − C = $50,000 − $44,400 = $5600. The rise in the real interest rate, with a given wealth target, reduces current saving.

2.

(a) This chart shows the MPKf as the increase in output from adding another fabricator: # Fabricators 0 1 2 3 4 5 6

Output 0 100 150 180 195 205 210

MPKf — 100 50 30 15 10 5

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(b) uc = (r + d)pK = (0.12 + 0.20)$100 = $32. HHHHC should buy two fabricators, since at two fabricators, MPK f = 50 > 32 = uc. But at three fabricators, MPK f = 30 < 32 = uc. You want to add fabricators only if the future marginal product of capital exceeds the user cost of capital. The MPK f of the third fabricator is less than its user cost, so it should not be added. (c) When r = 0.08, uc = (0.08 + 0.20)$100 = $28. Now they should buy three fabricators, since MPK f = 30 > 28 = uc for the third fabricator and MPK f = 15 < 28 = uc for the fourth fabricator. (d) With taxes, they should add additional fabricators as long as (1 − τ)MPK f > uc. Since τ = 0.4, 1 − τ = 0.6. They should buy just one fabricator, since (1 − τ)MPK f = 0.6 × 100 = 60 > 32 = uc. They shouldn’t buy two, since then (1 − τ)MPK f = 0.6 × 50 = 30 < 32 = uc. (e) When output doubles, the MPKf doubles as well. At r = 0.12, they should buy three fabricators, since then MPK f = 60 > 32 = uc; they shouldn’t buy four, since then MPK f = 30 < 32 = uc. At r = 0.08, they should buy four fabricators, since then MPK f = 30 > 28 = uc; they shouldn’t buy five, since then MPK f = 20 < 28 = uc. 3.

(a) The expected after-tax real interest rate is r = i(1 − t) − πe = 0.10 (1 − 0.30) − 0.05 = 0.07 − 0.05 = 0.02. (b) The cost of maintaining the house is depreciation. So the annual user cost of capital is uc = (r + d)pK = (0.02 + 0.06)$300,000 = $24,000. (c) You should be indifferent between buying and renting if the rent is $16,000 per year.

4.

Since the price of capital declines from 60 to 51, the depreciation rate is 9/60 = .15. (a) uc = (r + d)pK = (.10 + .15)60 = 15 units of output per year. (b) The desired capital stock is such that MPK f = uc, so 165 − 2K = 15, or 2K = 150, so K = 75. (c) The tax-adjusted user cost of capital is uc/(1 − τ), so with τ = .4, the condition for the desired capital stock is 165 − 2K = 15/0.6, or 2K = 140; the solution is K = 70. Thus taxation decreases the firm’s desired capital stock. (d) The investment tax credit basically lowers the price of capital from 60 to (1 − 0.2)60 = 48. So the tax-adjusted user cost of capital is only (.25 × 48)/0.6 = 20. Then the equation for setting the desired capital stock is 165 − 2K = 20, or 2K = 145; the solution is K = 72.5. Thus the investment tax credit increases the firm’s desired capital stock.

5.

(a) Desired consumption declines as the real interest rate rises because the higher return to saving encourages higher saving; desired investment declines as the real interest rate rises because the user cost of capital is higher, reducing the desired capital stock, and thus investment. (b) Use the following table, where Sd = Y − Cd − G = 9000 − Cd − 2000 = 7000 − Cd. Cd Id Sd Cd + Id + G r 2 6100 1500 900 9600 3 6000 1400 1000 9400 4 5900 1300 1100 9200 5 5800 1200 1200 9000 6 5700 1100 1300 8800 d d (c) Equation (4.7) says that Y = C + I + G at equilibrium. Looking at the last column of the table, with Y = 9000, this is true only at r = 5%. At this point, Sd = Id = 1200. Equation (4.8) says that Sd = Id at equilibrium. From the table, this occurs at r = 5%. ©2014 Pearson Education, Inc.

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(d) When government purchases fall by 400 to 1600, each Sd entry in the table is higher by 400, and each Cd + Id + G entry is lower by 400. Then Y = Cd + Id + G occurs at r = 3%, as does Sd = Id = 1400.

6.

r

Cd

Id

Sd

Cd + Id + G

2 3 4 5 6

6100 6000 5900 5800 5700

1500 1400 1300 1200 1100

1300 1400 1500 1600 1700

9200 9000 8800 8600 8400

(a) Sd = Y − Cd − G = Y − (3600 − 2000r + 0.1Y) − 1200 = −4800 + 2000r + 0.9Y (b) (1) Using Eq. (4.7): Y = Cd + Id + G Y = (3600 − 2000r + 0.1Y) + (1200 − 4000r) + 1200 = 6000 − 6000r + 0.1Y So 0.9Y = 6000 − 6000r At full employment, Y = 6000. Solving 0.9 × 6000 = 6000 − 6000r, we get r = 0.10. (2) Using Eq. (4.8): S d = Id −4800 + 2000r + 0.9Y = 1200 − 4000r 0.9Y = 6000 − 6000r When Y = 6000, r = 0.10. So we can use either Eq. (4.7) or (4.8) to get to the same result. (c) When G = 1440, desired saving becomes Sd = Y − Cd − G = Y − (3600 − 2000r + 0.1Y) − 1440 = −5040 + 2000r + 0.9Y. Sd is now 240 less for any given r and Y; this shows up as a shift in the Sd line from S1 to S2 in Figure 4.3.

Figure 4.3

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Setting Sd = Id, we get: −5040 + 2000r + 0.9Y = 1200 − 4000r 6000r + 0.9Y = 6240 At Y = 6000, this is 6000r = 6240 − (0.9 × 6000) = 840, so r = 0.14. The market-clearing real interest rate increases from 10% to 14%. 7.

(a) r = 0.10 uc/(1 − τ) = (r + d)pK/(1 − τ) = [(.1 + 0.2) × 1]/(1 − 0.15) = 0.35. MPK f = uc/(1 − τ), so 20 − 0.02K = 0.35; solving this gives K = 982.5. Since K − K-1 = I − dK, I = K − K-1 + dK = 982.5 − 900 + (.2 × 900) = 262.5. (b) i. Solving for this in general: uc/(1 − τ) = (r + d)pK/(1 − τ) = [(r + .2) × 1]/(1 − 0.15) = .235 + 1.176r. MPKf = uc/(1 − τ), so 20 − 0.02K = 0.235 + 1.176r; solving this gives K = 988.25 − 58.8r. I = K − K-1 + dK = 988.25 − 58.8r − 900 + (0.2 × 900) = 268.25 − 58.8r. ii. Y = C + I + G 1000 = [100 + (.5 × 1000) − 200r] + (268.25 − 58.8r) + 200 1000 = 1068.25 − 258.8r, so 258.8r = 68.25 r = 0.264 C = 100 + (0.5 × 1000) − (200 × 0.264) = 547.2 I = 268.25 − (58.8 × 0.264) = 252.7 = S uc/(1 − τ) = 0.235 + (1.176 × 0.264) = 0.545 K = 988.25 − (58.8 × 0.264) = 972.7

8.

(a) PVLR = y + [y f/(1 + r)] + a = 90 + (110/1.10) + 20 = 210. f (b) c + [c / (1 + r)] = PVLR. c + (c f / 1.10) = 210. When c = 0, c f = 231; this is the vertical intercept of the budget line, shown in Figure 4.4. When c f = 0, c = 210; this is the horizontal intercept of the budget line.

Figure 4.4

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(c) c = c f: c + (c/1.10) = 210. 1.10c + c = 210 × 1.10. 2.1c = 231. c = 110. s=y−c = 90 − 110 = −20. (d) y increases by 11, so new PVLR = 221. 2.1c = 221 × 1.1 = 243.1. c = 115.76. s = y − c = 101 − 115.76 = − 14.76. So part of the temporary increase in income is consumed and part is saved. (e) y f increases by 11, so PVLR rises by 11/1.10 = 10. New PVLR = 220. 2.1c = 220 × 1.1 = 242. c = 115.24. s = y − c = 90 − 115.24 = −25.24. So a rise in future income leads to an increase in current consumption but a decrease in saving. (f) A rise in initial wealth has the same effect on the PVLR and thus on consumption as an increase in current income of the same amount, so c = 115.76 as in part (d). s = y − c = 90 − 115.76 = −25.76. So an increase in wealth increases current consumption and decreases saving. 9.

(a) PVLR = a + yl + yw + yr = 1500. (1) No borrowing constraint: cl + cw + cr = 1500. cl = cw = cr = c = 1500/3 = 500. sl = 200 − 500 = −300; sw = 800 − 500 = 300; sr = 200 − 500 = −300. (2) A borrowing constraint is nonbinding, since a + y l = 500 = cl, and cw = 500 < 800 = yw. So consumption and saving are the same in each period as in part (1) above. (b) PVLR = 1200. (1) No borrowing constraint: c = 1200/3 = 400. sl = 200 − 400 = −200; sw = 800 − 400 = 400; sr = 200 − 400 = −200. (2) The borrowing constraint is now binding, since cl = 400 > a + yl = 200. So cl is constrained to be 200. That leaves PVLR of 1000 for cw + cr, so they both equal 500. cw = 500 < 800 = yw, so the borrowing constraint is not binding in working age. sl = 200 − 200 = 0; sw = 800 − 500 = 300; sr = 200 − 500 = −300. Consumption can’t be lower in all periods due to a binding borrowing constraint, because the present value of lifetime consumption must be the same with and without borrowing constraints.

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Analytical Problems 1.

(a) As Figure 4.5 shows, the shift to the right in the saving curve from S1 to S2 causes saving and investment to increase and the real interest rate to decrease.

Figure 4.5 (b) This is really just a transfer from the general population to veterans. The effect on saving depends on whether the marginal propensity to consume (MPC) of veterans differs from that of the general population. If there is no difference in MPCs, there will be no shift of the saving curve; neither investment nor the real interest rate is affected. If the MPC of veterans is higher than the MPC of the general population, then desired national saving declines and the saving curve shifts to the left; the real interest rate rises and investment declines. If the MPC of veterans is lower than that of the general population, the saving curve shifts to the right; the real interest rate declines and investment rises. (c) The investment tax credit encourages investment, shifting the investment curve from I1 to I2 in Figure 4.6. Saving and investment increase, as does the real interest rate.

Figure 4.6

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(d) The increase in expected future income decreases current desired saving, as people increase desired consumption immediately. The rise of the future marginal productivity of capital shifts the investment curve to the right. The result, as shown in Figure 4.7, is that the real interest rate rises, with ambiguous effects on saving and investment.

Figure 4.7 2.

(a) With a lower capital stock, the marginal product of labor is reduced, so the labor demand curve shifts to the left from ND1 to ND2 in Figure 4.8. Then the new equilibrium point is one with lower employment and a lower real wage. With lower employment and a lower capital stock, fullemployment output will be lower.

Figure 4.8 (b) Because the capital stock is lower, the marginal product of capital will be higher, so desired investment will increase. (c) Since current output declines, desired saving declines, because people do not want to reduce their consumption. On the other hand, since future output is also lower, people desire to save more today to make up for the loss of future income.

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(d) The increase in desired investment shows up as a shift to the right in the Id curve, from I1 to I2 in Figure 4.9. Then the new equilibrium (assuming no change in desired saving) is at a higher level of investment and a higher real interest rate.

Figure 4.9 3.

(a) The temporary increase in the price of oil reduces the marginal product of labor, causing the labor demand curve to shift to the left from ND1 to ND2 in Figure 4.10. At equilibrium, there is a reduced real wage and lower employment.

Figure 4.10

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The productivity shock results in a reduction of output. Because the shock is temporary, the only effect on desired saving or investment is due to the reduction in current output, causing desired national saving to fall. This shifts the saving curve to the left, raising the real interest rate and reducing the level of desired investment, as well as desired national saving, as shown in Figure 4.11.

Figure 4.11 (b) The permanent increase in the price of oil reduces the marginal product of labor, causing the labor demand curve to shift to the left, again as in Figure 4.10. (Also, the decline in future income means the labor-supply curve will shift to the right; but we’ll assume that this shift is less than the shift to the left of the labor-demand curve.) At equilibrium, there is a reduced real wage and lower employment. The productivity shock results in a reduction of current output. Because the shock is permanent, it reduces future output as well, and reduces the future marginal product of capital. The desired investment curve shifts to the left, from I1 to I2 in Figure 4.12, because the future marginal product of capital is lower. The effect on desired saving is ambiguous—the reduction in current income reduces desired saving, but the reduction in expected future income increases desired saving. Let’s assume that the former effect outweighs the latter, so that the desired saving curve shifts to the left from S1 to S2. Then national saving and investment both decline. Again, the effect on the real interest rate is ambiguous. (Alternatively, if the effects on desired saving of the reductions in current income and future income offset each other exactly, the desired saving curve does not shift. In this case, the leftward shift of the investment curve along an unchanged saving curve reduces the real interest rate, saving, and investment.)

Figure 4.12

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

A temporary increase in government spending reduces national saving. Whether the spending is financed by current taxes or by borrowing (and raising future taxes), consumption falls, but not by the full amount of the spending. Since S = Y − Cd − G, national saving declines. This is shown in Figure 4.13 as a shift to the left in the saving curve. The real interest rate must increase to get S = I, so I declines as well. It makes no difference whether the temporary increase in spending is funded by taxes or by borrowing.

Figure 4.13 In the case of infrastructure spending, MPK f rises, so investment increases. Saving shifts from S1 to S2 and investment shifts from I1 to I2 in Figure 4.14. With upward shifts in both saving and investment, the new equilibrium is one with a higher real interest rate. However, saving and investment at the new equilibrium may be higher or lower. The effect on consumption is unclear as well. The higher real interest rate reduces consumption, but future income is higher, which increases consumption. If investment actually rises, then the increase in government spending causes private investment to be “crowded in” rather than “crowded out.” In this case consumption is crowded out.

Figure 4.14 5.

When there is a temporary increase in government spending, consumers foresee future taxes. As a result, consumption declines, both currently and in the future. Thus current consumption does not fall

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by as much as the increase in G, so national saving (Sd = Y − Cd − G) declines at the initial real interest rate, and the saving curve shifts to the left from S1 to S2, as shown in Figure 4.15. Thus the real interest rate increases and consumption and investment both fall.

Figure 4.15 When there is a permanent increase in government spending, consumers foresee future taxes as well, with both current and future consumption declining. But if there is an equal increase in current and future government spending, and consumers try to smooth consumption, they will reduce their current and future consumption by about the same amount, and that amount will be about the same amount as the increase in government spending. So the saving curve in the saving-investment diagram does not shift, and there is no change in the real interest rate. Since the saving curve shifts upward more in the case of a temporary increase in government spending, the real interest rate is higher, so investment declines by more. However, consumption falls by more in the case of a permanent increase in government spending. 6.

See Figure 4.16. The consumer is originally on budget line BL1, with consumption at point D. An increase in the real interest rate shifts the budget line to BL2, with consumption at point Q. The change can be broken down into two steps. First, the substitution effect shifts the budget line from BL1 to BLint, and the consumption point changes from point D to point P. The substitution effect results in higher future consumption and lower current consumption. The income effect shifts the budget line from BLint to BL2, with the consumption point changing from point P to point Q. The income effect results in lower current and future consumption. Thus the income and substitution effects work in the same direction, reducing current consumption and increasing saving.

Figure 4.16

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The difference in interest rates between borrowing and lending means there is a kink in the budget constraint at the no-lending, no-borrowing point, as shown in Figure 4.17. Borrowing is zero when c = y + a. If current consumption is less than y + a, the person is a saver (lender), and the budget line has slope − (1 + rl). If current consumption is greater than y + a, the person is a borrower, and faces a steeper budget constraint with slope − (1 + rb), because the interest rate is higher.

Figure 4.17 An increase in either interest rate would steepen only the portion of the budget constraint for which that interest rate is relevant. An increase in the real interest rate on lending is shown as a shift in the budget line segment from BL1 to BL2 in Figure 4.18. An increase in the real interest rate on borrowing is shown as a shift in the budget line segment from BL3 to BL4. If the indifference curve hits the budget line at the no-borrowing, no-lending point, as shown, then there will be no change in current or future consumption due to a change in either interest rate.

Figure 4.18

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An increase in the consumer’s initial wealth would lead to a parallel rightward shift of both segments of the budget line, as shown in Figure 4.19.

Figure 4.19

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

Answers to Textbook Problems

Review Questions 1. Credit items in the current account are exports of goods and services and income receipts from abroad. Debit items in the current account are imports of goods and services, income payments to foreigners, and net unilateral transfers. Adding all of the credit items and subtracting all of the debit items gives the current account balance. The current account balance equals net exports plus net income from abroad plus net unilateral transfers. 2. The current account includes only the trade of currently produced goods and services. Trades of existing assets are counted in the capital and financial account. 3. The sale of books from the United States to Brazil is a credit item in the U.S. current account. Offsetting transactions include anything that is a debit item in either the current account or the capital and financial account. Some examples of offsetting transactions are: (1) A U.S. citizen buys $200 worth of stock in a Brazilian company, so that the offsetting debit item is an increase in U.S.-owned assets abroad, which is a debit in the capital and financial account. (2) A U.S. firm imports $200 worth of nuts from Brazil, so the offsetting debit item is an import of goods, which is a debit in the current account. 4. In any period, the net amount of new foreign assets that a country acquires equals its current account surplus, which in turn must equal its capital and financial account deficit. A country with greater net foreign assets than another is not necessarily better off. What really counts is total national wealth, which consists of both net foreign assets and net domestic assets. For example, the United States has lower net foreign assets than other countries, but has one of the world’s highest levels of total national wealth per citizen. 5. In a small open economy, saving does not have to be equal to investment. Saving can be used to finance domestic investment or it can be lent abroad. So saving equals investment plus net exports. Similarly, output need not equal absorption. Absorption is a country’s total spending on consumption, investment, and government purchases. Absorption may be different from output because some output may be exported. The difference between output and absorption is net exports. 6. A small open economy is likely to run a large current account deficit and to borrow abroad if desired investment increases substantially or if desired national saving declines substantially. Desired investment could increase if there is an increase in the expected future marginal product of capital or a decline in the user cost of capital, both of which would shift the desired investment curve to the right, reducing the current account balance, and possibly leading to a large current account deficit. Desired national saving might decrease if current output declines, if expected future output rises, if wealth increases, if government expenditures rise temporarily, or if taxes decline and Ricardian equivalence does not hold. For example, a temporary supply shock would cause a decline in current output but not future output, thus reducing desired national saving. A reduction in desired national saving would reduce the current account balance and possibly lead to a large current account deficit. 7. In a world with two large open economies, the world real interest rate is determined such that desired international lending by one country equals desired international borrowing by the other country. When the world real interest rate is at its equilibrium value, the current accounts of the two countries sum to zero. 8. An increase in desired national saving in a large open economy reduces the world real interest rate. The shift to the right in the saving curve increases the country’s current account at the current world

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real interest rate, so the international asset market is out of equilibrium. To restore equilibrium, the world real interest rate must fall. An increase in desired investment has the opposite effect. The increase in investment reduces the domestic country’s current account and leads to an increase in the world real interest rate to restore equilibrium. The reason that changes in desired saving and investment affect the world real interest rate in large open economies but not small open economies is that saving and investment in small open economies are so small relative to saving and investment in the world that changes in them simply have no impact. On the other hand, a large open economy may account for a substantial fraction of the world’s saving and investment, so a change there has a significant impact. 9. An increase in the government budget deficit raises the current account deficit of a small open economy if and only if the increase in the budget deficit reduces national saving. Since the current account is the difference between national saving and investment, the current account balance changes by the amount that national saving changes. 10. The twin deficits are the government budget deficit and the current account deficit. They are connected because if an increase in the government budget deficit reduces national saving it leads to an increased current account deficit. So the government budget deficit and the current account deficit move in the same direction.

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Numerical Problems 1. Current Account

Credit (+)

Debits (−)

100

125

90

80

Income from/to foreigners

110

150

Total

300

355

Goods Services

Current account balance (CA) = 300 – 355 = –55. Net exports (NX) = (100 + 90) – (125 + 80) = –15. Capital and Financial Account

Credit (+)

Debits (−)

Increase in home country assets abroad

160

Increase in foreign assets in home country

200

Total

200

160

Notice that the increase in home reserve assets is just a subcategory of the increase in home country assets, so it is not included separately. Similarly, the increase in foreign reserve assets is just a subcategory of the increase in foreign assets in the home country. The information about the changes in home and foreign reserve assets is included for calculation of the official settlements balance only; it does not affect the capital and financial account. Capital and financial account balance (KFA) = 200 − 160 = 40. Statistical discrepancy (SD): CA + KFA + SD = 0 −55 + 40 + SD = 0 SD = 15 Official settlements balance = increase in home official reserve assets minus increase in foreign official reserve assets = 30 − 35 = −5. 2.

The following table calculates key variables for this question for different values of the real interest rate. The column for S is calculated by the equation S = Y − (Cd + G). The column headed S − I is foreign lending. Absorption (A) is Cd + Id + G. Net exports (NX) are output (Y) minus absorption (A). Every column except r consists of dollar amounts in billions. r

Cd

Id

S

S−I

A

NX

5%

12

3

7

4

21

4

4% 3%

13 14

4 5

6 5

2 0

23 25

2 0

2%

15

6

4

–2

27

–2

Net exports and foreign lending are identical.

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3.

All variables but interest rates are in billions of dollars. (a) S = 10 + (100 × 0.03) = 13 15 − (100 × 0.03) = 12 I= NX = CA = S − I = 13 − 12 = 1 C = Y − ( I + G + NX ) = 50 − (12 + 10 + 1) = 27 A=C+I+G = 27 + 12 + 10 = 49 (b) S = 13, as before. I= 17 − (100 × 0.03) = 14 NX =CA =S − I =13 − 14 =−1 C = Y − ( I + G + NX ) = 50 − (14 + 10 − 1) = 27 A= C +I +G = 27 + 14 + 10 = 51

4.

(a) To find the equilibrium interest rate (rw), we must first calculate the current account for each country as a function of rw. Then we can find the value of rw that clears the goods market, that is, where CA + CAFor = 0. Home: Cd = 320 + 0.4(1000 − 200) − 200rw = 320 + 320 − 200 rw = 640 − 200 rw CA = NX = Sd – Id = Y – (Cd + Id + G) = 1000 – (640 – 200 rw + 150 – 200rw + 275) = –65 + 400 rw Foreign: d CFor =480 + 0.4(1500 − 300) − 300 ρ ω = 480 + 480 − 300r w = 960 − 300r w

CAFor = NXFor = SdFor − IdFor = YFor − (CdFor + IdFor + GFor) = 1500 − (960 − 300rw + 225 − 300rw + 300) = 15 + 600 rw At equilibrium, CA + CAFor = 0, so: –65 + 400 rw + 15 + 600 rw = 0 –50 + 1000 rw = 0 rw = 0.05 ©2014 Pearson Education, Inc.

Chapter 5 Saving and Investment in the Open Economy

C = 640 − 200 rw = 630 CFor = 960 − 300 rw = 945 S = Y − C − G = 1000 − 630 − 275 = 95 SFor = YFor − CFor − GFor = 1500 − 945 − 300 = 255 I = 150 − 200 rw = 140 IFor = 225 − 300 rw = 210 CA = S − I = 95 − 140 = −45 CAFor = SFor − IFor = 255 − 210 = 45 (b) Cd = 320 + 0.4(1000 − 250) − 200 rw = 320 + 300 − 200 rw = 620 − 200 rw CA = NX = Sd − Id = Y − (Cd + Id + G) = 1000 − (620 − 200 rw + 150 − 200 rw + 325) = −95 + 400 rw At equilibrium, CA + CAFor = 0, so: −95 + 400 rw + 15 + 600 rw = 0 −80 + 1000 rw = 0 rw = 0.08 C = 620 − 200 rw = 604 CFor = 960 − 300 rw = 936 S = Y − C − G = 1000 − 604 − 325 = 71 SFor = YFor − CFor − GFor = 1500 − 936 − 300 = 264 I = 150 − 200 rw = 134 IFor = 225 − 300 rw = 201 CA = S − I = 71 − 134 = −63 CAFor = SFor − IFor = 264 − 201 = 63 So a balanced-budget increase in government spending increases the home country’s current account deficit. 5.

(a) SH = YH − CH − GH = 1000 − [100 + (0.5 × 1000) − 500r] − 155 = 245 + 500r SF = Y F − C F − G F = 1200 − [225 + (0.7 × 1200) − 600r] − 190 = −55 + 600r (b) NXH = SH − IH = 245 + 500r − (300 − 500r) = −55 + 1000r NXF = SF – IF

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= −55 + 600r − (250 − 200r) = −305 + 800r In equilibrium, NXH + NXF = 0, so −55 + 1000r + (−305 + 800r) = 0 1800r = 360 r = 0.20 (c) CH = 100 + (0.5 × 1000) − (500 × 0.20) = 500 SH = 245 + (500 × 0.20) = 345 IH = 300 − (500 × 0.20) = 200 CAH = NXH = −55 + (1000 × 0.20) = 145 (assume NFP = 0) absorptionH = CH + IH + GH = 500 + 200 + 155 = 855 CF = 225 + (0.7 × 1200) − (600 × 0.20) = 945 SF = −55 + (600 × 0.20) = 65 IF = 250 − (200 × 0.20) = 210 CAF = NXF = –305 + (800 × 0.20) = −145 (assume NFP = 0) absorptionF = CF + IF + GF = 945 + 210 + 190 = 1345 6.

GDP = Y = $1,000,000 = total production of coconuts GNP = $1,025,000 = production of coconuts + net factor income from abroad NFP = $25,000 I = $0 S = Y + NFP − C − G = $1,000,000 + $25,000 − $1,025,000 − $0 = $0 CA = S − I = $0 NX = CA − NFP = $0 − $25,000 = −$25,000 KFA = −CA = $0 The $500,000 in foreign bonds provides income of $500,000 × 0.05 = $25,000 per year. Since people consume exactly $1,025,000, they must be using the $25,000 of foreign interest receipts to buy imported consumption goods. So net exports are –$25,000 and the current account balance is zero. Since the current account balance is zero, the capital and financial account balance is also zero.

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Analytical Problems Export of merchandise: + entry in current account. No entry: just changes the type of foreigner holding U.S. assets. Decrease in U.S. official reserve assets: + entry in capital and financial account. Income receipt from abroad: + entry in current account. Import of assets: − entry in capital and financial account. Import of services: − entry in current account. Increase in foreign ownership of U.S. assets: + entry in capital and financial account.

1.

(a) (b) (c) (d) (e) (f) (g)

2.

There are many possible answers; an example for each is given here. (a) U.S. citizens buy cars from the foreign country: − entry in current account. (b) No transaction needed. (c) The Federal Reserve sells dollars to, and buys deutsche marks from, the Bundesbank (the central bank of Germany): − entry in capital and financial account. (d) Brazilian citizens receive interest on U.S. Treasury bonds they own: − entry in current account. (e) The IRS sells a bankrupt singer’s home to an Egyptian citizen: + entry in capital and financial account. (f) Kuwait pays for the services of Red Adair’s U.S. team of oil fire fighters: + entry in current account. (g) A U.S. bank buys U.K. government bonds: − entry in capital and financial account.

3.

In Figure 5.3, before the capital controls are imposed, the home country has a current account deficit of the amount CA, while the foreign country has a matching current account surplus. The effect of the capital controls is to make saving equal investment in each country. In the home country, the real interest rate rises, investment declines, saving increases, and the current account balance increases to zero. The world real interest rate (the interest rate in the foreign country) declines.

Figure 5.3

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4.

Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

In Figure 5.4, suppose initially that both countries have a zero current account. A rise in the government budget deficit has no effect on desired investment, so it affects the current account only if it affects desired national saving. If desired national saving is affected, the saving curve shifts to the left from S1 to S2. This raises the world real interest rate, reduces investment in both countries, and increases the foreign country’s current account balance.

Figure 5.4 5.

(a) The home country’s saving curve shifts to the right, from S1 to S2 in Figure 5.5. The real world interest rate falls, so that the current account surplus in the home country equals the current account deficit in the foreign country. From Figure 5.5, S rises, I rises, CA rises, rw falls.

Figure 5.5

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Chapter 5 Saving and Investment in the Open Economy

1 2 (b) The foreign country’s saving curve shifts to the right, from SFor to SFor in Figure 5.6. The real world interest rate must fall, so the current account surplus in the foreign country equals the current account deficit in the home country. As shown in the figure, S falls, I rises, CA falls, rw falls.

Figure 5.6 1 2 (c) The foreign country’s saving curve shifts to the left, from SFor to SFor in Figure 5.7. The real world interest rate must rise, so the current account deficit in the foreign country equals the current account surplus in the home country. As shown in the figure, S rises, I falls, CA rises, rw rises.

Figure 5.7 (d) If Ricardian equivalence holds, there is no effect. If Ricardian equivalence does not hold, then the result is the same as in part (b), as the foreign country’s saving curve shifts to the right.

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

A temporary adverse supply shock hitting the foreign economy causes the foreign saving curve to 1 2 shift to the left, from SFor to SFor in Figure 5.7. This raises the equilibrium world real interest rate, increasing home country saving and decreasing home country investment. Since saving rises and investment falls, the home country’s current account balance increases. Now consider a worldwide temporary adverse productivity shock, which causes both the saving curve in the home country and the saving curve in the foreign country to shift to the left. As a result of these shifts, the world real interest rate increases (by more than if the productivity shock were confined to the foreign country). The increase in the world real interest rate reduces investment in both countries (by more than if the productivity shock were confined to the foreign country). Depending on the sizes of the shocks in both countries and the slopes of the saving and investment curves, the current account balance in the home country could either increase or decrease (but in any case it would be smaller than if the productivity shock were confined to the foreign country). Figure 5.8 shows the borderline case, in which the current account balances in both countries are unchanged. Finally, worldwide saving falls because worldwide saving equals worldwide investment, and we have shown that investment falls in both countries. Though worldwide saving, i.e., the sum of saving in the home country and saving in the foreign country, falls, it is possible that saving increases in one country, depending on the sizes of the productivity shocks in the two countries and the slopes of the saving and investment curves.

Figure 5.8 7.

The shock shifts the saving curve to the right, with no change in the investment curve, since the future marginal product of capital is unaffected. Since income rises and saving rises, consumption rises, but less than income. Thus, although imports rise somewhat, the amount is small, so that the current account increases, it doesn’t fall. The statement is false.

8.

Note that when the government of Eastland makes this change, it isn’t changing total government purchases, so there’s no effect on national saving. Thus the current account balance is unaffected. How can that be, given that Eastland’s government is now purchasing more goods from Westland? The answer is that the private sector offsets the government’s actions by increasing its net exports to Westland. The point of this exercise is to show that a government can’t affect the current account balance by changing its purchasing decisions if its total purchases of goods and services remain unchanged; it

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Chapter 5 Saving and Investment in the Open Economy

can only do so if it changes national saving or investment, since the current account equals saving minus investment.

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Answers to Textbook Problems

Review Questions 1.

The three sources of economic growth are capital growth, labor growth, and productivity growth. The growth accounting approach is derived from the production function.

2.

A decline in productivity growth is the primary reason for the slowdown in output growth in the United States since 1973. Productivity growth may have declined because of deterioration in the legal and human environment, reduced rates of technological innovation, and the effects of high oil prices. To some extent the apparent decline in productivity may be due to measurement difficulties.

3.

The rise in productivity growth in the 1990s occurred because of the revolution in information and communications technologies (ICT). Not only were there improvements in ICT, but also government regulations did not rein in the growth of productivity in the United States, as they did in other countries, such as those in Europe. In addition, intangible investment (research and development, reorganization of firms, and worker training) allowed the ICT improvements to boost productivity.

4.

A steady state is a situation in which the economy’s output per worker, consumption per worker, and capital stock per worker are constant.

5.

If there is no productivity growth, then output per worker, consumption per worker, and capital per worker will all be constant in the long run. This represents a steady state for the economy.

6.

The statement is false. Increases in the capital-labor ratio increase consumption per worker in the steady state only up to a point. If the capital-labor ratio is too high, then consumption per worker may decline due to diminishing marginal returns to capital, and the need to divert much of output to maintaining the capital-labor ratio.

7.

(a) An increase in the saving rate increases long-run living standards, as higher saving allows for more investment and a larger capital stock. (b) An increase in the population growth rate reduces long-run living standards, as more output must be used to equip the larger number of new workers with capital, leaving less output available to increase consumption or capital per worker. (c) A one-time increase in productivity increases living standards directly, by increasing output, and indirectly, since by raising incomes it also raises saving and the capital stock.

8.

Endogenous growth theory suggests that the main sources of productivity growth are accumulation of human capital (the knowledge, skills, and training of individuals) and technological innovation (research and development, as well as learning by doing). The production function in an endogenous growth model does not exhibit diminishing marginal productivity of capital. This differs from the production function in the Solow model, which has diminishing marginal productivity of capital.

9.

Government policies to promote economic growth include policies to raise the saving rate and policies to increase productivity. One way to increase the saving rate is to increase the real return to saving by providing a tax break, as Individual Retirement Accounts did in the United States. Unfortunately, the response of saving to increases in the real rate of return is small. Another way to increase the saving rate is to reduce the government budget deficit. However, the theory of Ricardian equivalence suggests that this will not do much to increase national saving. Note that an increase in the saving rate will increase the steady-state capital-labor ratio, but will not increase the long-run rate of economic growth. One way that government policy can increase productivity is by spending more on the economy’s infrastructure, which has been neglected over the past two decades in the United States. Another ©2014 Pearson Education, Inc.

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possibility is to support the creation of human capital by spending more on education and training programs, and reducing barriers to entrepreneurial activity. The issue is whether the government should intervene in the market to do these things, or whether the free market by itself provides an efficient outcome. A one-time increase in productivity will increase the steady-state capital-labor ratio but will not increase the long-run rate of economic growth. To increase the long-run rate of economic growth, the growth rate of productivity must be permanently increased. Endogenous growth theory modifies these conclusions to some extent. A rise in the saving rate leads to a higher long-run rate of economic growth in endogenous growth models.

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Long-Run Economic Growth

117

Numerical Problems 1.

Hare: $5000 × (1.03)70 = $39,589 Tortoise: $5000 × (1.01)70 = $10,034

2. 20 Years Ago

Today

Percent Change

1000 2500 500

1300 3250 575

30% 30% 15%

Y K N

(a) ∆A/A = ∆Y/Y − aK ∆K/K − aN ∆N/N = 30% − (0.3 × 30%) − 0.7 × 15% = 30% − 9% − 10.5% = 10.5% Capital growth contributed 9% (aK ∆K/K), labor growth contributed 10.5% (aN ∆N/N), productivity growth was 10.5%. (b) ∆A/A = 30% − (0.5 × 30%) − (0.5 × 15%) = 30% − 15% − 7.5% = 7.5% Capital growth contributed 15% (aK ∆K/K), labor growth contributed 7.5% (aN ∆N/N), productivity growth was 7.5%. 3.

(a) Year

K

N

Y

K/N

Y/N

1 2

200 250

1000 1000

617 660

0.20 0.25

0.617 0.660

3

250

1250

771

0.20

0.617

4

300

1200

792

0.25

0.660

This production function can be written in per-worker form since Y/N = K.3N.7/N = K.3/N.3 = (K/N).3. Note that K/N is the same in years 1 and 3, and so is Y/N. Also, K/N is the same in years 2 and 4, and so is Y/N. (b) Year

K

N

Y

K/N

Y/N

1 2

200 250

1000 1000

1231 1316

0.20 0.25

1.231 1.316

3

250

1250

1574

0.20

1.259

4

300

1200

1609

0.25

1.341

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This production function can’t be written in per-worker form since Y/N = K.3N.8/N = K.3/N.2. Note that K/N is the same in years 1 and 3, but Y/N is not the same in these years. The same is true for years 2 and 4. 4.

To answer this problem, an approximate solution can be found by finding the ratio GDP (2008)/GDP (1950), taking the natural logarithm of that ratio and dividing by 58. This is the answer given in the table below. Real GDP Per Capita 1950 2008

Ratio

Growth Rate

Australia Canada

7,412 7,291

25,301 25,267

3.41 3.47

2.1% 2.1%

France

5,186

22,223

4.29

2.5%

Germany

3,881

20,801

5.36

2.9%

Japan Sweden

1,921 6,769

22,816 24,409

11.88 3.61

4.3% 2.2%

United Kingdom

6,939

23,742

3.42

2.1%

United States

9,561

31,178

3.26

2.0%

Germany and Japan had the highest growth rates because damage from World War II caused capital per worker to be lower than its steady-state level, and thus output per worker was temporarily low. 5.

(a) sf(k) = (n + d)k 0.3 × 3k.5 = (0.05 + 0.1)k 0.9k.5 = 0.15k 0.9/0.15 = k/k.5 6 = k.5 k = 62 = 36 y = 3k.5 = 3 × 6 = 18 c = y − (n + d)k = 18 − (0.15 × 36) = 12.6 (b) sf(k) = (n + d)k 0.4 × 3k.5 = (0.05 + 0.1)k 1.2k.5 = 0.15k 1.2/0.15 = k/k.5 8 = k.5 k = 82 = 64 y = 3k.5 = 3 × 8 = 24 c = y − (n + d)k = 24 − (0.15 × 64) = 14.4 (c) sf(k) = (n + d)k 0.3 × 3k.5 = (0.08 + 0.1)k 0.9k.5 = 0.18k 0.9/0.18 = k/k.5 5 = k.5 ©2014 Pearson Education, Inc.

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k = 52 = 25 y = 3k.5 = 3 × 5 = 15 c = y – (n + d)k = 15 − (0.18 × 25) = 10.5 (d) sf(k) = (n + d)k 0.3 × 4k.5 = (0.05 + 0.1)k 1.2k.5 = 0.15k 1.2/0.15 = k/k.5 8 = k.5 k = 82 = 64 y = 4k.5 = 4 × 8 = 32 c = y – (n + d)k = 32 − (0.15 × 64) = 22.4 6.

7.

(a) In steady state, sf(k) = (n + d)k 0.1 × 6k.5 = (0.01 + 0.14)k 0.6k.5 = 0.15k 0.6/0.15 = k/k.5 4 = k.5 k = 42 = 16 = capital per worker y = 6k.5 = 6 × 4 = 24 = output per worker c = .9 y = .9 × 24 = 21.6 = consumption per worker (n + d)k = 0.15 × 16 = 2.4 = investment per worker (b) To get y = 2 × 24 = 48, since y = 6k.5, then 48 = 6k.5, so k.5 = 8, so k = 64. The capital-labor ratio would need to increase from 16 to 64. To get k = 64, since sf(k) = (n + d)k, s × 48 = 0.15 × 64, so s = 0.2. Saving per worker would need to double. First, derive saving per worker as sy = y − c − g = [1 − 0.5(1 − t) − t] 8k.5 = 0.5(1 − t)8k.5 = 4 (1 − t)k.5 (a) When t = 0, sy = 4 (1 − 0)k.5 = 4k.5 = national saving per worker Investment per worker = (n + d)k = 0.1k In steady state, sy = (n + d)k, so 4k.5 = 0.1k, or 40k.5 = k, so 1600k = k2, so k = 1600. Since k = 1600, y = 8 × 1600.5 = 320, c = 0.5(1 − 0)320 = 160, and (n + d)k = 0.1 × 1600 = 160 = investment per worker. (b) When t = 0.5, sy = 4 (1 − 0.5)k.5 = 2k.5 = national saving per worker Investment per worker = (n + d)k = .1k In steady state, sy = (n + d)k, so 2k.5 = 0.1k, or 20k.5 = k, so 400k = k2, so k = 400. Since k = 400, y = 8 × 400.5 = 160, c = 0.5(1 − 0.5)160 = 40, and (n + d)k = 0.1 × 400 = 40 = investment per worker, g = ty = 0.5 × 160 = 80.

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Analytical Problems 1.

(a) The destruction of some of a country’s capital stock in a war would have no effect on the steady state, because there has been no change in s, f, n, or d. Instead, k is reduced temporarily, but equilibrium forces eventually drive k to the same steady-state value as before. (b) Immigration raises n from n1 to n2 in Figure 6.3. The rise in n lowers steady-state k, leading to a lower steady-state consumption per worker.

Figure 6.3 (c) The rise in energy prices reduces the productivity of capital per worker. This causes sf(k) to shift down from sf 1(k) to sf 2(k) in Figure 6.4. The result is a decline in steady-state k. Steady-state consumption per worker falls for two reasons: (1) Each unit of capital has a lower productivity, and (2) steady-state k is reduced.

Figure 6.4 (d) A temporary rise in s has no effect on the steady-state equilibrium. (e) The increase in the size of the labor force does not affect the growth rate of the labor force, so there is no impact on the steady-state capital-labor ratio or on consumption per worker. However, because a larger fraction of the population is working, consumption per person increases.

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2.

Long-Run Economic Growth

121

(a) Solow model The rise in capital depreciation shifts up the (n + d)k line from (n + d1)k to (n + d2)k, as shown in Figure 6.5. The equilibrium steady-state capital-labor ratio declines. With a lower capital-labor ratio, output per worker is lower, so consumption per worker is lower (using the assumption that the capital-labor ratio is not so high that an increase in k will reduce consumption per worker). There is no effect on the long-run growth rate of the total capital stock, because in the long run the capital stock must grow at the same rate (n) as the labor force grows, so that the capital-labor ratio is constant.

Figure 6.5 (b) Endogenous growth model In an endogenous growth model, the growth rate of output is ∆Y/Y = sA − d, so the rise in the deprecia-tion rate reduces the economy’s growth rate. Similarly, the growth rate of capital equals ∆K/K = sA − d, which also declines when the depreciation rate rises. Since consumption is a constant fraction of output, its growth rate declines as well. So the increase in the depreciation rate reduces the long-run growth rate of the capital stock, as well as long-run capital, output, and consumption per worker. 3.

(a) With a balanced budget T/N = g. National saving is S = s(Y – T) = sN[(Y/N) − (T/N)] = sN( y – g). Setting saving equal to investment gives S = I, sN(y – g) = (n + d)K, s(y – g) = (n + d)k, s[f(k) – g] = (n + d)k. This equilibrium point k* is shown in Figure 6.6.

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Figure 6.6 (b) If the government permanently increases purchases per worker, the s[ f(k) – g] curve shifts down from s[ f(k) – g1] to s[ f(k) – g2] in Figure 6.7. In steady-state equilibrium, the capital-labor ratio is lower. Output per worker, capital per worker, and consumption per worker are lower in the steady state. The optimal level of government purchases is not zero—it depends on the benefits of the government purchases as well as on the costs of these purchases.

Figure 6.7 4.

St = sYt – hKt = Nt(syt – hkt). Setting St = It yields Nt(syt – hkt) = (n + d)Kt. Dividing through by Nt and eliminating time subscripts for steady-state variables gives sy – hk = (n + d)k. Rearranging and using the expression y = f(k) gives sf(k) = (n + d + h)k. The steady-state value of capital per worker, k*, is given by the intersection of the (n + d + h)k line with the sf(k) curve, as shown in Figure 6.8. Output per worker is f(k*). Since Ct = Yt – St, c = y – (sy – hk) = (1 – s)f(k*) + hk*. This expression gives consumption per worker.

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Long-Run Economic Growth

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Figure 6.8 A change in the steady-state value of h increases the slope of the (n + d + h)k line, as shown in Figure 6.9. This reduces the steady-state value of per-worker capital (k*), per-worker output [since y* = f(k*)], and per-worker consumption [since c* = (1 − s)y* + hk* and both y* and k* decline].

Figure 6.9 5.

The initial level of the capital-labor ratio is irrelevant for the steady state. Two economies that are identical except for their initial capital-labor ratios will have exactly the same steady state. Since the two economies must have the same growth rate at the steady state, and since the economy with the higher current capital-labor ratio has higher current output per worker, then the country with the lower current capital-labor ratio must grow faster.

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

The answer holds true regardless of which country is in a steady state. If the country with a higher initial capital-labor ratio is in a steady state at capital-labor ratio k*, then the other country’s capitallabor ratio will rise until it too equals k*. So the country with the lower capital-labor ratio grows faster than the one with the higher capital-labor ratio. If the country with the lower initial capital-labor ratio is in a steady state at capital-labor ratio k*, then the other country’s capital-labor ratio is too high and it will decline until it equals k*. So the country with the higher capital-labor ratio must grow more slowly than the country with the lower capitallabor ratio. If the two countries are allowed to trade with each other, then their convergence to the same capital-labor ratio and output per worker will occur even faster. 6.

The growth accounting equation is ∆Y/Y = ∆A/A + (aK ∆K/K) + (aN ∆N/N). We are just increasing the amount of capital and labor, and there is no change in productivity, so ∆A/A = 0. If the production function can be written in per-worker terms, then total output must increase in the same proportion as the percentage increase in capital and labor, so ∆K/K = ∆N/N = ∆Y/Y = X. Plugging this into the growth accounting equation, ∆Y/Y = ∆A/A + (aK ∆K/K) + (aN ∆N/N), X = 0 + aKX + aNX, X = (aK + aN)X, aK + aN = 1.

7.

Assume there are a constant number of workers, N, so that Ny = Y and Nk = K. Since y = Akah1–a and h = Bk, then y = Ak a(Bk)1–a = (AB1–a)k. Then Y = Ny = (AB1–a)K = XK, where X equals AB1–a. This puts the production function in notation used in the chapter. Investment is ∆K + dK = sY = national saving. Dividing through both sides of that expression by K and using the production function gives ∆K/K + d = sXK/K = sX, so ∆K/K = sX − d, which is the longrun growth rate of physical capital. Since output and human capital are proportional to physical capital, they will all grow at that same rate.

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Answers To Textbook Problems

Review Questions 1. Money is the economist’s term for assets that can be used in making payments, such as cash and checking accounts. In everyday speech, people often use the term “money” to refer to their income or wealth, but in economics money means only those assets that are widely used and accepted as payment. 2. The three functions of money are (1) the medium of exchange function, which contributes to a betterfunctioning economy by allowing people to make trades at a lower cost in time and effort than in a barter economy; (2) the unit of account function, which provides a single, uniform measure of value; and (3) the store of value function, by which money is a way of holding wealth that has high liquidity and little risk. 3. The size of the nation’s money supply is determined by its central bank; in the United States, the central bank is the Federal Reserve System. If all money is in the form of currency, the money supply can be expanded if the central bank uses newly minted currency to buy financial assets from the public or directly from the government itself. To reduce the money supply, the central bank can sell financial assets to the public or the government, taking currency out of circulation. 4. The four characteristics of assets that are most important to wealth holders are (1) expected return, (2) risk, (3) liquidity; and (4) time to maturity. Money has a low expected return compared to other assets, low risk since it always maintains its nominal value, is the most liquid of all assets, and has the lowest (zero) time to maturity. 5.

The expectations theory of the term structure of interest rates is the idea that investors compare bonds with different times to maturity and choose the ones that yield the highest return. In equilibrium, the theory implies that the expected rate of return on an N-year bond should equal the average of the expected rates of return on one-year bonds during the current year and the N–1 succeeding years. The expectations theory is not sufficient because on average, long-term interest rates exceed shortterm interest rates, in violation of the theory’s implications. To form a more accurate theory, a risk premium must be added to the analysis.

6.

The macroeconomic variables that have the greatest impact on money demand are the price level, real income, and the nominal interest rate on other assets. The higher the price level, the higher the demand for money, since more units of money are needed to carry out transactions. The higher the level of real income, the higher the need for liquidity, and so the higher is money demand. When the nominal interest rate on other assets is high, money demand is low, because the opportunity cost of holding money (that is, the interest you forgo on other assets because you are holding money instead) is high. 7. Velocity is a measure of how often money “turns over” in a period. It is equal to nominal GDP divided by the nominal money supply. The quantity theory of money assumes that velocity is constant, which implies that real money demand is proportional to real income and is unaffected by the real interest rate.

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Chapter 7

The Asset Market, Money, and Prices

137

8. Equilibrium in the asset market is described by the condition that real money supply equals real money demand because when supply equals demand for money, demand must also equal supply for nonmonetary assets. The aggregation assumption that is needed for this is that we can lump all wealth into two categories: (1) money and (2) nonmonetary assets. 9. In equilibrium, the price level is proportional to the nominal money supply; in particular it equals the nominal money supply divided by real money demand. Similarly, the inflation rate is equal to the growth rate of the nominal money supply minus the growth rate of real money demand. 10. Factors that could increase the public’s expected rate of inflation include a rise in money growth or a decline in income growth. With no effect on the real interest rate, the increase in the expected inflation rate would increase the nominal interest rate.

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

Numerical Problems 1.

2.

For a two-year bond, according to the expectations theory, the interest rate would be the average of the two one-year bonds, which is (6% + 4%)/2 = 5%. Adding the risk premium of 0.5% gives an interest rate on the two-year bond of 5.5%. For the three-year bond, according to the expectations theory, the interest rate would be the average of the three one-year bonds, which is (6% + 4% + 3%)/3 = 4.33%. Adding the risk premium of 1.0% gives an interest rate on the three-year bond of 5.33%. The yield curve would show the interest rate on a one-year bond of 6%, the interest rate on a two-year bond of 5.55%, and the interest rate on a three-year bond of 5.33%, so it would be downward sloping, which is called “inverted” in the market. (a) Real money demand is Md/P = 500 + 0.2Y − 1000i = 500 + (0.2 × 1000) − (1000 × 0.10) = 600. Nominal money demand is Md = (Md/P) × P = 600 × 100 = 60,000. Velocity is V = PY/Md = 100 × 1000/60,000 = 1 2/3. (b) Real money demand is unchanged, because neither Y nor i has changed. Nominal money demand is Md = (Md/P) × P = 600 × 200 = 120,000. Velocity is unchanged, because neither Y nor Md/P has changed, and we can write the equation for velocity as V = PY/Md = Y/(Md/P). (c) It is useful to use the last expression for velocity, V = Y/(Md/P) = Y/(500 + 0.2Y − 1000i). (1) Effect of increase in real income: When i = 0.10, V = Y/[500 + 0.2Y – (1000 × 0.10)] = Y/(400 + 0.2Y) = 1/[(400/Y) + 0.2]. When Y increases, 400/Y decreases, so V increases. For example, if Y = 2000, then V = 2.5, which is an increase over V = 1 2/3 that we got when Y = 1000. (2) Effect of increase in the nominal interest rate: When Y = 1000, V = 1000/[500 + (0.2 × 1000) − 1000i] = 1000/(700 − 1000i) = 1/(0.7 − i).

(3)

When i increases, 0.7 − i decreases, so V increases. For example, if i = 0.20, then V = 2, which is an increase over V = 1 2/3 that we got when i = 0.10. Effect of increase in the price level: There is no effect on velocity, since we can write velocity as a function just of Y and i. Nominal money demand changes proportionally with the price level, so that real money demand, and hence velocity, is unchanged.

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Chapter 7

3.

The Asset Market, Money, and Prices

139

(a) Md = $100,000 − $50,000 − [$5000 × (i − im) × 100]. (Multiplying by 100 is necessary since i and im are in decimals, not percent.) Simplifying this expression, we get Md = $50,000 − $500,000(i − im). (b) Bd = $50,000 + $500,000(i − im). Adding these together we get Md + Bd = $100,000, which is Mr. Midas’s initial wealth. (c) This can be solved either by setting money supply equal to money demand, or by setting bond supply equal to bond demand. Md = Ms $50,000 − $500,000(i − im) = $20,000 $30,000 = $500,000 i

[Setting im = 0]

i = 0.06 = 6% Bd = Bs $50,000 + $500,000i = $80,000 $500,000i = $30,000 i = 0.06 = 6% 4.

(a) From the equation MV = PY, we get M/P = Y/V. At equilibrium, Md = M, so Md/P = Y/V = 10,000/5 = 2000. Md = P × (Md/P) = 2 × 2000 = 4000. (b) From the equation MV = PY, P = MV/Y. When M = 5000, P = (5000 × 5)/10,000 = 2.5. When M = 6000, P = (6000 × 5)/10,000 = 3.

5.

(a) ∆P/P = − ηY ∆Y/Y = − 0.5 × 6% = −3%. The price level will be 3% lower. (b) ∆P/P = − ηr ∆r/r = −(−0.1) × 0.1 = 1%. The price level will be 1% higher. (c) With changes in both income and the real interest rate, to get an unchanged price level would require ηY ∆Y/Y + ηr ∆r/r = 0, so [0.5 × (Y – 100)/100] − [0.1 × 0.1] = 0, so Y = 102.

6.

(a) π e = ∆M/M = 10%. i = r + πe = 15%. M/P = L = 0.01 × 150/0.15 = 10. P = 300/10 = 30. (b) π e = ∆Μ/M = 5%. i = r + πe = 10%. M/P = L = 0.01 × 150/0.10 = 15. P = 300/15 = 20. The slowdown in money growth reduces expected inflation, increasing real money demand, thus lowering the price level.

7.

(a) With a constant real interest rate and zero expected inflation, inflation is given by the equation π = ∆M/M − ηY ∆Y/Y. To get inflation equal to zero, the central bank should set money growth so that ∆M/M = ηY ∆Y/Y = 2/3 × 0.045 = 0.03 = 3%. Note that the interest elasticity isn’t relevant, since interest rates don’t change. (b) Since V = PY/M, ∆V/V = ∆P/P + ∆Y/Y – ∆M/M = 0 + 0.045 − 0.03 = 0.015 So velocity should rise 1.5% over the next year.

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Analytical Problems 1.

(a) People would probably take money out of checking accounts and put it into money market mutual funds and money market deposit accounts. Money market mutual funds and money market deposit accounts are included in M2 but are not part of M1. The result is a decrease in M1, but no change in M2. M2 does not increase because M1 is part of M2, so the decrease in M1 offsets the increase in the rest of M2. (b) This would reduce both M1 and M2, as people would have reduced need for money in checking accounts, and home equity lines of credit are not included in either M1 or M2. (c) If people fear a stock market collapse, they will want greater liquidity, so they will hold more money. Also, since stocks are an alternative asset to money, and the expected return to stocks has fallen, money demand will increase. Both effects will lead to people investing less in stocks and more in cash, checking accounts, and other items that provide liquidity and safety, so M1 and M2 will both rise. (d) People would have less need for money in checking accounts, and would put more in savings deposits. So M1 will decrease, while M2 will remain unchanged. (Again, M1 is part of M2, so reducing the amount that is in M1, and increasing the amount that is in M2 but not in M1, has no effect on M2.) (e) If currency demand falls, this decreases M1, thus also decreasing M2.

2. The general rise in velocity from 1959 to 1980 is most likely due to changes in income, in interest rates, and in financial institutions. Higher income led to a less than proportional rise in real money demand, so velocity increased. Rising inflation and rising nominal interest rates in this period led people to seek alternatives to non–interest-bearing money, such as money market mutual funds. The result was lower money demand, and thus higher velocity. Financial innovations also reduced the need for money. Examples include the development of cash management accounts and the use of automated teller machines. 3.

(a) New cigarettes mean an increase in the money supply. With higher nominal money supply and no change in real money demand, the equilibrium price level must rise. (b) If people anticipate prices rising when the new cigarettes arrive, they will hold less money so that they will not lose purchasing power when prices go up. But if their real money demand is reduced, with the same nominal money supply the equilibrium price level must rise. The result is that when prices are anticipated to rise in the future, people may take actions that cause prices to rise immediately.

4.

(a) A temporary increase in government purchases reduces national saving, causing the real interest rate to rise for a fixed level of income. If the real interest rate is higher, then real money demand will be lower. So prices must rise to make money supply equal money demand. The result is that output is unchanged, the real interest rate increases, and the price level increases. (b) When expected inflation falls, real money demand increases. With no effect on employment or saving and investment, output and the real interest rate remain unchanged. With higher real money demand and an unchanged nominal money supply, the equilibrium price level must decline. So output and the real interest rate are unchanged and prices decline. (c) When labor supply rises, full-employment output increases. Also, with higher output, saving will increase, so the real interest rate will decline. Both higher output and a lower real interest rate increase real money demand. The price level must decline to equate money supply with money demand. The result is an increase in output and a decrease in both the real interest rate and the price level.

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The Asset Market, Money, and Prices

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(d) When the interest rate paid on money increases, real money demand rises. With no effect on employment or saving and investment, output and the real interest rate remain unchanged. With higher real money demand and an unchanged nominal money supply, the equilibrium price level must decline. So output and the real interest rate are unchanged and prices decline.

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Answers to Textbook Problems

Review Questions 1.

Figure 8.7 illustrates both the recurrence and persistence of the business cycle. The business cycle is recurrent, as there are repeated episodes of contractions and expansions over time. The business cycle also displays persistence, as declines in economic activity tend to be followed by further declines for some time, while growth in economic activity tends to be followed by further growth for some time.

Figure 8.7 2.

Comovement means that many economic variables move together in a predictable way over the business cycle. The business cycle facts presented in the chapter illustrate comovement among all the variables listed in text Summary Table 10 that are either procyclical (moving in the same direction as aggregate economic activity) or countercyclical (moving in the opposite direction as aggregate economic activity). Only those variables listed as acyclical do not show comovement.

3.

There is some question as to whether or not the business cycle has become less volatile over time. Originally it was thought that the cycle had been moderated, especially since World War II, but Romer challenged this notion. Further examination of the data by Balke and Gordon, however, shows that there has been some moderation of the business cycle. Whether the business cycle has become less severe or not is important, especially to economic policymakers. Since World War II, both fiscal policy and monetary policy have been used to try to smooth out business cycles to reduce their severity. If it were found that business cycles are no less severe than they used to be, it would point to the failure of government policy to achieve its objectives.

4.

A variable that moves in the same direction as aggregate economic activity is said to be procyclical, while a variable that moves in the opposite direction is countercyclical. If the peaks and troughs of a variable occur before the peaks and troughs in aggregate economic activity, it is said to be a leading variable. If a variable’s peaks and troughs occur at the same time as the peaks and troughs in aggregate economic activity, it is said to be a coincident variable. If a variable’s peaks and troughs come after the peaks and troughs of aggregate economic activity, it is said to be a lagging variable.

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5.

If the economy were entering a recession, you’d expect production, investment, average labor productivity, and the real wage to decline because they are all procyclical, and the unemployment rate to rise because it’s countercyclical.

6.

The fact that some economic variables are known to lead the business cycle is used to develop an index of leading economic indicators. The index is used to forecast economic turning points.

7.

The two components of a theory of business cycles are: (1) A description of the types of factors (called “shocks”) that have major impacts on the economy, such as wars, new inventions, harvest failures, and changes in government policy; and (2) a model of how the economy responds to the various shocks.

8.

Keynesians and classicals differ sharply in their beliefs about how long it takes the economy to reach a long-run equilibrium. Classical economists believe that prices adjust rapidly (within a few months) to restore equilibrium in the face of a shock, while Keynesians believe that prices adjust slowly, taking perhaps several years. Because of the time it takes for the economy’s equilibrium to be restored, Keynesians see an important role for the government in fighting recessions. But because classicals believe that equilibrium is restored quickly, there’s no need for government policy to fight recessions. Since classicals think equilibrium is restored quickly in the face of shocks, aggregate demand shocks can’t cause recessions, since they can’t affect output for very long. So classical economists think recessions are caused by aggregate supply shocks. Keynesians, however, think that both aggregate demand and aggregate supply shocks are capable of causing recessions.

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Chapter 8

Business Cycles

157

Analytical Problems 1.

Figure 8.8 illustrates the business cycle. The current NBER method picks peaks and troughs in the level of aggregate economic activity, which are points on the figure where the slope of the line is zero. These are shown in Figure 8.8 as P1 (at the peak of the cycle) and T1 (at the trough of the cycle). However, the older method picks peaks and troughs in detrended economic activity. This means the peaks and troughs occur at points that are the farthest away from the trend line, which means those points at which the slope of the line showing aggregate economic activity is the same as the slope of the trend line. These points are shown in Figure 8.8 as P2 and T2. Note that the point P2 occurs before P1, meaning that peaks in detrended economic activity are earlier than peaks in the level of economic activity. Note also that the point T2 occurs later than T1, which means that troughs in detrended economic activity are later than troughs in the level of economic activity. Since under the old method, troughs occur later and peaks occur earlier, contractions appear to be longer and expansions appear to be shorter using the pre-1927 method than using the current method. Thus the fact that after World War II expansions were longer and contractions were shorter than before World War I is somewhat illusory, since it’s based on two different accounting mechanisms. If expansions and contractions were in fact equally long in both periods, the change in accounting method would mean that our official dating of the business cycle would show longer expansions and shorter contractions after World War II than before World War I.

Figure 8.8 2.

Expenditure on durable goods is more sensitive to the business cycle than expenditure on nondurable goods and services, because people can more easily change the timing of their expenditure on durables. When economic activity is weak, and people face the danger of losing their jobs, they avoid making durable goods purchases. Instead, they may drive their cars a little longer before buying new ones, get the old washing machine repaired instead of buying a new one, and put off buying new furniture until a new expansion indicates greater income security. So in a recession, durable purchases decline a lot, but when an expansion begins, durable purchases pick up substantially. The exception was in the business cycle that began in March 2001, when very low interest rates supported expenditures on durable goods.

3.

(a) In symbols, let A = average labor productivity, Y = output, and H = total hours worked. By definition, A = Y/H, so in growth terms, ∆A/A = ∆Y/Y − ∆H/H. Since all three are procyclical, they all move in the same direction over the business cycle. If total hours worked varied more than output in an expansion, then ∆H/H would be greater than ∆Y/Y, so that ∆A/A would be negative, and average labor productivity would be countercyclical. So it must be the case that output varies more than total hours worked in an expansion. A similar argument holds in a contraction. ©2014 Pearson Education, Inc.

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(b) That average labor productivity is procyclical helps explain why the Okun’s Law coefficient is 2, not 1. A one-percentage point increase in unemployment is approximately a one percent fall in employment. Thus, if there were no change in average labor productivity, we might expect the percentage fall in output to equal the number of percentage points that the unemployment rate rises. But since average labor productivity moves in the same direction as output, it magnifies the output effect of a given amount of unemployment. 4.

Figure 8.9 illustrates the effects of a demand shock. The economy begins in equilibrium at point A, where the LRAS, SRAS, and AD curves intersect. The demand shock shifts the aggregate demand curve to the left to AD′. In the short run, the equilibrium is at point B, where AD′ intersects SRAS. This is a point at which output has declined (a recession), but the price level is unchanged. Over time, the short-run aggregate supply curve shifts down to SRAS′, restoring long-run equilibrium at point C. At this point, output is back at its full-employment level and the price level has declined. Thus the result of a demand shock on the price level is that the price level is unchanged in the short run and declines in the long run. Since the 1973–1975 recession was one in which the price level rose sharply, it must not have been due to a demand shock.

Figure 8.9 Figure 8.10 illustrates the effects of a supply shock. The economy begins in equilibrium at point A, where the LRAS, SRAS, and AD curves intersect. The supply shock shifts the long-run aggregate supply curve to the left to LRAS′. The new equilibrium is at point B, where AD intersects LRAS′. This is a point at which output has declined (a recession), but the price level has risen. This matches what happened in the 1973–1975 recession. Thus we conclude that the 1973–1975 recession was the result of a supply shock, not a demand shock.

Figure 8.10

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5.

Business Cycles

159

Growth that is “too rapid” most likely refers to a situation in which the aggregate demand curve has shifted to the right and, in the short run, intersects the SRAS curve at a level of output that’s greater than the full-employment level of output (Figure 8.11). This situation is associated with inflation because, in the long run, prices will rise, shifting the SRAS curve up to intersect with the LRAS and AD curves. The shock that is implicitly assumed to be hitting the economy is an aggregate demand shock, since that’s the only shock that increases output in the short run and inflation in the long run.

Figure 8.11

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Answers to Textbook Problems

Review Questions 1.

2.

The position of the FE line is determined by the labor market and the production function. Labor supply and demand determine equilibrium employment. Using equilibrium employment in the production function gives the full-employment level of output. The FE line is vertical at that point. The FE line shifts to the right if there is an increase in labor supply or the capital stock or if there is a beneficial supply shock. The IS curve shows combinations of the real interest rate (r) and output (Y) that leave the goods market in equilibrium. Equilibrium in the goods market occurs when the aggregate supply of goods (Y) equals the aggregate demand for goods (C d + I d + G). Since desired national saving (S d) is Y − C d − G, an equivalent condition is S d = I d. Equilibrium is achieved by the adjustment of the real interest rate to make the desired level of saving equal to the desired level of investment. For different levels of output, there are different desired saving curves, with different equilibrium interest rates. When plotted on a figure showing output and the real interest rate, this forms the IS curve, as shown in Figure 9.15. The curve slopes downward because as output rises, the saving curve shifts along the investment curve and the real interest rate declines.

Figure 9.15 The IS curve could shift down and to the left if: (1) expected future output falls, because this increases desired saving; (2) government purchases fall, because this increases desired saving; (3) the expected future marginal product of capital falls, because this decreases desired investment; or (4) corporate taxes increase, because this decreases desired investment. 3.

The LM curve shows the combinations of output and the real interest rate that maintain equilibrium in the asset market. Equilibrium in the asset market occurs when real money demand equals the real money supply. Figure 9.16 shows the derivation of the LM curve and why it slopes upward. An increase in output from Y1 to Y2 raises money demand, shifting the money demand curve from MD(Y1) to MD(Y2). With money supply fixed at MS, there must be a higher real interest rate to get equilibrium in the asset market. This gives two points of the LM curve, plotted on the right half of the figure. The result is that higher output increases the real interest rate along the LM curve, so the LM curve slopes upward.

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The IS-LM/AD-AS Model: A General Framework for Macroeconomic Analysis

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Figure 9.16 The LM curve would shift down and to the right if the nominal money supply or expected inflation increased or if the price level or nominal interest rate on money decreased. In addition, the curve would shift down and to the right if there were a decrease in wealth, a decrease in the risk of alternative assets relative to the risk of holding money, an increase in the liquidity of alternative assets, or an increase in the efficiency of payment technologies. 4.

For constant output, if real money supply exceeds the real quantity of money demanded, the real interest rate will decline to increase the real quantity of money demanded until equilibrium is reached. This process occurs because people who find themselves with excess money balances purchase nonmonetary assets, thus increasing the market price of the nonmonetary assets and reducing the real interest rate.

5.

General equilibrium is a situation in which all markets in an economy are simultaneously in equilibrium. This is shown in Figure 9.17 as the point at which the FE line and the IS and LM curves intersect. If the economy is not initially in general equilibrium, output and the real interest rate are determined by the intersection of the IS and LM curves. Then adjustment of the price level moves the LM curve until it intersects the FE line and IS curve.

Figure 9.17

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6.

There is monetary neutrality if a change in the nominal money supply changes the price level but has no effect on real variables. Once prices adjust, money is neutral in the IS–LM model, because a change in the money supply that shifts the LM curve is matched by a proportional change in the price level that returns the real money supply back to its original level and moves the LM curve back to its original location. Classical economists believe that money is neutral in the short run, but Keynesians believe that there may be sluggish adjustment of the price level, so that changes in the money supply affect output and the real interest rate in the short run. Both classicals and Keynesians believe money is neutral in the long run.

7.

The aggregate demand curve relates the price level to the aggregate demand for goods and services. It is downward sloping, because with a fixed nominal money supply, an increase in the price level shifts the LM curve up, so the level of output at the IS-LM intersection is lower. Factors that shift the aggregate demand curve up and to the right include (1) an increase in expected future output, which reduces desired saving, raises desired consumption, and shifts the IS curve up and to the right; (2) an increase in government purchases, which reduces desired saving and shifts the IS curve up and to the right; (3) an increase in expected future MPK, which increases desired investment and shifts the IS curve up and to the right; (4) a decrease in corporate taxes, which increases desired investment and shifts the IS curve up and to the right; (5) an increase in the nominal money supply, which raises the real money supply and shifts the LM curve down and to the right; (6) a decrease in the interest rate on money, which decreases the demand for money and shifts the LM curve down and to the right; and (7) an increase in the expected inflation rate, which reduces the demand for money and shifts the LM curve down and to the right.

8.

The short-run aggregate supply curve is horizontal and the long-run aggregate supply curve is vertical. The short-run aggregate supply curve is horizontal because prices remain fixed in the short run. The long-run aggregate supply curve is vertical because the aggregate amount of output supplied is the full-employment level, regardless of the price level.

9.

In the short run, money is not neutral, but in the long run it is neutral. Suppose the economy is initially in general equilibrium, as shown in Figure 9.18, where LRAS, SRAS1, and AD1 intersect. Now suppose the money supply declines by 10%, so the aggregate demand curve shifts down and to the left to AD2. In the short run, the equilibrium occurs at the intersection of AD2 and SRAS1, so output declines and the price level is unchanged. Since output declines, money is not neutral. In the long run, however, the price level will decline so the short-run aggregate supply curve shifts down to SRAS2. The long-run equilibrium occurs at the intersection of AD2, SRAS2, and LRAS, at which output has been restored to its original level and the price level is lower. Since output is back at its original level in the long run, money is neutral in the long run.

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Chapter 9

The IS-LM/AD-AS Model: A General Framework for Macroeconomic Analysis

Figure 9.18

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Numerical Problems 1.

(a) S d = Y − C d − G = Y − (4000 − 4000r + 0.2Y) − 2000 = −6000 + 4000r + 0.8Y. (b) (1) Using the equation that goods supplied equals goods demanded gives Y = Cd + Id + G = (4000 − 4000r + 0.2Y) + (2400 − 4000r) + 2000 = 8400 − 8000r + 0.2Y. So 0.8Y = 8400 − 8000r, or 8000r = 8400 − 0.8Y. (2) Using the equivalent equation that desired saving equals desired investment gives S d = Id −6000 + 4000r + 0.8Y = 2400 − 4000r 0.8Y = 8400 − 8000r, or 8000r = 8400 − 0.8Y. So we can use either equilibrium condition to get the same result. When Y = 10,000, 8000r = 8400 − (0.8 × 10,000) = 400, so r = 0.05. When Y = 10,200, 8000r = 8400 − (0.8 × 10,200) = 240, so r = 0.03. (c) When G = 2400, desired saving becomes S d = −6400 + 4000r + 0.8Y. S d is now 400 less for any given r and Y. Setting S d = I d, we get −6400 + 4000r + 0.8Y = 2400 − 4000r 8000r = 8800 − 0.8Y. Similarly, using the equation that goods supplied equals goods demanded gives: Y = Cd + Id + G = (4000 − 4000r + 0.2Y) + (2400 − 4000r) + 2400 = 8800 − 8000r + 0.2Y. So 0.8Y = 8800 − 8000r, or 8000r = 8800 − 0.8Y.

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At Y = 10,000, this is 8000r = 8800 − (0.8 × 10,000) = 800, so r = 0.10. The market-clearing real interest rate increases from 0.05 to 0.10. Thus the IS curve shifts up and to the right from IS1 to IS2 in Figure 9.19.

Figure 9.19 2.

(a) M d/P = 3000 + 0.1Y − 10,000i = 3000 + 0.1Y – 10,000(r + π e) = 3000 + 0.1Y – 10,000(r + .02) = 2800 + 0.1Y – 10,000r. Setting M/P = Md/P: 6000/2 = 2800 + 0.1Y − 10,000r 10,000r = −200 + 0.1Y r = −0.02 + (Y/100,000). When Y = 8000, r = 0.06. When Y = 9000, r = 0.07. These points are plotted as line LMa in Figure 9.20.

Figure 9.20

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(b) M = 6600, so M/P = 3300. Setting money supply equal to money demand: 3300 = 2800 + 0.1Y – 10,000r 10,000r = –500 + 0.1Y r = –0.05 + (Y/100,000). When Y = 8000, r = 0.03. When Y = 9000, r = 0.04. The LM curve is shifted down and to the right from LMa to LMb in Figure 9.20, since the same level of Y gives a lower r at equilibrium. (c) M d/P = 3000 + 0.1Y − 10,000(r + πe) = 3000 + 0.1Y − 10,000r − (10,000 × .03) = 2700 + 0.1Y − 10,000r. Setting money supply equal to money demand: 3000 = 2700 + 0.1Y − 10,000r 10,000r = − 300 + 0.1Y r = − 0.03 + (Y/100,000). When Y = 8000, r = 0.05. When Y = 9000, r = 0.06. The LM curve is shifted down and to the right from LMa to LMc in Figure 9.20, since there is a higher real interest rate for every given level of output. The LM curve shifts down and to the right by one percentage point (the increase in π e ) because for any given Y, the same nominal interest rate clears the asset market. With an unchanged nominal interest rate, the increase in π e is matched by an equal decrease in r. 3.

(a) First, we’ll find the IS curve. S d = Y – C d – G = Y − [200 + 0.8(Y − T) − 500r] − G = Y − [200 + (0.6Y − 16) − 500r] − G = −184 + 0.4Y + 500r − G Setting S d = I d gives −184 + 0.4Y + 500r − G = 200 − 500r. Solving this for Y in terms of r gives Y = (960 + 2.5G) − 2500r. When G = 196, this is Y = 1450 − 2500r. Next, we’ll find the LM curve. Setting money demand equal to money supply gives 9890/P = 0.5Y − 250r − 25, which can be solved for Y = 19,780/P + 50 + 500 r. With full-employment output of 1000, using this in the IS curve and solving for r gives r = 0.18. Using Y = 1000 and r = 0.18 in the LM curve and solving for P gives P = 23. Plugging these results into the consumption and investment equations gives C = 694 and I = 110. (b) With G = 216, the IS curve becomes Y = 1500 − 2500r. With Y = 1000, the IS curve gives r = 0.20, the LM curve gives P = 23.27, the consumption equation gives C = 684, and the investment equation gives I = 100.

4.

(a) First, look at labor market equilibrium. Labor supply is NS = 55 + 10(1 − t)w. Labor demand (ND) comes from the equation w = 5A − (0.005A × ND). Substituting the latter equation into the former, and equating labor supply and labor demand gives N = 100. Using this in either the labor supply or labor demand equation then gives w = 9. Using N in the production function gives Y = 950. ©2014 Pearson Education, Inc.

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(b) Next, look at goods market equilibrium and the IS curve. Sd = Y − Cd − G = Y − [300 + 0.8(Y − T) − 200r] − G = Y − [300 + (0.4Y − 16) – 200r] − G = − 284 + 0.6Y + 200r − G. Setting S d = I d gives − 284 + 0.6Y + 200r − G = 258.5 − 250r. Solving this for r in terms of Y gives r = (542.5 + G)/450 − 0.004/3Y. When G = 50, this is r = 1.317 − 0.004/3 Y. With full-employment output of 950, using this in the IS curve and solving for r gives r = 0.05. Plugging these results into the consumption and investment equations gives C = 654 and I = 246. (c) Next, look at asset market equilibrium and the LM curve. Setting money demand equal to money supply gives 9150/P = 0.5Y − 250(r + 0.02), which can be solved for r = [0.5Y − (5 + 9150/P)]/250. With Y = 950 and r = 0.05, solving for P gives P = 20. (d) With G = 72.5, the IS curve becomes r = 1.367 – 0.004/3 Y. With Y = 950, the IS curve gives r = 0.10, the LM curve gives P = 20.56, the consumption equation gives C = 644, and the investment equation gives I = 233.5. The real wage, employment, and output are unaffected by the change. 5.

The IS curve is found by setting desired saving equal to desired investment. Desired saving is S d = Y − C d − G = Y − [1275 + 0.5(Y − T) − 200r] − G. Setting S d = I d gives Y − [1275 + 0.5(Y − T) − 200r] − G = 900 − 200r, or Y = 4350 − 800r + 2G − T. The LM curve is M/P = L = 0.5Y − 200i = 0.5Y − 200(r + π ) = 0.5Y − 200r. (a) T = G = 450, M = 9000. The IS curve gives Y = 4350 − 800r + 2G − T = 4350 − 800r + (2 × 450) −450 = 4800 − 800r. The LM curve gives 9000/P = 0.5Y − 200r. To find the aggregate demand curve, eliminate r in the two equations by multiplying the LM curve through by 4 and rearrange the resulting equation and the IS curve. LM: 9000/P = 0.5Y − 200r. Multiplying by 4 gives 36,000/P = 2Y − 800r. Rearranging gives 800r = 2Y − 36,000/P. IS: Y = 4800 − 800r. Rearranging gives 800r = 4800 − Y. Setting the righthand sides of these two equations to each other (since both equal 800r) gives: 2Y − (36,000/P) = 4800 − Y, or 3Y = 4800 + (36,000/P), or Y = 1600 + (12,000/P); this is the AD curve. With Y = 4600 at full employment, the AD curve gives 4600 = 1600 + (12,000/P), or P = 4. From the IS curve Y = 4800 − 800r, so 4600 = 4800 − 800r, or 800r = 200, so r = 0.25. Consumption is C = 1275 + 0.5(Y − T) − 200r = 1275 + 0.5(4600 − 450) − (200 × 0.25) = 3300. Investment is I = 900 − 200r = 900 − (200 × 0.25) = 850. (b) Following the same steps as above, with M = 4500 instead of 9000, gives the aggregate demand curve AD: Y = 1600 + (6000/P). With Y = 4600, this gives P = 2. Nothing has changed in the IS equation, so it still gives r = 0.25. And nothing has changed in either the consumption or investment equations, so we still get C = 3300 and I = 850. Money is neutral here, as no real variables are affected and the price level changes in proportion to the money supply. (c) T = G = 330, M = 9000. The IS curve is Y = 4350 − 800r + 2G − T = 4350 − 800r + (2 × 330) − 330 = 4680 − 800r. LM: 36,000/P = 2Y − 800r, or 800r = 2Y − 36,000/P. IS: Y = 4680 − 800r, or 800r = 4680 − Y. AD: 2Y − (36,000/P) = 4680 − Y, or (36,000/P) + 4680 = 3Y, or Y = 1560 + (12,000/P). With Y = 4600 at full employment, the AD curve gives 4600 = 1560 + (12,000/P), or P = 3.95. From the IS curve, Y = 4680 − 800r, so 4600 = 4680 − 800r, or 800r = 80, so r = 0.10.

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Consumption is C = 1275 + 0.5(Y − T) − 200r = 1275 + 0.5(4600 − 330) − (200 × 0.10) = 3390. Investment is I = 900 − 200r = 900 − (200 × 0.10) = 880. 6.

(a) A = 2, f1 = 5, f2 = 0.005, n0 = 55, nw = 10, c0 = 300, cY = 0.8, cr = 200, t0 = 20, t = 0.5, i0 = 258.5, ir = 250, l0 = 0, lY = 0.5, lr = 250. (b) These values are all calculated directly, using the equations in the Appendix. They should match the results in Numerical Problem 4, above. (c) See the answer to part b.

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181

Analytical Problems 1.

(a) The increase in desired investment shifts the IS curve up and to the right, as shown in Figure 9.21. The price level rises, shifting the LM curve up and to the left to restore equilibrium. Since the real interest rate rises, consumption declines. In summary, there is no change in the real wage, employment, or output; there is a rise in the real interest rate, the price level, and investment; and there is a decline in consumption.

Figure 9.21 (b) The rise in expected inflation shifts the LM curve down and to the right, as shown in Figure 9.22. The price level rises, shifting the LM curve up and to the left to restore equilibrium. Since the real interest rate is unchanged, consumption and investment are unchanged. In summary, there is no change in the real wage, employment, output, the real interest rate, consumption, or investment; and there is a rise in the price level.

Figure 9.22 (c) The increase in labor supply is shown as a shift in the labor supply curve in Figure 9.23 (a). This leads to a decline in the real wage rate and an increase in employment. The rise in employment causes an increase in output, shifting the FE line to the right in Figure 9.23 (b). To restore equilibrium, the price level must decline, shifting the LM curve down and to the right. Since output increases and the real interest rate declines, consumption and investment increase. In summary, the real wage, the real interest rate, and the price level decline; and employment, output, consumption, and investment rise.

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Figure 9.23 (d) The reduction in the demand for money gives results identical to those in part (b). 2.

The increase in the price of oil reduces the marginal product of labor, causing the labor demand curve to shift to the left from ND1 to ND2 in Figure 9.24. Since households’ expected future incomes decline, labor supply increases, shifting the labor supply curve from NS1 to NS2 (but by assumption, the shift to the left in labor demand is larger than the shift to the right in labor supply). At equilibrium, there is a reduced real wage and lower employment. The productivity shock results in a shift to the left of the full-employment line from FE1 to FE2 in Figure 9.25, as both employment and productivity decline. Because the shock is permanent, it reduces future output and reduces the future marginal product of capital, both of which result in a downward shift of the IS curve. The new equilibrium is located at the intersection of the new IS curve and the new FE line. If, as shown in the figure, this intersection lies above and to the left of the original LM curve, the price level will increase and shift the LM curve upward (from LM1 to LM2) to pass through the new equilibrium point. The result is an increase in the price level, but an ambiguous effect on the real interest rate. Since output is lower, consumption is lower. Since the effect on the real interest rate is ambiguous, the effect on saving and investment are ambiguous as well, though the fall in the future marginal product of capital would tend to reduce investment.

Figure 9.24

Figure 9.25

The result is different from that of a temporary supply shock; when the shock is temporary there is no impact on future output or the marginal product of capital, so the IS curve does not shift. In that case the price level increases to shift the LM curve up and to the left from LM1 to LM2 in Figure 9.26 to restore equilibrium. In that case, the real interest rate unambiguously increases. Under a permanent

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shock, the IS curve shifts down and to the left, so the rise in the real interest rate is less than in the case of a temporary shock, and the real interest rate can even decline.

Figure 9.26 3.

(a) The decrease in expected inflation increases real money demand, shifting the LM curve up, as shown in Figure 9.27. The real interest rate rises and output declines.

Figure 9.27 (b) The increase in desired consumption shifts the IS curve up and to the right, as shown in Figure 9.28. This causes the real interest rate and output to rise.

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Figure 9.28 (c) The increase in government purchases shifts the IS curve up and to the right, with the same result as in part (b). (The FE line also shifts, as the increase in government expenditures reduces people’s wealth and leads them to increase labor supply, but this shift will not affect the short-run equilibrium, as the economy will be off the FE line.) (d) If Ricardian equivalence holds, the increase in taxes has no effect on either the IS or LM curves, so there is no change in either the real interest rate or output. If Ricardian equivalence doesn’t hold, so that the increase in taxes reduces consumption spending, the IS curve shifts down and to the left, as shown in Figure 9.29. Both the real interest rate and output decline.

Figure 9.29 (e) An increase in the expected future marginal productivity of capital shifts the IS curve up and to the right, with the same result as in part (b). 4.

The change in Eq. (9.B.10) has no effect on employment, the real wage, or output. The only effect this has is on the term β IS, which is now βIS = [1 − (1 − t)cY − iY]/(cr + ir). The real interest rate and price level are still determined by Eqs. (9.B.22) and (9.B.23), respectively.

5.

The change in the money demand function affects only the equation determining the price level, Eq. (9.B.23). It is now P = M/[l0 + lY Y − lr(αIS − βIS Y + π e − im)]

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Answers to Textbook Problems

Review Questions 1. The main feature of the classical IS-LM model that distinguishes it from the Keynesian IS-LM model is the classical model’s assumption that prices adjust quickly to restore equilibrium. Keynesians assume that prices are slow to adjust to restore equilibrium. The distinction is of practical importance because classicals are less likely than Keynesians to recommend government intervention to restore equilibrium. 2. The two main components of any theory of the business cycle are (1) a specification of the types of shocks or disturbances that are believed to be the most important in affecting the economy and (2) a model of the macroeconomy that describes how key variables respond to these economic shocks. In the real business cycle theory, productivity shocks are the primary source of cyclical fluctuations. The model of the economy is the classical IS-LM model. 3. A real shock is a disturbance to the real side of the economy that affects the IS curve or the FE line. A nominal shock is a disturbance to money supply or money demand that affects the LM curve. Real shocks include changes in the production function, in the size of the labor force, in the real quantity of government purchases, or in the spending and saving decisions of consumers. Real business cycle theorists consider shocks to the production function to be the most important. These include the development of new products or production methods, the introduction of new management techniques, changes in the quality of capital or labor, changes in the availability of raw materials or energy, unusually good or unusually bad weather, and changes in government regulations affecting production. 4. RBC theory is successful at explaining that employment is procyclical, that average labor productivity is procyclical, that the real wage is mildly procyclical, and that investment is more volatile than consumption. It is not so successful at measuring or identifying the productivity shocks that have caused business cycle fluctuations, or at explaining why unemployment occurs in downturns. 5. The Solow residual is the most common measure of productivity shocks. It is strongly procyclical, rising in expansions and declining in contractions. The Solow residual changes when total factor productivity changes, when capital utilization changes, and when labor utilization changes. 6. The increase in government purchases does not affect labor demand, but causes an increase in labor supply at any given real wage. This occurs because workers are poorer due to the current or future taxes they must pay to finance the increased government spending. Since labor demand is unchanged but labor supply increases, the real wage declines and employment rises. The rise in employment raises output in the economy. If the shift in the FE line is much smaller than the shift in the IS curve, the combination of shifts to the right in the FE line and IS curve also leads to a rise in the real interest rate and the price level. According to classical economists, fiscal policy should not be used to smooth out the business cycle because free markets produce efficient outcomes without government intervention, and because imperfect knowledge of the economy, political constraints on policy actions, and time lags make such stabilization policies impractical.

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Reverse causation means that expected future increases in output cause increases in the current money supply, and expected future decreases in output cause decreases in the current money supply. It may occur, for example, because businesses increase their money demand for transactions before they increase output. It is intended to explain the fact that money is procyclical and a leading variable in the context of a model in which money is neutral.

8. According to the misperceptions theory, an increase in the price level fools producers of goods into producing more, because they are unable to tell whether the increase in prices is a relative price increase or a rise in the general price level. The change in prices must be unexpected for this to occur, because to the extent that the price change was expected, producers would not be fooled into changing production. 9. In the classical model, money is neutral in both the short run and the long run. This is modified in the misperceptions theory in that anticipated monetary changes are neutral in the short run, but unanticipated monetary changes are not neutral in the short run. Both anticipated and unanticipated monetary changes are neutral in the long run. 10. Rational expectations means that the public’s forecasts of various economic variables are based on reasoned and intelligent examination of available economic data. If the public has rational expectations, the central bank will not be able to surprise the public systematically, and so it cannot use monetary policy to stabilize output.

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Numerical Problems 1.

(a) Labor supply is given by the equation NS = 45 + 0.1w. Before the shock, labor demand is determined by the equation w = 1.0(100 − N). Setting labor supply equal to labor demand by substituting the labor demand equation into the labor supply equation gives N = 45 + 0.1 w = 45 + [0.1 × 1.0(100 − N)] = 45 + 10 − 0.1N, or 1.1 N = 55, so N = 50. Then w = 1.0(100 − N) = 50. Output is Y = 1.0[(100 × 50) − (0.5 × 502)] = 3750. After the shock, repeating the above steps gives N = 45 + 0.1 w = 45 + [0.1 × 1.1(100 − N)] = 45 + 11 − 0.11N, or 1.11 N = 56, so N = 50.45. Then w = 1.1(100 − N) = 54.505. Output is Y = 1.1[(100 × 50.45) − (0.5 × 50.452)] = 4150. (b) Now NS = 10 + 0.8w. Before the shock, N = 10 + 0.8 w = 10 + [0.8 × 1.0(100 − N)] = 10 + 80 − 0.8N, or 1.8 N = 90, so N = 50. Then w = 1.0(100 – N) = 50. Output is Y = 1.0[(100 × 50) − (0.5 × 502)] = 3750. After the shock, N = 10 + 0.8 w = 10 + [0.8 × 1.1(100 − N)] = 10 + 88 − 0.88N, or 1.88 N = 98, so N = 52.13. Then w = 1.1(100 − N) = 52.66. Output is Y = 1.1[(100 × 52.13) − (0.5 × 52.132)] = 4240. (c) If the real wage is only slightly procyclical, then a flat labor supply curve, as in part (b) is necessary, rather than a steep labor supply curve as in part (a). Figure 10.4 illustrates the difference in slopes of the two labor supply curves. When labor demand increases from ND1 to ND2, the real wage rises a lot (from w1a to w2a ) with a steep labor supply curve, but the real wage rises only a little bit (from w1b to w2b ) if the labor supply curve is fairly flat. A calibrated RBC model would fit the facts better if the labor supply curve were fairly flat, that is, labor supply is sensitive to the real wage, as in part (b).

Figure 10.4 2.

The IS curve gives Y = C + I + G = 600 + 0.5(Y − T) − 50r + 450 − 50r + G = 1050 − 100r + 0.5Y − 0.5T + G, or 0.5Y = 1050 − 100r − 0.5T + G, or Y = 2100 − 200r − T + 2G. The LM curve gives M/P = L = 0.5Y − 100i = 0.5Y − 100(r + π ) = 0.5Y − 100(r + 0.05) = 0.5Y − 100r − 5. (a) M = 4320, G = T = 150. The IS curve is Y = 2100 − 200r − T + 2G = 2100 − 200r − 150 + (2 × 150) = 2250 − 200r. Output must be at its full-employment level of 2210. From the IS curve, 2210 = 2250 − 200r, or 200r = 40, so r = 0.20. Using this in the LM curve to find the price level gives M/P = 0.5Y − 100r − 5, or 4320/P = (0.5 × 2210) − (100 × 0.20) − 5, so P = 4320/(1105 − 20 − 5) = 4320/1080 = 4. Then consumption is C = 600 + 0.5(Y − T) – 50r = 600 + 0.5(2210 − 150) −

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(50 × 0.20) = 600 + 1030 − 10 = 1620. Investment is I = 450 − 50r = 450 − (50 × 0.20) = 440. (b) When M increases to 4752, nothing in the IS curve is affected, so Y and r are the same as in part (a), as are C and I. The LM curve becomes 4752/P = 1080, or P = 4.4. No real variables are affected, and the price level rises 10% just as the money supply did, so money is neutral. (c) When G = T = 190, the IS curve shifts. It becomes Y = 2100 − 200r − T + 2G = 2100 − 200r − 190 + (2 × 190) = 2290 − 200r. With Y = 2210, this gives 2210 = 2290 − 200r, or 200r = 80, so r = 0.40. From the LM curve, 4320/P = 0.5Y − 100r − 5 = (0.5 × 2210) − (100 × 0.40) − 5 = 1105 − 40 − 5 = 1060, so P = 4320/1060 = 4.075. C = 600 + 0.5(Y − T) – 50r = 600 + 0.5(2210 − 190) − (50 × 0.40) = 600 + 1010 − 20 = 1590. I = 450 − 50r = 450 − (50 × 0.40) = 430. Fiscal policy is not neutral since the change in policy has real effects on the interest rate, consumption, and investment. 3.

The IS curve is found by setting desired saving equal to desired investment. Desired saving is Sd = Y − Cd − G = Y − [250 + 0.5(Y − T) − 500r] − G. Setting Sd = Id gives Y − [250 + 0.5(Y − T) − 500r] − G = 250 − 500r, or Y = 1000 − 2000r + 2G − T. The LM curve is M/P = L = 0.5Y − 500i = 0.5Y − 500(r + π e) = 0.5Y − 500r. (a) T = G = 200, M = 7650. The IS curve gives Y = 1000 − 2000r + 2G − T = 1000 − 2000r + (2 × 200) − 200 = 1200 − 2000r. The LM curve gives 7650/P = 0.5Y − 500r. To find the aggregate demand curve, eliminate r in the two equations by multiplying the LM curve through by 4 and rearrange the resulting equation and the IS curve. LM: 7650/P = 0.5Y − 500r. Multiplying by 4 gives 30,600/P = 2Y − 2000r. Rearranging gives 2000r = 2Y − 30,600/P. IS: Y = 1200 − 2000r. Rearranging gives 2000r = 1200 − Y. Setting the right-hand sides of these two equations to each other (since both equal 2000r) gives: 2Y − (30,600/P) = 1200 − Y, or 3Y = 1200 + (30,600/P), or Y = 400 + (10,200/P); this is the AD curve. With Y = 1000 at full employment, the AD curve gives 1000 = 400 + (10,200/P), or P = 17. From the IS curve Y = 1200 − 2000r, so 1000 = 1200 − 2000r, or 2000r = 200, so r = 0.10. Consumption is C = 250 + 0.5(Y − T) − 500r = 250 + 0.5(1000 − 200) − (500 × 0.10) = 600. Investment is I = 250 − 500r = 250 − (500 × 0.10) = 200. (b) Following the same steps as above, with M = 9000 instead of 7650, gives the aggregate demand curve AD: Y = 400 + (12,000/P). With Y = 1000, this gives P = 20. Nothing has changed in the IS equation, so it still gives r = 0.10. And nothing has changed in either the consumption or investment equations, so we still get C = 600 and I = 200. Money is neutral here, as no real variables are affected and the price level changes in proportion to the money supply. (c) T = G = 300, M = 7650. The IS curve is Y = 1000 − 2000r + 2G − T = 1000 − 2000r + (2 × 300) − 300 = 1300 − 2000r. IS: Y = 1300 − 2000r, or 2000r = 1300 − Y. LM: 30,600/P = 2Y − 2000r, or 2000r = 2Y − 30,600/P. AD: 2Y − (30,600/P) = 1300 − Y, or (30,600/P) + 1300 = 3Y, or Y = 433 1/3 + (10,200/P). With Y = 1000 at full employment, the AD curve gives 1000 = 433 1/3 + (10,200/P), or P = 18. From the IS curve, Y = 1300 − 2000r, so 1000 = 1300 − 2000r, or 2000r = 300, so r = 0.15. Consumption is C = 250 + 0.5(Y − T) − 500r = 250 + 0.5(1000 − 300) − (500 × 0.15) = 525. Investment is I = 250 − 500r = 250 − (500 × 0.15) = 175.

4.

AD: Y = 300 + 30(M/P), AS: Y = 500 + 10(P – Pe), M = 400. (a) P e = 60. Setting AD = AS to eliminate Y, we get 300 + 30(M/P) = 500 + 10(P − P e ). Plugging in the values of M and Pe gives 300 + (30 × 400/P) = 500 + 10(P − 60), or 300 + (12,000/P) = 500 + 10P − 600, or 400 + (12,000/P) = 10P. Multiplying this equation through by P/10 gives 40P + 1200 = P 2, or P 2 − 40P − 1200 = 0. This can be factored into (P − 60)(P + 20) = 0. P can’t be ©2014 Pearson Education, Inc.

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negative, so the only solution to this equation is P = 60. At this equilibrium P = P e, so Y = 500, and the economy is at full-employment output. (b) With an unanticipated increase in the money supply to M = 700, the expected price level is unchanged at Pe = 60. The aggregate demand curve is Y = 300 + 30(M/P) = 300 + (30 × 700/P) = 300 + (21,000/P). The aggregate supply curve is Y = 500 + 10(P − Pe) = 500 + 10(P − 60) = 10P − 100. Setting AD = AS to eliminate Y gives 300 + (21,000/P) = 10P − 100, or 400 + (21,000/P) = 10P, or P − 40 − (2100/P) = 0. Multiplying through by P gives P2 − 40P − 2100 = 0. This can be factored as (P − 70)(P + 30) = 0, which has the positive solution P = 70. From the AD curve, Y = 300 + (21,000/P) = 300 + (21,000/70) = 600. (c) When M = 700 and is anticipated, P = Pe. Then the AD curve is Y = 300 + (21,000/P) and the AS curve is Y = 500. Setting AD = AS gives 500 = 300 + (21,000/P), which has the solution P = 105. 5.

6.

(a) To find the Solow residual, use the equation for the production function, dividing through to solve for A: A = Y/K 0.3N 0.7. Assuming there’s no change in utilization rates, this is the measured Solow residual. Given that equation, plugging in the values for Y, K, and N, gives the Solow residual as 1.435 in 2006 and 1.507 in 2007. The growth rate of the Solow residual is [(1.507/1.435) − 1] × 100% = 5.0%. (b) With no change in utilization rates, the growth rate of the Solow residual equals the growth rate of productivity (A), 5.0%. (c) With a change in utilization rates, the production function is modified, as shown in Eq. (10.2). Now productivity is measured as A = Y/(uKK) 0.3(uNN) 0.7 but the Solow residual is still measured as in part (a). Setting uN = 1 in year 2006 and 1.03 in year 2007, we calculate the value of A as 1.435 in 2006 (as in part a), and 1.476 in 2007. This is an increase in productivity of [(1.476/1.435) − 1] × 100% = 2.9%, significantly less than the 5.0% increase in the Solow residual. (d) Setting uN = 1 in year 2006 and 1.03 in year 2007, and uK = 1 in year 2006 and 1.03 in year 2007, we calculate the value of A as 1.435 in 2006 (as in part a), and 1.463 in 2007. This is an increase in productivity of [(1.463/1.435) − 1] × 100% = 2.0%, again significantly less than the 5.0% increase in the Solow residual. This problem illustrates the idea that the measured Solow residual grows faster than productivity when the utilization rates of capital and labor increase. An example is shown in Figure 10.5. There are several long cycles in output.

Figure 10.5

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7.

(a) With an unemployment rate of 5%, there are initially 5 million unemployed and 95 million employed. Since 1% of the employed become unemployed, 95 million × 0.01 = 950,000 move from employment to unemployment each month. Since 19% of the unemployed become employed, 5 million × 0.19 = 950,000 from unemployment each month. Since the same number move from employed to unemployed as the number moving from unemployed to employed, the unemployment rate remains 5% in February and March. (b) Note: All amounts are in millions. April: Employed (E) to Unemployed (U): 95 × 0.03 = 2.85. U to E is 5 × 0.19 = 0.95. So U = 5 + 2.85 − 0.95 = 6.9. The unemployment rate (u) = 6.9%. May: E to U: 93.1 × 0.01 = 0.931. U to E is 6.9 × 0.19 = 1.311. So U = 6.9 + 0.931 − 1.311 = 6.52 and u = 6.52%. June: E to U: 93.48 × 0.01 = 0.9348. U to E is 6.52 × 0.19 = 1.2388. So U = 6.52 + 0.9348 − 1.2388 = 6.216 and u = 6.216%. July: E to U: 93.784 × 0.01 = 0.93784. U to E is 6.216 × 0.19 = 1.18104. So U = 6.216 + 0.93784 − 1.18104 = 5.9728 and u = 5.9728%.

8.

(a) αIS = 2.47, β IS = 0.0004, αLM = 0, βLM = 0.001, lr = 500, b = 100. (b) Y = [2.47 + 88,950/(P × 500)]/(.0004 + .001) = (2.47 + 177.9/P)/.0014 (c) Y = 6000 + 100P − 2915 = 3085 + 100P; use this in the AD curve to eliminate Y. 3085 + 100P = (2.47 + 177.9/P)/.0014; multiply through by P and .0014 to get 4.319P + .14P 2 = 2.47P + 177.9, or .14P 2 + 1.849P − 177.9 = 0; use quadratic formula: P = 29.65. Y = 3085 + 100P = 6050. (d) Long run: Y = 6000; 6000 = (2.47 + 177.9/P)/0.0014, so P = 30.

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Analytical Problems 1.

(a) The increase in MPK f leaves aggregate supply unchanged, since expected future labor income and expected future wages are unchanged. But aggregate demand increases, because firms increase investment, shifting the IS curve up and to the right. There is no shift in either the LM curve or the FE line. Figure 10.6(a) shows that the increase in aggregate demand causes no change in output, since the AS curve is vertical, but the price level increases. Figure 10.6(b) shows the shift up and to the right of the IS curve from IS 1 to IS 2. To get the economy to equilibrium, the price level rises so that the LM curve shifts from LM 1 to LM 2. The real interest rate increases as a result. In the labor market, there is no change in labor demand or supply, so employment and output are unchanged. Since the real interest rate rises, saving increases and consumption declines. Since investment equals saving, investment also rises. (b) The misperceptions theory gets a different result. As shown in Figure 10.7, the shift in the aggregate demand curve from AD1 to AD2 increases both output and the price level as the economy moves along the short-run aggregate supply curve SRAS. The difference in this result compared to the result in part (a) comes from producers misperceiving the change in the price level as a change in relative prices, and increasing their labor demand and output.

2.

(a) In the case of a permanent increase in government purchases, the income effect on labor supply, which arises because the present value of taxes increases to pay for the added government spending, is much higher than in the case of a temporary increase in government spending. So workers increase their labor supply more when the government spending change is permanent than when it is temporary. (b) Desired national saving is unaffected by the change in government spending if the change in consumption is just equal to the change in taxes, so there is no shift in the saving curve. If investment is also unaffected by the change in government spending, then the IS curve does not shift. (c) Figure 10.8 shows the effect of the increase in government purchases on the economy. The FE line shifts to the right from FE1 to FE2 due to the increase in labor supply. To restore equilibrium, the price level must decline to shift the LM curve from LM 1 to LM 2. So output rises and the real interest rate declines. If consumption falls less than the increase in government purchases, the IS curve shifts up and to the right from IS1 to IS2 in Figure 10.9. As a result of the shift in the IS curve, the real interest rate and the price level will fall by less than in the case in which current consumption falls by 100, and in fact, the real interest rate and the price level may even rise if the IS curve shifts by a lot, as shown in the figure.

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Figure 10.6

Figure 10.7

Figure 10.8

Figure 10.9

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The temporary increase in government purchases causes an income effect that increases workers’ labor supply. This results in an increase in the full-employment level of output from FE1 to FE2 in Figure 10.10. The increase in government purchases also shifts the IS curve up and to the right from IS1 to IS2, as it reduces national saving. Assuming that the shift up of the IS curve is so large that it intersects the LM curve to the right of the FE line, the price level must rise to get back to equilibrium at full employment, by shifting the LM curve up and to the left from LM1 to LM2. The result is an increase in output and the real interest rate.

Figure 10.10 Figure 10.11 shows the impact on the labor market. Labor supply shifts from NS1 to NS2, leading to a decline in the real wage and a rise in employment. Average labor productivity declines, since employment rises while capital is fixed. Investment declines, since the real interest rate rises.

Figure 10.11 To summarize, in response to a temporary increase in government purchases, output, the real interest rate, the price level, and employment rise, while average labor productivity and investment decline. (a) The business cycle fact is that employment is procyclical. The model is consistent with this fact, since employment rises when government purchases rise, causing output to rise. (b) The business cycle fact is that the real wage is mildly procyclical. The model is inconsistent with this fact, since it shows a decline in the real wage when government purchases rise and output rises. ©2014 Pearson Education, Inc.

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(c) The business cycle fact is that average labor productivity is procyclical. The model is inconsistent with this fact, since it shows a decline in average labor productivity when government purchases rise and output rises. (d) The business cycle fact is that investment is procyclical. The model is not consistent with this fact, as investment falls when government purchases rise and output rises. (e) The business cycle fact is that the price level is procyclical. The model is consistent with this fact, as the price level rises when government purchases increase and output increases. 4.

(a) An increase in expected future output increases money demand, so the LM curve shifts up and to the left. As shown in Figure 10.12, the LM curve shifts from LM1 to LM2. General equilibrium in the economy can be restored by shifting the LM curve from LM2 to LM3, which occurs as the price level declines.

Figure 10.12 (b) If the Fed wants to stabilize the price level, then it increases the money supply in response to the increase in money demand, so that the LM curve shifts from LM2 to LM3 without a decline in the price level. This represents reverse causation, because the rise in future output causes the current money supply to increase. It might appear that the rise in the current money supply caused the rise in future output because of this timing, but in fact the reverse is true. 5.

The temporary wage tax has a small income effect but a large substitution effect, so labor supply is reduced. As Figure 10.13 shows, this increases the (pretax) real wage rate and reduces employment. The reduction in employment shifts the FE line from FE1 to FE2 in Figure 10.14, while the increase in government purchases shifts the IS curve from IS1 to IS2. To restore equilibrium, where IS, LM, and FE intersect, the price level must rise, so that the LM curve shifts from LM1 to LM2. The result is an increase in the real interest rate and a decline in output.

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Figure 10.13

Figure 10.14

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Answers to Textbook Problems

Review Questions 1. The efficiency wage is the real wage that maximizes effort or efficiency per dollar of real wages. It assumes that workers will exert more effort, the higher the real wage. The real wage will remain rigid even if there is an excess supply of labor, because firms won’t reduce the wage they pay; doing so would reduce their profits, since workers wouldn’t work as hard. 2. Full-employment output is the amount of output produced by firms with employment determined by the labor demand curve at the point where the marginal product of labor equals the efficiency wage. A productivity shock does not lead to a change in the efficiency wage, since it does not affect work effort. But it does affect the marginal product of labor, so employment changes. A beneficial productivity shock, for example, leads to an increase in employment. Both the employment increase and the increase in productivity lead to an increase in full-employment output. Labor supply changes have no effect on the efficiency wage or employment; they simply affect the amount of unemployment. So they have no impact on full-employment output. 3. Price stickiness is the tendency of prices to adjust only slowly to changes in the economy. Keynesians believe it is important to allow for price stickiness to explain why monetary policy is not neutral. 4. Menu costs are the costs of changing prices. Menu costs may lead to price stickiness in monopolistically competitive markets but not in perfectly competitive markets, because a monopolistically competitive firm’s demand is not as sensitive to the price as is a perfectly competitive firm’s demand. Monopolistically competitive firms may meet the demand at a fixed price when demand increases, because price exceeds marginal cost, so that profits still rise, and because the cost of changing prices may exceed the additional profit earned from doing so. A perfect competitor would lose all of its customers if its price were a little above the price charged by its competitors. But a monopolistically competitive firm would lose only some of its customers in this case. 5. In the Keynesian model, money is not neutral in the short run, but it is neutral in the long run. In the short run, an increase in the money supply increases output and the real interest rate, while the price level and real (efficiency) wage are unchanged. In the long run, however, only the price level is changed, with no change in output, the real interest rate, or the real wage. In the basic classical model, money is neutral in both the short run and the long run, so only the price level is affected by a change in the money supply, just as in the long-run Keynesian model. The extended classical model with misperceptions is similar to the Keynesian model. In the short run, an increase in the money supply increases output and the real interest rate, just as in the Keynesian model. However, unlike the Keynesian model, the price level rises, as does the real wage. The long run of the extended classical model is identical to the classical model or the long run of the Keynesian model—only the price level is affected. 6. In the Keynesian model in the short run, output and the real interest rate increase due to an increase in government purchases. In the long run, the real interest rate is higher, but output returns to its fullemployment level. Since the real interest rate is higher in the long run, investment is lower and consumption is lower.

7.

In response to a recession, policymakers can (1) make no change in macroeconomic policy, (2) increase the money supply, or (3) increase government purchases.

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If they make no change in macroeconomic policy, then during the recession output is below its full-employment level. Over time, the price level will decline to restore equilibrium. In the long run, the price level will be lower and employment will return to the full-employment level. If policymakers increase the money supply, the economy returns to full employment without a change in the price level. The composition of output is the same as when the economy returns to full employment without monetary or fiscal policy. If policymakers increase government purchases, again the economy returns to full-employment equilibrium without a change in the price level. However, the higher real interest rate caused by the expansionary fiscal policy reduces consumption and investment, and the higher taxes to pay for the government spending also reduce consumption relative to either the situation in which monetary policy is used, or in which there is no policy response at all. There are practical difficulties with increasing the money supply or increasing government purchases to return the economy to full employment. It is difficult to tell how far the economy is below full employment to know the right amount of fiscal or monetary stimulus to apply. We do not know exactly how much output will increase in response to a monetary or fiscal expansion. And since these policies take time to implement and more time to affect the economy, we really need to know where the economy will be six months or a year from now, not just where it is today, but such knowledge is very imprecise. 8. Employment is procyclical because a contractionary aggregate demand shock reduces both output and employment. Money is procyclical because price stickiness means that an increase in the money supply increases output as the aggregate demand curve moves along the flat, short-run, aggregate supply curve. Inflation is procyclical, because in a recession the price level declines over time to restore general equilibrium. Investment is procyclical for two reasons. First, shifts in the expected future marginal product of capital are important causes of cycles, shifting the IS and AD curves, thus affecting output in the same direction. Also, a shift in the LM curve leads to a change in the real interest rate, moving investment in the same direction as the change in output. 9. The Keynesian theory assumes that demand shocks cause most cyclical fluctuations. This means that during expansions when employment rises, average labor productivity declines, so it is countercyclical. But the business cycle fact is that average labor productivity is mildly procyclical. However, if labor hoarding occurs, so that a given measured amount of employment produces less output during recessions and more output during expansions, then measured average labor productivity would be procyclical. 10. In Keynesian analysis, a supply shock may reduce output in two ways: (1) a reduction in output, because the supply shock reduces the marginal product of labor, shifting the FE line to the left; and (2) a further reduction in output if the supply shock is something like an oil price shock that is large enough to cause many firms to raise prices, shifting the LM curve up and to the left so much that it intersects the IS curve to the left of the FE line. Supply shocks create problems for stabilization policy because: (1) policy can do nothing to affect the location of the FE line; and (2) using expansionary policy risks worsening the already-high rate of inflation.

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Numerical Problems 1.

The following table shows the real wage (w), the effort level (E), and the effort per unit of real wages (E/w). w

E

E/w

8 10 12 14 16 18

7 10 15 17 19 20

0.875 1.00 1.25 1.21 1.19 1.11

The firm will pay a wage of 12, since that wage provides the maximum effort per unit of the real wage (E/w = 1.25). The firm will employ 88 workers, since that is the number of workers for which w = MPN. As long as the supply of labor exceeds the demand for labor, labor supply has no effect on the firm’s decision. 2.

(a) The IS curve is found from the equation Y = C d + I d + G = 130 + 0.5(Y − 100) − 500r + 100 − 500r + 100, or 0.5Y = 280 − 1000r, or Y = 560 − 2000r. The LM curve comes from the equation M/P = L, which in this case is 1320/P = 0.5Y − 1000r, or Y = (2640/P) + 2000r. (b) At full employment, Y = 500. Using this in the IS curve gives 500 = 560 − 2000r, which has the solution r = 0.03. Plugging the values for Y and r in the LM curve gives 500 = (2640/P) + (2000 × 0.03), or 440 = 2640/P, which has the solution P = 6. Then consumption is C = 130 + 0.5(Y − 100) − 500r = 130 + 0.5(500 − 100) − (500 × 0.03) = 315. Investment is I = 100 − (500 × 0.03) = 85. (c) If desired investment increases to 200 − 500r, the IS curve shifts from IS1 to IS2 in Figure 11.11. This can be seen in the equation Y = C d + I d + G = 130 + 0.5(Y − 100) − 500r + 200 − 500r + 100, or 0.5Y = 380 − 1000r, or Y = 760 − 2000r. In the short run, the price level remains fixed at 6, so the LM curve remains at LM1. With the price level equal to 6, the LM curve has the equation Y = (2640/P) + 2000r = 440 + 2000r. The IS and LM curves intersect where 760 − 2000r = 440 + 2000r, or 320 = 4000r, which has the solution r = 0.08. At r = 0.08, output is given from the IS curve as Y = 760 − 2000r = 760 − (2000 × 0.08) = 600. Then consumption is C = 130 + 0.5 (Y − 100) − 500r = 130 + 0.5(600 − 100) − (500 × 0.08) = 340. Investment is I = 200 − 500r = 200 − (500 × 0.08) = 160.

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Figure 11.11 In the long run, the price level rises to shift the LM curve from LM1 to LM2 to restore equilibrium. The IS curve is given by the equation Y = 760 − 2000r. At full employment, Y = 500, so the IS curve is 500 = 760 − 2000r, or 2000r = 260, which has the solution r = 0.13. The LM curve is given by the equation Y = (2640/P) + 2000r, or 500 = (2640/P) + (2000 × 0.13), or 240 = 2640/P, which has the solution P = 11. Then consumption is C = 130 + 0.5(500 − 100) − (500 × 0.13) = 265. Investment is I = 200 − 500r = 200 − (500 × 0.13) = 135. 3.

(a) Y = C + I + G = [388 + 0.4(Y − 300) − 600r] + [352 − 400r] + 280 = 900 + 0.4Y − 1000r, so 0.6Y = 900 − 1000r. Therefore, Y = 1500 − (1666 + 2/3)r. Equivalently, r = 0.9 − 0.0006Y. (b) 12600/7 = M/P = L = 1750 + 0.75Y − 8750(r + 0.02), so 1800 = 1750 + 0.75Y − 8750r − 175. Therefore, 225 = 0.75Y − 8750r, so Y = 300 + (11,666+2/3)r. Equivalently, r = −0.0257143 + 0.0000857143Y or r = −9/350 + (3/35000)Y. (c) IS-LM intersection: 1500 − (1666 + 2/3)r = Y = 300 + (11,666 + 2/3)r, so 1200 = (13,333 + 1/3)r. Therefore, r = 0.09. Substitute r = 0.09 into the IS curve to obtain Y = 1500 − [(1666+2/3) × 0.09], so Y = 1350. As a check, you can substitute r = 0.09 into the equation for the LM curve, to obtain Y = 300 + [(11,666 + 2/3) × 0.09] = 1350. Consumption = C = 388 + 0.4(Y − T) − 600r = 388 + 0.4(1350 − 300) − (600 × 0.09) = 388 + 420 − 54, so C = 754. Investment = I = 352 − 400r = 352 − (400 × 0.09), so I = 316. Note that C + I + G = 754 + 316 + 280 = 1350 = Y. (d) In long-run equilibrium, output equals its full-employment level, so Y = 1400. Substitute Y = 1400 into the IS curve to obtain r = 0.9 − 0.0006Y = 0.9 − (0.0006 × 1400), so r = 0.06. Consumption = C = 388 + 0.4(Y − T) − 600r = 388 + 0.4(1400 − 300) − (600 × 0.06), so C = 792. Investment = I = 352 − 400r = 352 − (400 × 0.06), so I = 328. Note that C + I + G = 792 + 328 + 280 = 1400 = Y. (e) M/P = L, so P = M/L = 12,600/[1750 + 0.75Y − 8750(r + πe )] = 12,600/{1750 + (0.75 × 1400) − [8750(0.06 + 0.02)]}= 12,600/2100, so P = 6. Velocity = real output/real money supply = Y/(M/P), where Y = 1400 and M/P = 12600/6 = 2100. Therefore, velocity = 1400/2100, so velocity = 2/3.

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(f) (1) (2)

(3)

(4)

Set I = 320 in the investment equation (I = 352 − 400r) to obtain 320 = 352 − 400r, which implies 400r = 32. Therefore, the real interest rate must be r = 0.08 to attain I = 320. In long-run equilibrium, output equals its full-employment level, so Y = 1400. Therefore, Y = C + I + G implies 1400 = C + 320 + 350, so C = 730 in long-run equilibrium when I = 320 and G = 350. In long-run equilibrium with I = 320 and G = 350, Y = 1400 and r = 0.08. Set C = 730 in the consumption function C = 388 + 0.4(Y − T) − 600r to obtain 730 = 388 + 0.4(1400 − T) − (600 × 0.08). Therefore, 0.4T = 388 + 560 − 48 − 730 = 170, which implies T = 425 to attain the level of consumption in part (2) in long-run equilibrium with I = 320 and G = 350. In long-run equilibrium, Y = 1400 and r = 0.08, so L = 1750 + 0.75Y − 8750(r + π e ) = 1750 + (0.75 × 1400) − [8750 × (0.08 + 0.02)] = 1925. Since M/P = L = 1925, we have M = 1925 × P. To attain P = 6 in long-run equilibrium with I = 320 and G = 350, the nominal money supply must be M = 1925 × 6, so M = 11,550.

4.

(a) The IS curve is given by Y = C d + I d + G = 300 + 0.5(Y − 100) − 300r + 100 − 100r + 100 = 450 + 0.5Y − 400r. This can be rewritten as 0.5Y = 450 − 400r, or Y = 900 − 800r. The LM curve is M/P = L, or 6300/P = 0.5Y − 200r. To find the aggregate demand curve, substitute the LM curve into the IS curve to eliminate r. To do this, multiply both sides of the LM curve by 4 to get 25,200/P = 2Y − 800r, or 800r = 2Y − (25,200/P). Then substitute this in the IS curve: Y = 900 − 800r = 900 − [2Y − (25,200/P)]. This can be rewritten as 3Y = 900 + (25,200/P), or Y = 300 + (8400/P). (b) With P = 15, the AD curve is Y = 300 + (8400/15) = 860. From the IS curve, 860 = 900 − 800r, which has the solution r = 0.05. Consumption is C = 300 + 0.5(860 − 100) − (300 × 0.05) = 665. Investment is I = 100 − (100 × 0.05) = 95. (c) In the long run, Y = 700. From the IS equation, 700 = 900 − 800r, which has the solution r = 0.25. The LM curve then is 6300/P = (0.5 × 700) − (200 × 0.25) = 300, which has the solution P = 21. Consumption is C = 300 + 0.5(700 − 100) − (300 × 0.25) = 525. Investment is I = 100 − (100 × 0.25) = 75.

5.

(a) Setting w = MPN, w = 10/ N . This is the labor demand curve. (b) At W = 20, w = W/P = 20/P. Since labor demand is given by w = 10/ N , then 20/P = 10/ N , or 2 N = P. (c) Y = 20 N = 10P, or P = (1/10) Y, as shown in Figure 11.14 by the SRAS curve.

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(d) The IS curve is Y = 120 − 500r. The LM curve is M/P = 0.5Y − 500r, which can be rewritten as 500r = 0.5Y − (M/P). Plugging the LM curve into the IS curve to eliminate r gives Y = 120 − 500r = 120 − [0.5Y − (M/P)]. This can be rewritten as 1.5Y = 120 + (M/P). This is the AD curve. With M = 300, the AD curve is 1.5Y = 120 + (300/P), or Y = 80 + (200/P). The AD curve is shown in Figure 11.14. (e) To find the intersection of the SRAS curve (Y = 10P) and the AD curve [Y = 80 + (200/P)], find the price level such that 10P = 80 + (200/P). This can be rewritten as 10P2 − 80P − 200 = 0, or as P2 − 8P − 20 = 0. This can be factored as (P − 10)(P + 2) = 0. The nonnegative root is P = 10. At P = 10, from the SRAS curve, Y = 10 P = 10 × 10 = 100. On the IS curve, 100 = 120 − 500r, or r = 0.04. Since P = 2 N , or 10 = 2 N , then N = 5, or N = 25. The real wage is w = 20/P = 20/10 = 2. (f) When the money supply falls to 135, the AD curve becomes 1.5Y = 120 + (135/P), or Y = 80 + (90/P). The AD curve intersects the SRAS curve where 10P = 80 + (90/P). This can be rewritten as 10P2 − 80P − 90 = 0, or P2 − 8P − 9 = 0. This can be factored as (P − 9)(P + 1) = 0, which has the nonnegative solution P = 9. From the SRAS curve, Y = 10P = 10 × 9 = 90. From the IS curve 90 = 120 − 500r, which has the solution r = 0.06. Since P = 2 N , N = (P/2)2 = 4.52 = 20.25. The real wage is w = W/P = 20/9 = 2 2/9. 6.

(a) Y = C d + I d + G = [325 + 0.5(1000 − 150) − 500r] + [200 − 500r] + 150, so 1000r = 100, so r = 0.10. M/P = L, so 6000/P = 0.5Y − 1000r = (0.5 × 1000) − (1000 × 0.10) = 400, so P = 15. C = 325 + 0.5(Y − T) − 500r = 325 + 0.5(1000 − 150) − (500 × .10) = 700. I = 200 − 500r = 200 − (500 × .10) = 150. (b) αIS = (c0 + i0 + G − cYt0)/(cr + ir) = [325 + 200 + 150 − (0.5 × 150)]/(500 + 500) = 0.6. βIS = [1 − (1 − t)cY]/(cr + ir) = [1 − (1 − 0) 0.5]/(500 + 500) = .0005. αLM =  0 /  r − πe= 0/1000 − 0 = 0.

βLM =  Y /  r = 0.5/1000 = .0005.  r = 1000.

(c) Since P = 15 at full employment, then Y = 1000 and r = 0.10. (d) αIS = (c0 + i0 + G − cYt0)/(cr + ir) = [325 + 200 + 250 − (0.5 × 150)]/(500 + 500) = 0.7. M/P = 6000/15 = 400. Y = [αIS − αLM + (1/  r )(M/P)]/[βIS + βLM] = [0.7 − 0 + (400/1000)]/(.0005 + .0005) = 1.1/.001 = 1100. (e) ∆Y/∆G = 1/[(cr + ir)(βIS + βLM)] = 1/[(500 + 500)(.0005 + .0005)] = 1. The result is the same as in part (d). In part (d), ∆Y = 100 when ∆G =100, so ∆Y/∆G = 1.

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Analytical Problems 1.

In Figures 11.15 and 11.16, point A is the starting point, point B shows the short-run equilibrium after the change, and point C shows the long-run equilibrium after the change.

Figure 11.15

Figure 11.16

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(a) In Figure 11.15, the increase in tax incentives increases investment, shifting the IS curve up and to the right from IS1 to IS2 in Figure 11.15(a), and shifting the AD curve from AD1 to AD2 in Figure 11.15(b). The short-run equilibrium is at point B. Output increases, the real interest rate increases, employment increases, and the price level is unchanged. To restore long-run equilibrium, the price level rises, shifting the LM curve from LM1 to LM2 in Figure 11.15(a) and the short-run aggregate supply curve from SRAS1 to SRAS2 in Figure 11.15(b). The long-run equilibrium is at point C. Compared to the starting point, output is the same, the real interest rate is higher, employment is the same, and the price level is higher. (b) In Figure 11.16, the increase in tax incentives increases saving—shifting the IS curve from IS1 to IS2 in Figure 11.16(a), and shifting the AD curve from AD1 to AD2 in Figure 11.16(b). The shortrun equilibrium is at point B. Output decreases, the real interest rate decreases, employment decreases, and the price level is unchanged. To restore long-run equilibrium, the price level declines, shifting the LM curve from LM1 to LM2 in Figure 11.16(a) and the short-run aggregate supply curve from SRAS1 to SRAS2 in Figure 11.16(b). The long-run equilibrium is at point C. Compared to the starting point, output is the same, the real interest rate is lower, employment is the same, and the price level is lower. (c) A wave of investor pessimism reduces investment. This shifts the IS curve down and to the left and the AD curve down and to the left, having the same result as in problem part (b). (d) An increase in consumer confidence increases consumption spending, shifting the IS curve up and to the right and the AD curve up and to the right, with the same result as in problem part (a). 2.

In Figures 11.17–11.20, point A is the starting point, point B shows the short-run equilibrium after the change, and point C shows the long-run equilibrium after the change. (a) In Figure 11.17, when banks pay a higher interest rate on checking accounts, the demand for money rises, shifting the LM curve up and to the left from LM1 to LM2 in Figure 11.17(a). As a result, the AD curve shifts down and to the left from AD1 to AD2 in Figure 11.17(b). The new short-run equilibrium occurs at point B, where output is lower, the real interest rate is higher, employment is lower, and the price level is unchanged.

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In the long run, the price level decreases to shift the LM curve from LM2 to LM3, which is the same as LM1, to restore equilibrium at point C. As a result, the short-run aggregate supply curve shifts down from SRAS1 to SRAS2. At the new equilibrium, compared to the starting point, output is the same, the real interest rate is the same, employment is the same, and the price level is lower.

Figure 11.17 (b) In Figure 11.18, the introduction of credit cards reduces the demand for money—shifting the LM curve down and to the right from LM1 to LM2 in Figure 11.18(a). As a result, the AD curve shifts from AD1 to AD2 in Figure 11.18(b). The new short-run equilibrium occurs at point B, where output is higher, the real interest rate is lower, employment is higher, and the price level is unchanged.

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In the long run, the price level increases to shift the LM curve from LM2 to LM3, which is the same as LM1, to restore equilibrium at point C. As a result, the short-run aggregate supply curve shifts up from SRAS1 to SRAS2. At the new equilibrium, compared to the starting point, output is the same, the real interest rate is the same, employment is the same, and the price level is higher.

Figure 11.18 (c) In Figure 11.19, the reduction in agricultural output shifts the FE curve to the left from FE1 to FE2, and shifts the LRAS line from LRAS1 to LRAS2. The rise in agricultural prices increases the price level, so the short-run aggregate supply curve shifts up from SRAS1 to SRAS2. Also, the rise in the price level shifts the LM curve up and to the left from LM1 to LM2. The short-run equilibrium is at point B, assuming that the LM curve shifts so much that it intersects the IS curve to the left

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of the FE line. At point B, compared to the starting point, output is lower, the real interest rate is higher, employment is lower, and the price level is higher.

Figure 11.19 If the water shortage persists, a new long-run equilibrium occurs at point C. To get to this equilibrium, the price level must decline, shifting the LM curve from LM2 to LM3, and the short-run aggregate supply curve from SRAS2 to SRAS3. Relative to point B, the new equilibrium has a higher output level, a lower real interest rate, higher employment, and a lower price level. (Relative to the initial equilibrium at point A, output and employment are lower, and the real interest rate and the price level are higher.) When the water shortage is over, then the economy goes back to point A in the long run, with no permanent effects.

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(d) In Figure 11.20, the beneficial supply shock makes more production possible at full employment, so the FE line shifts to the right in Figure 11.20(a) from FE1 to FE2, and the LRAS line shifts from LRAS1 to LRAS2 in Figure 11.20(b). There is no immediate change in the price level, so the LM curve remains at LM1 and the short-run aggregate supply curve remains at SRAS1. The shift of the FE curve does not affect aggregate demand in the short run: output, the real interest rate, and the price level are all unchanged in the short run. The shift in the production function shifts the effective labor demand curve and reduces employment in the short run.

Figure 11.20 If the supply shock persists, prices will decline, so the LM curve will shift from LM1 to LM2 and the SRAS curve will shift from SRAS1 to SRAS2. As shown in the diagrams, the economy reaches a new equilibrium at point C, with a higher output level, a lower real interest rate, and a lower price level. When the supply shock disappears, the economy returns to its equilibrium at point A.

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Abel/Bernanke/Croushore • Macroeconomics, Eighth Edition

A lag in the impact of policy of six months, which is about the time it takes firms to adjust prices, could cause policy to be destabilizing. That is, monetary policy may be pushing the economy away from equilibrium. To see this, suppose the economy is in a recession at point A in Figure 11.21. The short-run aggregate supply curve SRAS1 intersects the aggregate demand curve AD1 at point A, to the left of the long-run aggregate supply curve LRAS. Suppose the Fed engages in expansionary monetary policy to try to shift the aggregate demand curve from AD1 to AD2 in six months, to push the economy to point B. But the recession leads firms to reduce their prices, dropping the SRAS curve from SRAS1 to SRAS2. In the absence of monetary policy action, the economy would get back to full employment because of the fall in the price level to point C. But the Fed action leads to a new equilibrium at point D. So the Fed causes the economy to overshoot the equilibrium point. The result may be to exaggerate the business cycle, pushing output too high in expansions. Then if the Fed responds to an expansion by using contractionary monetary policy, it may overshoot on the other side, causing a new recession.

Figure 11.21 If the Fed could forecast recessions well, it could stabilize the economy by using monetary policy appropriately before a recession begins. Or if the Fed’s policy takes effect before firms adjust prices, then it can also help stabilize output by shifting the AD curve before the SRAS curve shifts. 4.

An increase in government purchases shifts the IS curve up and to the right and the AD curve up and to the right to return the economy to full employment, instead of waiting for the price level to fall to get there. The advantage of doing so, according to Keynesians, is that full employment is restored quickly, whereas if the price level must adjust, it may take a long time for full employment to be restored. In the short run, the fiscal expansion does not affect the real wage, since it is an efficiency wage. However, it increases employment and it increases current and future taxes to pay for the higher government spending. The effect on consumption is ambiguous, with the rise in output raising consumption, while the rise in taxes reduces consumption. In the long run, at full employment, the lasting effects of the fiscal expansion are to decrease consumption, because of the higher real interest rate and the higher taxes, with more of the economy’s output devoted to government purchases and less to the private sector. Whether a program of fiscal stimulus in response to a recession is worthwhile depends on the benefits of the government purchases and on how long it takes the economy to return to a full-employment equilibrium by a change in the price level. The more beneficial are government purchases, the more likely such a program is to increase economic welfare. The longer the free market takes to restore equilibrium, the more likely such a program is to increase economic welfare.

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(a) In response to expansionary monetary policy, aggregate demand increases, increasing output and labor demand. This causes the labor demand curve to shift from ND1 to ND2 in the primary labor market, shown in Figure 11.22. The result is an increase in employment and output with no change in the real wage in the primary labor market. Since more workers are now in the primary labor market, the labor supply in the secondary labor market decreases from NS1 to NS2. This causes an increase in the real wage, a decrease in employment, and a decrease in output in the secondary labor market.

Figure 11.22 (b) Increased immigration has no effect in the primary labor market, since labor supply changes in general have no effect. In the secondary labor market, the immigration shifts the labor supply curve to the right from NS1 to NS2, causing a reduction in the real wage, increased employment, and increased output. However, to some extent these effects may be mitigated by the fact that increased immigration leads to increased aggregate demand, increasing labor demand in both the primary and secondary markets (Figure 11.23).

Figure 11.23

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(c) If there is a shift in the effort curve, the efficiency wage rises in the primary labor market. Since effort exerted at the higher wage is the same as before the change, the shift in the effort curve has no impact on the marginal product of labor, so there is no shift in the labor demand curve. So the effect of the higher real (efficiency) wage is to reduce employment and thus output in the primary labor market. This means that labor supply in the secondary labor market increases, shifting the labor supply curve from NS1 to NS2. The real wage falls, employment rises, and output rises in the secondary labor market, as Figure 11.24 shows.

Figure 11.24 (d) The productivity improvement shifts the labor demand curve to the right, so at the fixed real (efficiency) wage, firms demand more labor. Employment increases, so output increases in the primary labor market. The increase in employment in the primary labor market reduces the labor supply in the secondary labor market, shifting the labor supply curve from NS1 to NS2. This increases the real wage, and reduces employment and output in the secondary labor market. See Figure 11.25.

Figure 11.25

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(e) The productivity improvement in the secondary labor market has no effect on the primary labor market. In the secondary labor market, increased productivity increases the marginal product of labor so that labor demand increases from ND1 to ND2. The result is a higher real wage, higher employment, and increased output (Figure 11.26).

Figure 11.26

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Answers to Textbook Problems

Review Questions 1. The Phillips curve is an empirical negative relationship between inflation and unemployment. The Phillips curve relationship held for U.S. data in the 1960s, but broke down in the 1970s and 1980s. 2. In the traditional Phillips curve, inflation itself is related to the unemployment rate. In the expectations-augmented Phillips curve, it is unanticipated inflation (the difference between actual and expected inflation) that is related to cyclical unemployment (the difference between the unemployment rate and the natural rate of unemployment). The traditional Phillips curve appears in the data at times when both expected inflation and the natural rate of unemployment are fixed. 3. In the early 1960s the rate of inflation was fairly low (about 1% to 2%), and it didn’t vary much from year to year. But supply shocks hit the economy in both the mid- and the late-1970s, causing a rise in expected inflation and an upward shift in the Phillips curve. Expansionary monetary and fiscal policies kept inflation high in the 1970s until the Federal Reserve began pursuing contractionary monetary policy to reduce inflation during 1979–1982. This moved the economy to a lower Phillips curve, which was maintained in the 1980s. The instability of the Phillips curve is largely because of higher expected inflation associated with supply shocks in the 1970s. 4. According to the classical point of view, the economy adjusts quickly to changes in inflation, so there is only a very short period in which unemployment changes because of a change in inflation. Further, any systematic attempt to reduce unemployment by increasing inflation would be fully anticipated, and would have no effect on unemployment. Keynesians believe, however, that there is a temporary trade-off between unemployment and inflation. If policymakers want to, they can increase inflation to reduce unemployment in the short run. However, the economy must return to the natural rate of unemployment in the long run, so the reduction in unemployment is only temporary. 5. Policymakers want to keep inflation low because inflation imposes costs on the economy. Costs of anticipated inflation include shoe leather costs and menu costs. Costs of unanticipated inflation include unpredictable transfers of wealth between lenders and borrowers, resources used to reduce the risk of such transfers, and reduced efficiency because of the difficulty in observing relative prices. When there is cyclical unemployment, society as a whole loses because of output that is not produced and the families of the unemployed suffer personal and psychological costs. 6. The natural rate of unemployment is the rate of unemployment that exists when output is at its fullemployment level. This occurs when the only unemployment is frictional and structural, not cyclical. The natural rate is crucial in understanding the Phillips curve. The natural rate of unemployment has moved higher over time in the United States and Europe due to a number of factors. First, demographic changes occurred that raised the natural rate. Groups in the labor force that have higher rates of unemployment have increased in size relative to groups that have lower rates of unemployment. Also, there have been structural changes in the economy that may have raised the natural rate in the 1970s. In Europe, hysteresis has kept the unemployment rate from declining much after it hit very high levels in the early 1980s. Hysteresis arises because of government regulation and bureaucratic aspects of firms and labor unions, and due to insiders keeping outsiders from gaining employment. To reduce the natural rate of unemployment, the government could support job training and worker relocation, reduce regulations to increase labor market flexibility, reform unemployment insurance, or

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create a high-pressure economy. 7. Two costs of anticipated inflation are shoe-leather costs and menu costs. Two costs of unanticipated inflation are transfers of wealth and confusion of price signals. If the economy experiences hyperinflation, shoe-leather costs become very large as people try to minimize their cash holdings. Also, prices change so frequently they cease to serve as signals. Menu costs do not rise too much, as firms simply quote prices in terms of some other unit of account (a different country’s currency). Transfers of wealth also occur, especially since the government loses tax revenue as people delay paying taxes. 8. The greatest potential cost of disinflation is that it may cause a recession. This occurs because inflation may fall below expected inflation, causing the unemployment rate to rise along the Phillips curve. However, if the public anticipates the disinflation, expected inflation will adjust quickly and the costs of disinflation will be low. 9. One approach to disinflation is a cold turkey strategy. It has the advantage of reducing inflation quickly, but it may have high costs from increasing unemployment, according to Keynesians. So Keynesians suggest a gradualist policy to reduce inflation more slowly, but with less rise in unemployment. This also has the advantage of being politically sustainable, since policymakers are less likely to back off from disinflation. 10. The Federal Reserve works hard to establish its credibility so that the costs of reducing inflation will be low. If the Federal Reserve has a great deal of credibility, then people will believe that the inflation rate will not rise in the future, so the expected inflation rate will be low and stable. The sacrifice ratio will also be low, so the costs of disinflation will be reduced.

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Numerical Problems 1.

Since the natural rate of unemployment is 0.06, π = π e − 2(u − 0.06), so u − 0.06 = 0.5(π e − π), or u = 0.06 + 0.5(π e − π). (a) Year 1: u = 0.06 + 0.5(0.08 − 0.04) = 0.06 + 0.02 = 0.08. The unemployment rate is 0.02 higher than the natural rate. The percentage that output falls short of full-employment output is 2 × 0.02 = 0.04, or 4%. Year 2: u = 0.06 + 0.5(0.04 − 0.04) = 0.06. The unemployment rate equals the natural rate, since inflation equals expected inflation. Since unemployment is at its natural rate, output is at its full-employment level. Since the output loss was 4 percentage points and inflation declined by 8 percentage points, the sacrifice ratio is 4/8 = 0.5. (b) Use equations: u = 0.06 + 0.5(π e – π), output shortfall = 2 (u – 0.06). Year

π

πe

u

u − 0.06

Output Shortfall

1 2 3 4

0.08 0.04 0.04 0.04

0.10 0.08 0.06 0.04

0.07 0.08 0.07 0.06

0.01 0.02 0.01 0.0

0.02 0.04 0.02 0.0

The total output shortfall is 0.02 + 0.04 + 0.02 + 0.0 = 0.08 = 8-percentage points of output lost. Inflation fell by 8 percentage points. So the sacrifice ratio is 8/8 = 1. Notice that, compared with part a, the sacrifice ratio is higher, for this slower disinflation. 2.

(a) Equating aggregate demand to short-run aggregate supply gives: 300 + 10(M/P) = 500 + P − Pe, or 300 + (10 × 1000/P) = 500 + P − 50, or 10,000/P = 150 + P. Multiplying both sides of the equation by P and rearranging gives P2 + 150P − 10,000 = 0, which can be factored as (P − 50) (P + 200) = 0. This has the nonnegative solution P = 50. Since Pe is also 50, the expected price level equals the actual price level, so output is at its full-employment level of 500 and the unemployment rate is at the natural rate of 6%. These are the long-run equilibrium values of the three variables as well. (b) When the nominal money supply increases unexpectedly to 1260, we again equate aggregate demand to short-run aggregate supply, which gives: 300 + 10(M/P) = 500 + P − Pe, or 300 + (10 × 1260/P) = 500 + P − 50, or 12,600/P = 150 + P. Multiplying both sides of the equation by P and rearranging gives P2 + 150P − 12,600 = 0, which can be factored as (P − 60)(P + 210) = 0. This has the nonnegative solution P = 60. When P = 60, the short-run aggregate supply curve gives Y = 500 + P − Pe = 500 + 60 − 50 = 510. Output of 510 is 2% above full-employment output of 500, because (510 − 500)/500 = 0.02. With a natural unemployment rate of 0.06, Okun’s Law gives 0.02 = − 2(u − 0.06). This can be solved to get u = 0.05. In the long run, Pe adjusts to equal P, output adjusts to its full-employment level of 500, and unemployment adjusts to the natural rate of 0.06. To find P, use the aggregate demand curve to get 500 = 300 + 10(1260/P), or 200 = 12,600/P, which can be solved to get P = 63. The results of this exercise are consistent with the existence of an expectations-augmented Phillips curve. Unexpected inflation reduces unemployment in the short run. In the long run, however, inflation is higher and unemployment returns to its natural rate.

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(a) π = 0.10 − 2(u − 0.06) = 0.22 − 2u. This is shown as the Phillips curve labeled PCa in Figure 12.6. If the Fed keeps inflation at 0.10, then u = 0.06, the natural rate of unemployment.

Figure 12.6 (b) With expected inflation rising to 12%, the Phillips curve is π = 0.12 – 2(u – 0.06) = 0.24 – 2u. This is the Phillips curve labeled PC b in the figure. The higher rate of expected inflation has caused the curve to shift up relative to where it was in part (a). With the actual inflation rate at 10%, the Phillips curve equation is 0.10 = 0.12 – 2(u – 0.06), which has the solution u = 0.07. So if the Fed tries to maintain the existing rate of inflation after a shock has raised inflation expectations, the unemployment rate increases. However, if the Fed could convince people that the inflation rate really would not rise, so that π e remains at 0.10, then the short-run Phillips curve would remain at PC a, and the unemployment rate would not increase. (c) With the natural rate of unemployment rising to 0.08 at the same time that expected inflation rises to 0.12, the Phillips curve equation is π = 0.12 − 2(u − 0.08) = 0.28 − 2u. This is the Phillips curve labeled PC c in the figure. The new short-run Phillips curve is even higher than those for parts (a) and (b). With the actual inflation rate held to 10%, the equation becomes 0.10 = 0.28 − 2u, which can be solved to get u = 0.09. The unemployment rate rises both because the Fed holds inflation below expected inflation and because the natural rate has increased. This time, even if the Fed convinced people that inflation would remain just 10%, the unemployment rate would still rise to 8%, since the natural rate has increased to that level. 4.

(a) Beginning in long-run equilibrium, with M = 4000, output must be at its full-employment level of 6000 and the unemployment rate must be equal to the natural rate of .05. Using the values for Y and M in the AD curve, 6000 = 4000 + 2(4000/P), which gives P = 4. This is also the expected price level. Because M has been constant for a long time and is expected to remain constant, π e = 0. (b) With P e = 4, the SRAS curve is Y = 6000 + 100(P − 4). The AD curve is Y = 4000 + 2(4488/P). The intersection of the two curves occurs when 6000 + 100(P − 4) = 4000 + 2(4488/P). Simplifying terms gives 100P2 + 1600P − 8976 = 0, which has the solution P = 4.4. Plugging this into the SRAS curve gives Y = 6040. From the Okun’s Law equation we get (6040 − 6000)/6000 = −2 (u − 0.05), so – 0.00333 = u − 0.05, so u = .0467. Cyclical unemployment is u − u = − 0.0033. Unanticipated inflation is (P − Pe)/Pe = 0.10 = 10%. ©2014 Pearson Education, Inc.

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(c) The Phillips curve equation is π = π e − h(u − u ), which gives .10 = 0 − h(.0467 − 0.05). This is solved to get h = 30. So the slope of the Phillips curve is −30.

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Analytical Problems 1.

(a) The reduction in structural unemployment would reduce the natural rate of unemployment and thus would shift both the expectations-augmented Phillips curve and the long-run Phillips curve to the left. (b) Despite the expense of the government program to reduce structural unemployment, it would have a permanent effect. Monetary expansion can work only temporarily—in the long run it has no effect.

2. The slope of the short-run aggregate supply curve will be much steeper in economy B, because producers increase their output only a small amount in response to an increase in price. But economy A’s short-run aggregate supply curve will be flatter, as people are likely to perceive price changes as changes in relative price rather than the aggregate price level, and thus will respond more strongly to changes in prices. The short-run Phillips curve will also be steeper in economy B, since unemployment, like output, won’t respond much to a change in inflation. But in economy A, unemployment and output will respond more strongly to price changes, and the short-run Phillips curve will be flatter. 3.

(a) In Figure 12.7, the SRAS curve shifts up 10% each year, as does the AD curve. Unanticipated inflation is zero, as both actual and expected inflation are 10%. The economy is at full employment, since firms set their prices to exactly match the increase in the general price level.

Figure 12.7 (b) The surprise increase in the money supply at mid-year leads to a rise in output, as shown in Figure 12.8 by the shift of the AD curve from AD1 to AD2. Firms don’t adjust their prices, so the SRAS curve remains fixed at SRAS1. When the money supply rises by its regular 10% at the end of the year, the AD curve shifts up to AD3 and firms raise their prices by 15%, shifting the SRAS curve up to SRAS3. Actual inflation is 15%, but expected inflation was only 10%. As a result, there was a temporary increase in output above its full-employment level, and a temporary decline in unemployment below the natural rate. Thus for the year as a whole, cyclical unemployment was negative and unanticipated inflation was positive, just as in the expectationsaugmented Phillips curve.

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Figure 12.8 4.

In the cashless society, there would be no shoe-leather costs, as there would be no cash balances on which to economize. But menu costs would remain for anticipated inflation. The costs of unanticipated inflation would remain as well: both the risk of wealth transfers plus confusion in price signals.

5.

(a) Figure 12.9 shows the effects of increasing the money supply while holding the price level constant. Beginning at point A, the intersection of aggregate demand curve AD1 and short-run aggregate supply curve SRAS1, the increase in the money supply shifts the aggregate demand curve to AD2. Since prices cannot rise, the short-run equilibrium is at point B, with output above its full-employment level.

Figure 12.9 (b) When the price controls are removed, the price level will jump up, with the short-run aggregate supply curve shifting to SRAS2. The new equilibrium is at point C, where there is full employment. 6.

(a) A new law that prohibits people from seeking employment before age eighteen is likely to reduce the natural rate of unemployment because teenagers have a higher-than-average unemployment rate. With no teenagers allowed in the labor force, the average unemployment rate would be lower. (b) A service that makes looking for a job easier is able to match people and jobs more rapidly, which should reduce the natural rate of unemployment.

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(c) If unemployed workers can receive benefits longer, they’ll be in less of a rush to take a job, so the job-matching process will take longer. As a result, the natural rate of unemployment will rise. (d) A structural shift in the types of products people buy is likely to raise the natural rate of unemployment, because it will take time for the economy to shift workers from some types of occupations to others. (e) A recession leads to a rise in cyclical unemployment, but doesn’t affect the natural rate of unemployment.

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Answers to Textbook Problems

Review Questions 1. The nominal exchange rate is the rate at which two currencies can be exchanged for each other in the market. The real exchange rate is the price of domestic goods relative to foreign goods. Changes in the real exchange rate are related to changes in the nominal exchange rate depending on the inflation rates of the two countries: ∆e/e = ∆enom/enom + π − π For. 2. The two major types of exchange-rate systems are fixed exchange rates and flexible exchange rates. In a fixed-exchange-rate system, exchange rates are set at officially determined levels. In a flexibleexchange-rate system, exchange rates are determined by conditions of demand and supply in the foreign exchange market. Currently, the major currencies of the world are on a flexible-exchangerate system. 3. Purchasing power parity, PPP, is the idea that similar foreign and domestic goods, or baskets of goods, should have the same price when priced in terms of the same currency. Purchasing power parity does seem to explain exchange rates in the long run, but over shorter periods it doesn’t work well because countries produce very different sets of goods, because some goods aren’t traded internationally, and because there are transportation costs and legal barriers. 4. The J curve shows the response of net exports to a real depreciation. At first the real depreciation reduces net exports, as the decline in the real exchange rate means that a country pays more for its imports and receives less for its exports. But as time passes, the higher price of imports reduces the demand for imports, while the lower price of the country’s exports increases their demand abroad. So eventually net exports begin to increase. 5. An increase in domestic income leads people to buy more goods, including imported goods, so net exports decline. An increase in foreign income leads foreigners to buy more goods, including goods exported from the domestic country, so net exports increase. An increase in the domestic real interest rate makes domestic assets more attractive and foreign assets less attractive to both domestic and foreign investors. This causes a reduction in the supply of the domestic currency on the foreign exchange market and an increase in demand for the domestic currency on the foreign exchange market. The result is an appreciation of the domestic currency, which leads to a decline in net exports. 6. Foreigners demand dollars in the foreign exchange market to be able to buy U.S. goods and services (U.S. exports) and U.S. real and financial assets (U.S. capital inflows). Americans supply dollars to the foreign exchange market to be able to buy foreign goods and services (U.S. imports) and real and financial assets in foreign countries (U.S. capital outflows). The demand for dollars increases if the demand for U.S. goods increases, the domestic real interest rate increases, foreign income increases, or the foreign real interest rate decreases. The supply of dollars increases if the demand for foreign goods increases, the domestic real interest rate decreases, domestic income increases, or the foreign real interest rate increases.

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7. The IS-LM model for the open economy differs from the closed-economy IS-LM model in that international influences may shift the IS curve. Factors that raise a country’s net exports, given domestic output and the domestic real interest rate, shift the IS curve upward, while factors that reduce a country’s net exports shift the IS curve downward. A recession could be transmitted from one country to another because a recession in one country reduces the net exports of other countries, shifting their IS curves down. In the Keynesian model in the short run, this would lead to a reduction in output in the other countries. 8. Expansionary fiscal policy increases output and the real interest rate in the short run (using a Keynesian model), both of which lead to a reduction of net exports. Expansionary monetary policy increases output in the short run, which tends to reduce net exports, but reduces the real interest rate, which tends to increase net exports (by reducing the exchange rate). The overall effect is potentially ambiguous, but the effects of changes in the real exchange rate on net exports may be weak in the short run, so it is likely that net exports will decline. 9. In the short run, expansionary monetary policy increases output (using a Keynesian model), which decreases net exports, leading to an increased supply of the domestic currency in the foreign exchange market, causing it to depreciate. Expansionary monetary policy also reduces the real interest rate, causing reduced demand for domestic assets, again causing the currency to depreciate. With the price level fixed, there is both a real and nominal depreciation. In the long run, expansionary monetary policy causes a depreciation in the nominal exchange rate alone. In the long run, no real variables are affected by the expansionary policy; only nominal variables are affected. So the price level is higher, but real exchange rates are not affected. Using Eq. (13.6), enom = ePFOR /P, since the real exchange rate, e, and the foreign price level PFOR are unaffected, the nominal exchange rate declines. 10. The fundamental value of a currency is the value of the exchange rate that would be determined by free-market forces of demand and supply without government intervention. When the official exchange rate is higher than its fundamental value, it is said to be overvalued. This is a problem, because to maintain the official exchange rate, the central bank will have to buy the currency with official reserve assets. To prevent having an overvalued currency, the country can change the official exchange rate, restrict international transactions, or use contractionary monetary policy. 11. A country is limited in changing its money supply under a fixed-exchange-rate system, because only one level of the money supply is consistent with the official exchange rate being equal to its fundamental value. As a result, a country isn’t free to use expansionary monetary policy to combat recession. The only exception occurs when different countries coordinate their use of monetary policy. If countries use expansionary monetary policy at the same time, then the currencies won’t become overvalued or undervalued relative to each other. But coordination is likely only if countries face the same economic circumstances and share common macroeconomic goals. 12. Flexible exchange rates have the advantage of allowing a country to use expansionary monetary policy to combat recessions, but currency values fluctuate substantially, introducing uncertainty into international transactions. Fixed exchange rates avoid this problem, but a country may have to give up the independent use of monetary policy. This latter factor is a disadvantage when it comes to combating recessions, but might be an advantage in helping keep inflation low. As long as countries can coordinate on overall monetary policy, the fixed exchange rate system can be maintained. A currency union is very similar to a system of fixed exchange rates, but has further advantages. Costs of trading goods and assets across countries are even lower than under fixed exchange rates and speculative attacks on the currency cannot occur. But a currency union requires even greater coordination of political and financial institutions than a fixed-exchange-rate system does.

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Numerical Problems 1. The price level in the West is PW = 5 guilders per ordinary soap bar. The price level in the East is PE = 100 florins per deluxe soap bar. The real exchange rate is 2 ordinary soap bars per deluxe soap bar. (a) Use Eq. (13.6) to get enom = ePFOR /P = 2 ordinary soap bars per deluxe soap bar × 5 guilders per ordinary soap bar/100 florins per deluxe soap bar = 0.10 guilders per florin, or 10 florins per guilder. (b) Inflation in the West is πW = 10%. Inflation in the East is π E = 20%. The real exchange rate is constant. Use Eq. (13.3) to get ∆enom/enom = (∆e/e) + πFOR − π = 0 + 10% − 20% = −10%. So the nominal exchange rate (guilders per florin) depreciates at a 10% rate. The East Bubble florin depreciates, the West Bubble guilder appreciates. 2.

(a) Japan imports 64 barrels of oil, worth 16 cameras at 4 barrels of oil per camera. It exports 40 cameras, so the real value of its net exports is 24 cameras. (b) Japan now imports 60 barrels of oil, worth 20 cameras at 3 barrels of oil per camera. It exports 42 cameras, so the real value of its net exports declines to 22 cameras. (c) In the long run, Japan imports 54 barrels of oil, worth 18 cameras at 3 barrels of oil per camera. It exports 45 cameras, so the real value of its net exports rises to 27 cameras. (d) This illustrates the J curve, as a real depreciation leads to an initial decline in net exports followed by a later rise in net exports.

3. Begin by writing the equation for the IS curve, which is S d − I d = NX. S d = Y − C d − G = Y − (300 + 0.5Y − 200r) − G. NX = 150 − 0.1Y − 0.5e = 150 − 0.1Y − 0.5(20 + 600r) = 140 − 0.1Y − 300r. Using these in the IS curve equation gives: (0.5Y − 300 + 200r − G) − (200 − 300r) = 140 − 0.1Y − 300r. Rearranging terms and simplifying gives the IS curve: 800r = 640 − 0.6Y + G. (a) With G = 100 and Y = 900, the IS curve gives 800r = 640 − 540 + 100 = 200, so r = 0.25. Then e = 20 + 600r = 170, NX = 150 − 90 − 85 = −25, C = 300 + 450 − 50 = 700, and I = 200 − 75 = 125. (b) With Y = 940, the IS curve gives 800r = 640 − 564 + 100 = 176, so r = .22. Then e = 20 + 600r = 152, NX = 150 − 94 − 76 = −20, C = 300 + 470 − 44 = 726, and I = 200 − 66 = 134. The rise in domestic output reduces the real interest rate and real exchange rate, and increases net exports, consumption, and investment. (c) With G = 132, the IS curve gives 800r = 640 − 564 + 132 = 208, so r = .26. Then e = 20 + 600r = 176, NX = 150 − 94 − 88 = −32, C = 300 + 470 − 52 = 718, and I = 200 − 78 = 122. The rise in government spending increases the real interest rate and the real exchange rate, and decreases net exports, consumption, and investment. 4.

(a) Begin by writing the equation for the IS curve, which is S d − I d = NX. NX = 150 − 0.08Y − 500r. S = Y − C − G = Y − {200 + 0.6[Y − (20 + 0.2Y)] − 200r} − G = 0.52Y − (188 + G) + 200r. d

d

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Using these in the IS curve equation gives: 0.52Y − (188 + G) + 200r − (300 − 300r) = 150 − 0.08Y − 500r. Rearranging terms and simplifying gives the IS curve: 1000r = (638 + G) − 0.6Y. The LM curve comes from the expression M/P = L, which is 924/P = 0.5Y − 200r. In the long run we’ll use this equation to find the price level, so we’ll write this as P = 924/(0.5Y − 200r). In the short run we’ll combine the LM curve with the IS curve to find equilibrium, so we’ll write it as 200r = 0.5Y − 924/P. With G = 152 and Y = Y = 1000, the IS curve gives 1000r = 790 − 600 = 190, so r = 0.19. From the LM curve, P = 924/(500 − 38) = 2. Then NX = 150 − 80 − 95 = −25, C = 200 + 0.6(1000 − 220) − 38 = 630, and I = 300 − 57 = 243. (b) In the short run with G = 214 and P = 2, the IS curve now gives 1000r = (638 + 214) − 0.6Y, and the LM curve is 200r = 0.5Y − 462. Take five times the LM equation and subtract it from the IS equation to get (852 + 2310) − 3.1Y = 0, or Y = 1020. Plug this in the LM equation to get r = 0.24. Then NX = 150 − 81.6 − 120 = −51.6, C = 200 + 0.6(1020 − 224) − 48 = 629.6, and I = 300 − 72 = 228. In the long run, using Y = 1000 in the IS curve gives 1000r = (638 + 214) − (0.6 × 1000) = 252, so r = 0.252. From the LM curve, P = 924/(500 − 50.4) = 2.055. Then NX = 150 − 80 − 126 = −56, C = 200 + 468 − 50.4 = 617.6, and I = 300 − 75.6 = 224.4. (c) With G = 152 and an increase in net exports of 62, the IS curve is the same as in part (b). The only difference in the results is the amount of G and NX. In the short run, NX is 62 higher, or 10.4, while G is 62 lower, or 152. In the long run, NX is 62 higher than before (NX = 6), while G is 62 lower at 152. 5.

(a) AD intersects AS at 1000 = 400 + 50M/P, which means M/P = 12. With M = 48 francs, P = 4 francs/bottle. Use the formula e nom = ePFor /P = 5 wedges/bottle × 20 crowns/wedge/4 francs/ bottle = 25 crowns/franc. (b) At 50 crowns/franc, the franc is overvalued as the official rate exceeds the fundamental value. The domestic central bank will lose reserve assets over time if it tries to maintain the official rate. (c) To get enom = 50 crowns/franc for the fundamental value, use the formula enom = ePFor/P to find the necessary price level. This is 50 crowns/franc = 5 wedges/bottle × 20 crowns/wedge/P francs/bottle, so P = 2 francs/bottle. Since M/P = 12, you need M = 24 francs to get P = 2 francs/bottle.

6.

(a) c0 = 200, cY = 0.6, t0 = 20, t = 0.2, cr = 200 i0 = 300, ir= 300 x0 =150, xY = 0.08, xYF = 0, xr = 500, xrF = 0 r = α IS′ − β IS′ Y

α IS′ = (c0 + i0 + G − cYt0 + x0 + xYFYFor + xrFrFor)/(cr + ir + xr) = (200 + 300 + 152 − (0.6 × 20) + 150 + 0 + 0)/(200 + 300 + 500) = 790/1000 = 0.79 β IS′ = [1 − (1 − t)cY + xY]/(cr + ir + xr) = [1 − (1 − 0.2)0.6 + 0.08]/1000 = 0.0006

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(b)

r = αLM − (1/ r ) M/P + βLMY

αLM = ( 0 /  r ) − π e, βLM =  Y / r  0 = 0,  r = 200,  Y = 0.5, π e = 0

αLM = 0 β LM = 0.5/200 = 0.0025 (c) In general equilibrium, Y = 1000, so IS: r = 0.79 − (0.0006 × 1000) = 0.19 LM: r = 0 − (1/200)924/P + (0.0025 × 1000), so 4.62/P = 2.31, so P = 2. (d) AD: Combine IS and LM in terms of P and Y: LM: r = − 0.005M/P + 0.0025Y IS: r = 0.79 − 0.0006Y −0.005M/P + 0.0025Y = 0.79 − 0.0006Y, so 0.0031Y = 0.79 + 0.005M/P = 0.79 + (0.005 × 924/P), so Y = 254.84 + 1490.3/P. If NX rises by 62, x0 rises, which changes α IS′ by 62/1000, or 0.062, increasing the constant term in the equation for α IS′ from 0.79 to 0.852. So the AD curve becomes: 0.0031Y = 0.852 + 0.005M/P = 0.852 + (0.005 × 924/P), so Y = 274.84 + 1490.3/P. (e) With P = 2, Y = 274.84 + 1490.3/2, so Y = 1020.

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Analytical Problems 1.

(a) The temporary import restriction increases net exports. Since it raises the demand for domestic goods relative to foreign goods, the real exchange rate increases. The rise in the exchange rate mitigates somewhat the increase in net exports caused by the restriction, but the latter dominates, so net exports rise. Suppose the economy is initially in a recession at the intersection of the IS1 and LM curves in Figure 13.12. The increase in net exports due to the restriction shifts the IS curve from IS1 to IS2, and (if done in the right amount) returns the economy to full employment. The real interest rate increases, as does output. Since output rises, employment rises. The price level does not change.

Figure 13.12 (b) Since the restriction increases the home country’s net exports, it must decrease foreign countries’ net exports. This is shown by the shift to the left of the IS curve from IS1 to IS2 in Figure 13.13. Thus output and the real interest rate decline in the foreign country. The fall in output leads to a decline in employment. The price level is unchanged in the short run. The foreign currency depreciates, since the domestic currency appreciates.

Figure 13.13

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Although the results of this exercise indicate that import restrictions can be used to fight recessions in the short run, this is a poor method for doing so. The main objection to this method is simply that foreign countries may retaliate by imposing similar restrictions. The reduction in worldwide trade makes everyone worse off, because the gains to specialization are lost. Indeed, many economists believe that in the 1930s import restrictions contributed to the decline in output during the Great Depression. It makes more sense to fight a recession by other means, such as expansionary fiscal and monetary policies. (c) In the classical model, import restrictions can’t affect output, just the composition of output. Import restrictions shift the IS curve up, but the price level rises to restore equilibrium as the LM curve shifts up. The real interest rate is higher, so the real exchange rate will be higher, but there will be no effect on output or employment. Net exports are higher at the expense of consumption and investment. 2.

The fall in the MPK f abroad and the rise in the MPK f in the United States increases U.S. investment for any given real interest rate, shifting the IS curve up and to the right. This is shown in Figure 13.14 as a shift from IS1 to IS2. To restore equilibrium, prices must rise so that the LM curve shifts up from LM1 to LM2. At the new equilibrium the real interest rate is higher. So the result is an increase in the price level, an increase in the real interest rate, and no change in output. (Note: The reduction in MPKf abroad reduces investment abroad, leading to a decline in domestic net exports. If this effect is large enough, the domestic IS curve would shift down instead of up.)

Figure 13.14 The rise in the U.S. real interest rate increases the real exchange rate. This leads eventually to a decline in U.S. net exports. Capital is flowing into the United States because of the higher return relative to the return in other countries.

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(a) West Bubble’s contractionary monetary policy shifts its LM curve up and to the left, from LM 1 to LM 2 in part (a) of Figure 13.15. The intersection of the IS and LM curves is one in which output is below full-employment output and the real interest rate is higher than before.

Figure 13.15 The decrease in West Bubble’s output increases its net exports. The higher real interest rate causes the currency to appreciate, which decreases its net exports. It is likely that the reduction in income increases net exports by more. So West Bubble’s net exports rise. Since West Bubble’s net exports increase, East Bubble’s must decrease, thus East Bubble’s IS curve shifts down from IS1 to IS2. As part (b) of the figure shows, for East Bubble both the real interest rate and output decrease. Since West Bubble’s currency appreciates, East Bubble’s currency must depreciate. In the long run, of course, the price level in West Bubble adjusts to return the economy to its initial equilibrium, so there are no permanent effects on real variables, including the real exchange rate.

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(b) In the short run East Bubble’s real exchange rate decreases, and since the price level does not change in the short run, East Bubble’s nominal exchange rate must also decrease [since enom = ePFor /P]. In the long run the price level declines in West Bubble, but there is no effect on the price level in East Bubble. The decline in the price level in West Bubble occurs as the LM curve shifts from LM2 back to LM1 to restore equilibrium. With equilibrium restored in West Bubble, income and the real interest rate return to their original levels, so net exports return to their original levels in both countries. In East Bubble the IS curve shifts back to IS1. So the only difference between the new equilibrium and the old is that West Bubble has a lower price level. Using the expression enom = ePFor/P for East Bubble, the only term that has changed on the righthand side is the decline in PFor, so enom must decrease. (c) If East Bubble wants to offset West Bubble’s contractionary policy to keep it from affecting the exchange rate, it must also use contractionary policy. When West Bubble uses contractionary policy, East Bubble’s IS curve shifts down, because its net exports decline. To prevent the nominal exchange rate from declining, East Bubble must itself use contractionary monetary policy to shift the LM curve to the left. The contractionary policy causes East Bubble’s output to decline. Since the nominal exchange rate is unchanged and the price levels of the two countries do not change in the short run, the real exchange rate is unchanged. The effect on net exports is ambiguous. Both East Bubble and West Bubble have declines in income, so the effect on net exports depends on the sensitivity in each country of net exports to changes in income. Comparing the case in which East Bubble does not respond to the change in the exchange rate in part (a) to the case in which East Bubble fixes its exchange rate in part (c) gives the following table:

No response Fix exchange rate

Output

Real Exchange Rate

Net Exports

falls falls

falls no change

fall uncertain

(d) If East Bubble doesn’t change its macroeconomic policies, its currency will become overvalued. Then it must devalue the currency, impose restrictions on international transactions, or support the currency by buying it in the foreign exchange market, losing official reserve assets. 4.

(a) If people don’t want to spend more at a given real interest rate, they must increase desired saving, so the S − I curve shifts to the right. Since people aren’t spending more on imports, the NX curve doesn’t shift. The new equilibrium is one with a lower real interest rate and higher net exports. (b) If people spend the full amount of the additional income, there will be no change in saving, so the S − I curve won’t shift. But some of the additional spending is on imports, so net exports fall, and the NX curve shifts to the left. (c) A temporary increase in income is more likely to be saved, as in part (a), so net exports are likely to be higher. This confirms the prediction of the model in Chapter 5, Section 5.3, which showed that a temporary adverse supply shock would reduce the current account balance; so a beneficial supply shock would increase the current account and hence increase net exports.

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The IEB-IRP Model

The real exchange rate, the quantity of foreign goods that can be acquired in exchange for one unit of the domestic good, is an important determinant of a country’s net exports and therefore of domestic production and employment. But what determines a country’s real exchange rate? We will see that the real exchange rate is determined by two equilibrium conditions, each of which is economically significant in its own right. One of these conditions applies to the international market for goods and one applies to the international market for assets. We study these conditions in turn below.

The International Flow of Goods: Intertemporal External Balance As discussed in Chapter 5, a country with positive net exports produces more goods than are purchased by its consumers, firms, and governments. The country’s excess of output over spending equals its lending to other countries. In the future the country will be paid back what it has lent with interest, which will allow it to spend more than it produces and have negative net exports. Similarly, a country with negative net exports produces less output than is bought by domestic consumers, firms, and governments and therefore must borrow from abroad an amount equal to the excess of its spending over its output. Ultimately, the country must repay with interest the funds that it borrows from other countries. In order to repay foreign loans, countries with negative net exports today must at some point in the future achieve positive net exports. The requirement that countries that have positive net exports and lend today have negative net exports in the future—and similarly, that countries that have negative net exports and borrow today have positive net exports in the future—is known as intertemporal external balance. (External refers to the flows of goods across international borders, and intertemporal emphasizes that the flow of goods between countries need not balance in every period but must balance over time.) Put simply, intertemporal external balance—or external balance, for short—says that no country can borrow abroad indefinitely without repaying, and that no country would want to lend abroad indefinitely without being repaid. To illustrate the concept of external balance, consider a numerical example with only two periods, the current period and the future period. Suppose that a country’s current net exports NX are negative, equal to −100 home goods. To pay for this deficit, the country borrows in the international capital market at a real interest rate r of 8% per period. In the future period the country must repay its international borrowing with interest, for a total repayment of 108 goods. Where will the country get the 108 goods it needs to repay its foreign debt? To obtain the 108 goods it needs, in the future period the country must spend 108 goods less than it produces, so that its future net exports NX f equal 108 goods. In general, for a country to achieve external balance, its future net exports NX f must equal −(1 + r)NX, where NX is current net exports and r is the real interest rate. (For simplicity, we continue to assume two periods.) In our example NX = −100 and r = 0.08, so NX f = 108, as we found. Alternatively, suppose that the country’s current net exports were positive and equal to 100 home goods. With net exports of 100 goods, the country lends 100 goods abroad today. If the real interest rate is 0.08, the country will be repaid 108 goods in the future, which means that it will be able to have future net exports of −108 goods. This result is once again as implied by the formula NX f = −(1 + r)NX. Formally, we write the intertemporal external balance (IEB) condition as NX(e, . . .) + NX f(e f, . . .)/(1 + r) = 0,

(13.6)

which is a rearrangement of the condition that NX f = −(1 + r)NX. In Eq. (13.6) e is the real exchange rate in the current period and e f is the real exchange rate in the future period. The notations NX(e, . . .) and NX f(e f, . . .) emphasize that the country’s net exports in each period depend on the real exchange rate in that period, as well as on other factors. [Those readers who covered Chapter 8 will recognize that

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Eq. (13.6) requires the present value of net exports to equal zero.]

The Intertemporal External Balance Curve The intertemporal external balance curve IEB in Figure 13.16 shows the combinations of the current real exchange rate e and the future real exchange rate e f that satisfy the external balance condition, Eq. (13.6). To understand why this relation slopes downward, suppose the economy starts with the combination of current and future real exchange rates represented by point A in Figure 13.16. The exchange rates at point A, eA and e fA, lie on the IEB curve and thus satisfy the external balance condition. Now suppose that the current real exchange rate increases to eB, a real appreciation. The real appreciation reduces the country’s net exports in the current period. So that external balance is maintained and the country can repay foreign borrowings, lower net exports today must be offset by higher net exports in the future. This increase in future net exports can be achieved by real depreciation in the second period, or a decrease in the future real exchange rate to e fB. The new equilibrium combination of exchange rates, eB and e fB, is represented by point B in Figure 13.16. Since points A and B both satisfy external balance, the IEB curve slopes downward.

Figure 13.16 In general, external balance requires that an increase in the current real exchange rate be offset by a decline in the expected future real exchange rate. Intuitively, a high real exchange rate today causes negative net exports today, so a low real exchange rate in the future is needed to allow net exports to be positive in the future. Thus the IEB curve slopes downward, as shown in Figure 13.16.

Factors That Shift the IEB Curve The IEB curve shows the combinations of current and future real exchange rates that lead to external balance. Factors other than real exchange rates that affect current net exports or future net exports will shift the IEB curve. We discuss three important IEB curve shifters: a change in domestic income, a change in foreign income, and shifts in demand. Table 13.1 gives a summary of these shifters. Domestic Income Suppose that a country’s current and future real exchange rates are represented by point E on the curve IEB1 in Figure 13.17, so that the country is initially in external balance. Now imagine that current income (output) increases. At the initial values of e and ef the increase in income makes domestic consumers wealthier, leading them to spend more on all goods, including imported foreign goods, in both the current and future periods. The increase in imports reduces net exports in both periods, so that the country is no longer in external balance. For external balance to be restored, real exchange rates must fall. For example, a depreciation of the current real exchange rate, with the future real exchange rate held constant—represented by the movement to point F in Figure 13.17—would increase current net exports and restore external balance. Alternatively, future net exports could be increased by a depreciation ©2014 Pearson Education, Inc.

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of the future real exchange rate, with the current real exchange rate held constant—represented by the movement to point H. Thus the increase in domestic income causes the IEB curve to shift downward to IEB2, which passes through points F and H.

Figure 13.17 Foreign Income The effect of an increase in foreign income on the IEB curve is just the opposite of the effect of an increase in domestic income. Suppose that before the increase in foreign income the current and future real exchange rates are represented by point E on IEB1 in Figure 13.18. Because foreign consumers are made wealthier by the increase in income, they will buy more of the goods produced by the home country in the current period and in the future, which increases net exports by the home country in both periods. An appreciation of the current real exchange rate, represented by the movement to point F, will reduce the net exports of the home country and restore external balance. Alternatively, an appreciation of the future real exchange rate, represented by the movement to point H, would restore external balance. Therefore the new IEB curve, IEB2, which passes through points F and H, lies above the original IEB curve, IEB1.

Figure 13.18 Shifts in Demand A shift in demand away from foreign goods toward goods produced by the home country shifts the IEB curve upward, just as an increase in foreign income does. The reason is that, like an increase in foreign income, a shift in demand toward domestic goods increases both current and future net ©2014 Pearson Education, Inc.

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exports by the home country. For external balance to be restored, the current real exchange rate or the future real exchange rate must appreciate; so the IEB curve shifts upward.

The International Asset Market: Interest Rate Parity Besides affecting the international flow of goods, the real exchange rate also plays a key role in international asset markets. We will see in this section that there is a close link between the expected behavior of the exchange rate and the interest rates that are paid on assets in different countries.

Returns on Domestic and Foreign Assets To illustrate the role of the real exchange rate in international asset markets, we again use a numerical example. Imagine that you want to invest $10,000 in a financial asset for one year, and suppose that you have limited your choice to either U.S. government bonds or German government bonds. U.S. government bonds are denominated in dollars and pay a nominal interest rate of 8% for one year (that is, i = 0.08). German government bonds, which are denominated in euros, pay a nominal interest rate of 6% for one year (iFor = 0.06). The two financial investments have comparable risk and liquidity. If you want to maximize your financial return, which bonds should you buy? Table 13.1 Summary: Factors That Shift the IEB Curve An Increase in

Shifts the IEB Curve

Domestic income (output) Y

Down

Foreign income (output) YFor

Up

Demand for domestic goods relative to foreign goods

Up

Reason Higher domestic income raises import demand and reduces net exports, so real exchange rates must fall to restore external balance Higher foreign income raises demand for domestic exports and increases net exports, so real exchange rates must rise to restore external balance Net exports increase, so exchange rates must rise to restore external balance

At first glance, the answer seems obvious: Buy the U.S. government bonds, because they offer a higher interest rate. But this answer may not be right. The correct answer depends on what you think is going to happen to the exchange rate between the U.S. dollar and the euro over the next year. We can compare the financial returns on the two assets by calculating the value in dollars one year from now of $10,000 invested in each asset. For the U.S. government bond the answer is easy. At a nominal interest rate of 8% per year, the bond will earn $800 in interest and will be worth $10,800 in one year. For the German bond, however, we must take into account that the $10,000 must first be converted into euros in order to buy the bond; then when the German bond matures in one year, the principal and interest (which will be in euros) must be converted back into dollars. Table 13.2 illustrates the calculation of the future dollar value of the German bond, assuming that (1) the current nominal exchange rate enom is 2.00 euros per dollar and that (2) the exchange rate is expected to f depreciate by 3% over the coming year, so that the expected future nominal exchange rate enom equals 1.94 euros per dollar (1.94 is 97% of 2.00). Converting $10,000 to euros at an exchange rate of 2 euros per dollar yields 20,000 euros (step 1 in Table 13.2), which are used to buy a German bond. At a 6% nominal interest rate the German bond earns 1200 euros interest and is worth 21,200 euros at the end of one year (step 2). Finally, converting 21,200 euros to dollars at 1.94 euros per dollar yields $10,928

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(step 3)—which is higher than the $10,800 that would be obtained from investing in a U.S. bond! Thus the German bonds have a higher expected rate of return in this case, even though they pay a lower nominal interest rate. The German bonds have a higher rate of return in this example because, relative to the dollar asset, the German bonds have two sources of return. The first source is the nominal interest paid on the bonds (iFor = 0.06). The second source of return is the appreciation of the euro relative to the dollar. At the end of the year, when you convert your investment back into dollars, the value of a euro in terms of dollars is 3% higher than at the beginning of the year, when you converted your dollars into euros. The gross nominal rate of return on an investment is the value at the end of the year (in terms of dollars) of one dollar invested at the beginning of the year. The gross nominal rate of return from investing in U.S. government bonds is 1 + i, which is 1.08 in this example because each dollar invested in these bonds is worth $1.08 at the end of the year. The bottom section of Table 13.2 calculates the gross nominal rate of return on the German bond. One dollar will buy enom euros (step 1), which can be invested in a German bond at a nominal interest rate of iFor to yield (1 + iFor)enom euros at the end of a year (step 2). Converting f the (1 + iFor)enom euros to dollars yields (1 + iFor) enom /enom dollars at the end of the year (step 3). Thus the gross nominal rate of return from investing in the German government bond is f gross nominal rate of return on foreign bond = (1 + iFor) enom /enom

= (1.06) (2 euros per dollar)/1.94 euros per dollar = 1.0928.

(13.7)

With a gross nominal rate of return equal to 1.0928, a $10,000 investment grows to a value of $10,928 at the end of one year, just as we calculated previously. Equation (13.7) is an exact expression for the gross nominal rate of return. A simple approximation (≈) to the gross nominal rate of return is gross nominal rate of return on foreign bond ≈ 1 + iFor − ∆enom/enom

(13.8)

In our example of the German government bond with iFor = 0.06 and ∆enom/enom = −0.03, Eq. (13.8) indicates that the gross nominal rate of return from investing in the German government bond is approximately 1.09, which is very close to the exact value of 1.0928. The approximation in Eq. (13.8) permits easy calculation of the gross nominal return, generally without using pencil and paper (or a calculator). The other virtue of this approximation is that it makes clear the two sources of return from holding the German government bond: the interest on the bond iFor, and the nominal appreciation of the euro relative to the dollar over the course of the year, −∆enom/enom.

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Table 13.2

Calculating the Gross Nominal Rate of Return for a Foreign Asset Example f Today: enom = 2 euros/dollar iFor = 0.06 Future: enom = 1.94 euros/dollar Step 2 Step 3 Step 1

Convert home currency to foreign currency $10,000 → 20,000 euros General Case Today Step 1 Convert home currency to foreign currency 1 unit of → enom units of home currency foreign currency

Earn interest on foreign bond →

21,200 euros

Step 2 Earn interest on foreign bond →

(1 + iFor)enom units of foreign currency

Convert foreign currency to home currency → $10,928 Future Step 3 Convert foreign currency to home currency →

f [(1 + iFor)enom]/ enom units of home currency

Interest Rate Parity In our example the gross nominal rate of return expected on the German government bond exceeded the gross nominal rate of return on the U.S. government bond. However, if both types of government bonds have the same risk and liquidity, this difference in rates of return would not persist for long. If savers are free to choose between German bonds and U.S. bonds, they will choose the German bonds as long as they offer a higher gross nominal rate of return than U.S. bonds. But if investors choose German bonds in preference to U.S. bonds, the rate of return on German bonds will fall and the rate of return on U.S. bonds will increase until the two rates of return are equal. In general, when the international asset market is in equilibrium, the gross nominal rates of return to domestic and foreign assets of comparable risk and liquidity must be the same. This equilibrium condition can be written as f (enom /enom ) (1 + iFor) = 1 + i,

(13.9)

where the left side is the gross nominal rate of return on the foreign bond (Eq. 13.7) and the right side is the gross nominal rate of return on the domestic bond. The equilibrium condition in Eq. (13.9) is the nominal interest rate parity condition, which says that the nominal returns on foreign and domestic financial investments with equal risk and liquidity, when measured in a common currency, must be the same. [With the approximation in Eq. (13.8) the nominal interest rate parity condition can also be expressed more simply as iFor − ∆enom/enom ≈ i. According to this approximate formula for interest rate parity, the difference between nominal interest rates in two countries equals the rate at which the currency of the country with the higher nominal interest rate is expected to depreciate.] Interest rate parity can also be expressed in terms of real interest rates and real exchange rates as the real interest rate parity condition: (e/ef )(1 + rFor) = 1 + r,

(13.10) f

where rFor is the foreign real interest rate, r is the domestic real interest rate, and e and e are the current and future real exchange rates. The real interest rate parity condition, Eq. (13.10), is identical to the

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nominal interest parity condition, Eq. (13.9), except that the nominal interest and exchange rates in Eq. (13.9) are replaced by real interest and exchange rates in Eq. (13.10). Notice that real interest rate parity does not require that the domestic real interest rate r and the foreign real interest rate rFor be equal. The two real interest rates are not directly comparable, since r is measured in terms of the domestic good and rFor is measured in terms of the foreign good. Instead, real interest rate parity requires that the real returns on domestic and foreign assets be equal when real returns are measured in terms of the same good. [If there is only one good, as we assumed in Chapter 5, then e = e f = 1, and Eq. (13.10) reduces to rFor = r.]

The Interest Rate Parity Line Like the intertemporal external balance condition in the international goods market, the real interest rate parity condition in the international asset market can be shown graphically as a relationship between the current and future real exchange rates, e and ef. To write the real interest rate parity condition in a form that is easily graphed, we multiply both sides of Eq. (13.10) by ef and then divide both sides by 1 + r, to obtain e f = [(1 + rFor)/(1 + r)]e.

(13.11)

f

Equation (13.11) shows that the future real exchange rate e is proportional to the current real exchange rate e if the domestic and foreign real interest rates are held constant. Equation (13.11) also shows that if the foreign real interest rate is greater than the domestic real interest rate, then the future real exchange rate must exceed the current real exchange rate. The reason is that no financial investor will hold domestic assets paying a lower real return than is available on foreign assets unless a real appreciation of the domestic exchange rate is expected. Similarly, if the real return on foreign assets is lower than the real return on domestic assets, a real depreciation must be expected. An expected real depreciation implies that the future real exchange rate is lower than the current real exchange rate. Figure 13.19 graphs the real interest rate parity (IRP) condition in Eq. (13.11). Given values of r and rFor, the IRP line relates the expected future real exchange rate ef to the current real exchange rate e. Because the future real exchange rate ef is proportional to the current real exchange rate e, the IRP line is a straight line through the origin.

Figure 13.19

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Factors That Shift the IRP Line The position of the IRP line depends on only two factors: the domestic real interest rate r and the foreign real interest rate rFor. As you can see in Eq. (13.11), the slope of the IRP line is (1 + rFor)/(1 + r). So if we are given the values of r and rFor, the IRP line is completely determined. A fall in the foreign real interest rate rFor or a rise in the domestic real interest rate r reduces the slope of the IRP line, (1 + rFor)/(1 + r), thus causing the IRP line to pivot clockwise (see Figure 13.20). A decline in the real rate of return on the foreign asset relative to the domestic asset is possible only if financial investors expect the domestic real exchange rate to depreciate. Thus for any given current real exchange rate e, the future real exchange rate ef must fall, which causes the IRP line to pivot clockwise. Similarly, a rise in the real return on foreign assets relative to the real return on domestic assets would increase the slope of the IRP line and cause it to pivot counterclockwise.

Figure 13.20 Table 13.3 summarizes the effects of domestic and foreign real interest rates on the IRP line. Table 13.3 Summary: Factors That Shift the IRP Line An Increase in

Shifts the IRP Line

Reason

Domestic real interest rate r

Down (clockwise)

Foreign real interest rate rFor

Up (counterclockwise)

Increase in the domestic real interest rate requires an expected real depreciation, or a fall in the future real exchange rate for any given current real exchange rate Increase in the foreign real interest rate requires an expected real appreciation, or a rise in the future real exchange rate for any given current real exchange rate

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The Determination of the Real Exchange Rate In the previous two sections we focused on the role of real exchange rates in the international markets for goods and assets. We derived and discussed two equilibrium conditions, the intertemporal external balance (IEB) condition in the goods market and the real interest rate parity (IRP) condition in the asset market. In this section we put these two conditions together to discuss the determinants of real exchange rates. The determination of the current and future real exchange rates is shown in Figure 13.21, which graphs both the intertemporal external balance (IEB) curve and the interest rate parity (IRP) line. As you can see in the figure, the only combination of e and ef that simultaneously satisfies both the intertemporal external balance condition and the real interest rate parity condition is represented by point E, the intersection of the IEB curve and the IRP line. The values of the current and future real exchange rates that correspond to point E are the values that will occur in equilibrium.

Figure 13.21 Using the diagram in Figure 13.21, we can examine the factors that influence real exchange rates. As an aid to intuition, it is helpful to keep in mind that the real value of a currency, say the dollar, depends on supplies and demands in the foreign exchange market. When foreigners want to buy American goods or assets, they must trade their own currency for dollars (they demand dollars in the foreign exchange market); and when Americans want to buy foreign goods or assets, they must trade dollars for foreign currencies (they supply dollars to the foreign exchange market). Thus factors that make American goods or assets more attractive to foreigners raise the demand for dollars and increase the real value of the dollar (the real exchange rate). Likewise, factors that make foreign goods or assets more attractive to Americans increase the supply of dollars and thus reduce the real value of the dollar.

Factors That Change the Real Exchange Rate Any factor that shifts the IEB curve or the IRP line will change the equilibrium combination of current and future real exchange rates. Table 13.4 summarizes the effects of several factors on the real exchange rate, which we discuss below. Table 13.4 Summary: The Determination of Real Exchange Rates Current Real An Increase in Shifts Exchange Rate Domestic income (output) Y

IEB down

Falls

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Foreign income (output) YFor Demand for domestic gods relative to foreign goods Domestic real interest rate r Foreign real interest rate rFor

IEB up

Rises

Rises

IEB up

Rises

Rises

IRP clockwise

Rises

Falls

IRP counterclockwise

Falls

Rises

Domestic Income (Output) An increase in domestic income raises the home country’s demand for foreign goods. To buy foreign goods, domestic residents supply their own currency to the foreign exchange market, which—by the intuitive argument suggested a few moments ago—lowers the real exchange rate. In terms of the IEB-IRP diagram (Figure 13.22), if we start from an initial equilibrium at point E, an increase in domestic income raises imports by the home country and causes the IEB curve to shift downward, from IEB1 to IEB2 (see Table 13.1). The interest rate parity line is unaffected by the change in domestic income. At the new equilibrium, point F, both the current and the future real exchange rates have fallen. The fall in the current and future real exchange rates restores external balance while maintaining interest rate parity.

Figure 13.22 Foreign Income (Output) An increase in foreign income has exactly the opposite effect of an increase in domestic income. Intuitively, higher foreign income increases the demand for home country exports, raises the demand for the home country’s currency, and thus causes the real exchange rate to rise. In terms of Figure 13.23, an increase in foreign income shifts the IEB curve upward, from IEB1 to IEB2 (see Table 13.1). The IRP line is not affected by the change in foreign income. At point F, the new equilibrium, the values of the current and future real exchange rates both increase. The higher real exchange rates restore external balance in a way that is consistent with interest rate parity. Again, notice that the effects of the increase in foreign income are just the opposite of the effects of an increase in the home country’s income.

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Figure 13.23 Shifts in Demand A shift in demand toward the goods produced by the home country increases the demand for the home country’s currency and thus raises the real exchange rate. In terms of the IEB-IRP diagram, a shift in demand toward the home country’s exports causes the IEB curve to move upward (see Table 13.1). The IRP line is not affected by the shift in the demand for goods. Figure 13.23, which was introduced to illustrate the effects of an increase in foreign income, applies to the shift in demand toward home goods as well. As a result of the shift in demand toward the goods produced by the home country, both the current and future equilibrium values of the real exchange rate increase. The Domestic Real Interest Rate An increase in the domestic real interest rate makes domestic assets more attractive, which increases the demand for the home country’s currency and thus causes the current real exchange rate to appreciate. Diagrammatically, an increase in the domestic real interest rate reduces the slope of the IRP line and causes it to pivot clockwise, from IRP1 to IRP2 in Figure 13.24 (see Table 13.3). The IEB curve is unaffected by the change in the domestic real interest rate. [To say that the domestic real interest rate does not affect the IEB curve is not quite accurate, since the real interest rate r does appear in the external balance condition, Eq. (13.6). A change in r has no effect on the IEB curve at the point at which exports equal imports in both periods (NX = NX f = 0), and the effect is small at points at which exports and imports in each period are close to being in balance. Since allowing for an effect of the domestic real interest on the IEB curve does not significantly affect our results, for simplicity we ignore this effect.] Therefore, the equilibrium moves from point E to point F, where IEB intersects IRP2. The result of an increase in the domestic real interest rate is a rise in the current real exchange rate and a fall in the future real exchange rate, or a larger expected rate of exchange rate depreciation. Since the domestic real interest rate has increased, the larger expected depreciation is needed to make financial investors willing to hold foreign assets.

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Figure 13.24 The Foreign Real Interest Rate An increase in the foreign real interest rate has the opposite effects of an increase in the domestic real interest rate. As you can verify, an increase in the foreign real interest rate (by rotating the IRP line counterclockwise and leaving the IEB curve unaffected) depreciates the current real exchange rate and appreciates the future real exchange rate. Intuitively, the fall in the current real exchange rate occurs because the rise in the foreign real interest rate makes foreign assets more attractive.

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Answers to Textbook Problems

Review Questions 1. The monetary base, or high-powered money, consists of the sum of currency held by the non-bank public and banks’ reserves. In an all-currency economy, the money supply equals the monetary base; more generally, the money supply equals the money supply times the money multiplier. 2. The money multiplier is the number of dollars of the money supply that can be created from each dollar of monetary base. Changes in the desire by the public for holding currency affect the currencydeposit ratio, thus changing the money multiplier. Similarly, changes in banks’ desire to hold reserves affect the reserve-deposit ratio, thus changing the money multiplier. Increases in either the currencydeposit ratio or the reserve-deposit ratio reduce the money multiplier. But these effects do not mean that the central bank cannot control the money supply, because changes in the money multiplier can be offset by changes in the monetary base to leave the money supply unchanged. 3. An open-market purchase increases the monetary base. The increase in the monetary base leads to an increase in the money supply through the multiple expansions of loans and deposits. 4. Monetary policy in the United States is determined by the Federal Reserve System. The President appoints the seven members of the Board of Governors of the Federal Reserve System, including the chairman, but otherwise has no direct influence on monetary policy. 5. Means of controlling the money supply other than open-market operations include: (1) Reserve requirements. An increase in reserve requirements forces banks to hold more reserves, increasing the reserve-deposit ratio, thus reducing the money multiplier. With a lower money multiplier, the money supply is reduced for a given size of the monetary base. (2) Discount window lending. A reduction in discount window lending, which may be caused by the Fed increasing the discount rate or by the Fed refusing to lend, causes a reduction in banks’ reserves, decreasing the monetary base. Also, a higher discount rate may lead banks to choose a higher reserve-deposit ratio, so the money multiplier declines. Both effects reduce the money supply. (3) Interest rate on reserves. The Fed can increase reserve holdings by banks by increasing the interest rate on reserves, thus reducing the money multiplier and the money supply. 6. Intermediate targets are macroeconomic variables that the Fed cannot directly control, but can influence fairly predictably, and that are related to the ultimate goals of monetary policy. The ultimate goals of monetary policy are achieving price stability and promoting stable growth of aggregate economic activity. Since the Fed can’t control its ultimate goals directly, it influences its intermediate targets as a method for achieving those goals. If the Fed targets the Fed funds rate, then it engages in monetary policy to peg a particular real interest rate, thus allowing the LM curve to shift to whatever location is necessary to hit its target for the real interest rate. Implicitly, then, the target for the real interest rate becomes a horizontal LR curve, replacing the LM curve. 7. The three main sources of uncertainty that affect monetary policymakers are (1) uncertainty about the current state of the economy; (2) incompleteness of their models of the economy; and (3) uncertainty about how the expectations of the public will be affected by economic shocks and policy actions. Examples of uncertainty about the current state of the economy include the fact that different economic variables often give conflicting signals about the current strength of the economy and the fact that data are often revised, and the initial releases of the data are much less accurate than later releases of the data. Examples of incompleteness of models of the economy include the fact that no

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one is certain whether a classical model or the Keynesian model is the best description of the economy, our lack of knowledge about the slopes and locations of each of the curves in each model, and uncertainty about the levels of full-employment output and the natural rate of unemployment. In addition, there is uncertainty about the predominant source of shocks to the economy. Examples of uncertainty about expectations include the idea that the public is not sure of the central bank’s motives, which might affect their expectations. 8. The three tools the Fed used in the Great Recession to avoid problems caused by the zero lower bound include forward guidance, credit easing, and quantitative easing. Using forward guidance, the Fed tried to convince people about the path of future short-term interest rates, to affect long-term interest rates and spending decisions. Using credit easing, the Fed bought mortgage-market-related assets to help the housing market and used Operation Twist to reduce long-term interest rates. Using quantitative easing, the Fed bought many assets to increase the amount of assets on its balance sheet, leading to higher inflation expectations, preventing deflation. 9. The monetarist response to the argument that discretion is more flexible than following a rule is to argue that (1) because of information lags, it is difficult for the central bank to tell what the appropriate policy is at a particular time; (2) there are long and variable lags between monetary policy actions and their economic results; and (3) the lags mean that by the time a policy change has an effect, it may be destabilizing—moving the economy in the wrong direction. Further, discretion allows political manipulation of the economy. The more recent argument is that the central bank’s credibility can be enhanced by tying itself to rules rather than relying on discretion. If people believe that the central bank is committed to a rule, they will know that the Fed will not take advantage of them by using unexpected inflation to increase output temporarily. As a result, inflation will be lower. 10. The Taylor rule sets the Fed funds rate target depending on recent inflation, the deviation of output from the level of full-employment output, and the deviation of recent inflation from its target of 2%. The rule has explained the movements of inflation fairly well in the past; when the Fed has set interest rates below those called for by the Taylor rule, inflation has often increased and when the Fed has followed the Taylor rule, inflation has been stable. 11. Inflation targeting may improve a central bank’s credibility because the public can easily observe whether the central bank has achieved its goals. The main disadvantage is the long lag between changes in monetary policy and changes in inflation, so that the Fed may not know exactly how to change policy to hit its goals and the public may not know at any time if the Fed is engaging in the best policy.

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Numerical Problems 1.

Initial balance sheet of banks (all amounts in dollars): Assets Reserves

Liabilities

500,000

Deposits

500,000

Banks want to hold reserves equal to only 20% of deposits. This is 0.20 × 500,000 = 100,000. So they have 400,000 they’d like to lend. If they lend 400,000, the public will hold half of it (200,000) in deposits and the other 200,000 in currency. Since the public holds 200,000 of additional currency, banks’ reserves are 500,000 − 200,000 = 300,000. The first-round balance sheet of banks is: Assets Reserves Loans

Liabilities

300,000 400,000

Deposits 700,000

Banks still want reserves to equal just 20% of deposits, or 0.20 × 700,000 = 140,000. Since they are still holding reserves of 300,000, they can lend another 160,000. Of this amount, 80,000 comes back to the bank in the form of new deposits, and the other 80,000 is held by the public in the form of currency. Banks have reduced their reserves by 80,000 from 300,000, so reserves are 220,000. The second-round balance sheet of banks is: Assets Reserves Loans

Liabilities

220,000 560,000

Deposits

780,000

The process continues until banks reach their desired reserve-deposit ratio. Since the public wants to hold its money in equal amounts of currency and deposits, the currency-deposit ratio is 1. The money multiplier in this case is (cu + 1)/(cu + res) = (1 + 1)/(1 + 0.20) = 2/1.2 = 1 2/3. Since the monetary base is 1 million dollars, the money supply is 1 2/3 million dollars. Since half of the money supply is in currency and half is in deposits, these are each equal to 833 1/3 thousand dollars. With a reserve-deposit ratio of 0.2, total reserves held by banks are 0.2 × 833 1/3 = 166 2/3 thousand dollars. The final balance sheets are: Central Bank Assets Securities

1,000,000

Liabilities Currency

1,000,000

Banks Assets Reserves 166,666 2/3 Loans 666,666 2/3

Liabilities Deposits 833,333 1/3 Public

Assets Currency 833,333 1/3 Deposits 833,333 1/3

Liabilities Loans 666,666 2/3 Net Worth 1,000,000

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2.

Dollar amounts are in millions of dollars. (a) DEP = M − CU = 6 − 2 = 4. RES = res × DEP = 0.25 × 4 = 1. BASE = CU + RES = 2 + 1 = 3. Multiplier = M/BASE = 6/3 = 2. (b) RES = vault cash + reserves at central bank = 1 + 4 = 5. CU = BASE − RES = 10 − 5 = 5. M = CU + DEP = 5 + 20 = 25. Multiplier = M/BASE = 25/10 = 2.5.

3.

(a) res = 0.4 − 2(0.10) = 0.2. Multiplier = (cu + 1)/(cu + res) = (0.4 + 1)/(0.4 + 0.2) = 2 1/3. M = multiplier × BASE = 2 1/3 × 60 = 140. Setting M/P = L gives 140/1 = 0.5Y − 10(0.10), or 140 + 1 = 0.5Y, which has the solution Y = 282. (b) res = 0.4 − 2(0.05) = 0.3. Multiplier = (cu + 1)/(cu + res) = (0.4 + 1)/(0.4 + 0.3) = 2. M = multiplier × BASE = 2 × 60 = 120. Setting M/P = L gives 120/1 = 0.5Y − 10(0.05), or 120 + 0.5 = 0.5Y, which has the solution Y = 241. (c) In this case the multiplier is unchanged from part (a) at 2 1/3, so the money supply is unchanged at 140. Setting M/P = L gives 140/1 = 0.5Y − (10 × 0.05), or 140 + 0.5 = 0.5Y, which has the solution Y = 281. (d) If the reserve-deposit ratio is unaffected by the real interest rate, the LM curve is steeper than when it is affected by the real interest rate. To see why, consider the effect of a decline in the real interest rate. If the reserve-deposit ratio is affected by the real interest rate, the fall in the real interest rate causes banks to hold more reserves, since they are cheaper (they have a lower opportunity cost). The increase in reserves reduces the money multiplier, reducing the nominal money supply. At the same time, the fall in the real interest rate increases the real demand for money. Since the price level is fixed in the short run, the decline in the nominal money supply means that the real money supply has declined as well. Since the real money supply declines while real money demand increases, something must adjust to restore equilibrium. Along an LM curve, given a particular real interest rate, output adjusts to restore equilibrium. A decline in output is necessary to reduce real money demand and restore equilibrium in the asset market. If the reserve-deposit ratio is not affected by the fall in the real interest rate, then there is no effect on money supply, just an increase in money demand. So it takes a smaller decline in output to restore the asset market to equilibrium. Since output need not change as much, this means that the LM curve is steeper.

4.

(a) The Taylor rule is i = π + 0.02 + 0.5y + 0.5 (π − 0.02). The inflation rate over the past year is [(149.2 − 147.3)/147.3] = 0.013. The percentage deviation of output from potential output is (12,892.5 − 13,534.2)/13,534.2 = −0.047. So the Taylor rule suggests a target Fed funds rate equal to: i = π + 0.02 + 0.5y + 0.5 (π − 0.02) = 0.013 + 0.02 + [0.5 × (−0.047)] + 0.5[0.013 − 0.02] = 0.006 = 0.6%. (b) Now the inflation rate over the past year is –0.004 and the percentage deviation of output from potential output is its old deviation – 0.043 (because potential output increased .03 and actual output declined .013, for a net decline of 0.043), or y = –0.047 – 0.043 = –0.09. The Taylor rule is i = π + 0.02 + 0.5y + 0.5 (π – 0.02) = –0.004 + 0.02 + [0.5× (–0.09)] + 0.5[–0.004 – 0.02] = – 0.041 = –4.1%. The Fed would like to set the Fed funds rate at a negative level, but nominal interest rates cannot be negative.

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Analytical Problems 1.

(a) The increase in banks’ reserve-deposit ratio reduces the money multiplier, causing the money supply to decline. (b) The increased holding of cash raises the currency-deposit ratio, reducing the money multiplier and causing the money supply to decline. (c) The sale of gold to the public has the same effect as an open-market sale of government securities—it reduces the monetary base, thus causing the money supply to decline. (d) If the Fed pays a lower interest rate on reserves, banks are likely to decrease their reserve-deposit ratio, thus increasing the money multiplier, causing the money supply to increase. (e) As people sell their stocks and increase their deposits, the currency-deposit ratio will decline. This causes the money multiplier to increase, which causes the money supply to increase. (f) When the Fed monetizes the government debt, the monetary base increases, so the money supply increases. (g) When the Fed sells securities in exchange for yen, there is no change in the U.S. monetary base or in the U.S. money supply. The Fed has simply changed the composition of its assets.

2.

To examine the Taylor rule, we’ll use the classical model with misperceptions. (a) An increase in money demand causes the aggregate demand curve to shift down and to the left, reducing the price level and inflation and decreasing output, if the money supply is unchanged. In response to these changes in output and inflation, the Taylor rule decreases the nominal Fed funds rate, which means the money supply is increased. This shifts the aggregate demand curve up and to the right and helps stabilize the economy. (b) A temporary increase in government purchases causes the aggregate demand curve to shift up and to the right, increasing the price level and inflation and increasing output, if the money supply is unchanged. In response to these changes, the Taylor rule increases the nominal Fed funds rate, which means the money supply is decreased. The decrease in the money supply shifts the aggregate demand curve down and to the left and helps stabilize the economy. (c) An adverse supply shock causes the aggregate supply curve to shift up and to the left, increasing the price level and inflation and decreasing output, if the money supply is unchanged. In response to these changes, the Taylor rule is ambiguous about which way to move the nominal Fed funds rate, since higher inflation increases the funds rate but lower output decreases the funds rate. (d) A decline in consumer confidence causes the aggregate demand curve to shift down and to the left, reducing the price level and inflation and decreasing output, if the money supply is unchanged. In response to these changes in output and inflation, the Taylor rule decreases the nominal Fed funds rate, which means the money supply is increased. The increase in the money supply shifts the aggregate demand curve up and to the right and helps stabilize the economy. (e) An increase in export demand causes the aggregate demand curve to shift up and to the right, increasing the price level and inflation and increasing output, if the money supply is unchanged. In response to these changes in output and inflation, the Taylor rule increases the nominal Fed funds rate, which means the money supply is decreased. The decrease in the money supply shifts the aggregate demand curve down and to the left and helps stabilize the economy.

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(a) The investment tax credit causes desired investment to rise, shifting the IS curve up and to the right (Figure 14.4). The short-run equilibrium occurs at point B, with a higher level of output and an unchanged real interest rate. In the long run (Figure 14.5), the equilibrium must occur at the intersection of the FE line and the IS curve, so the existing real interest rate is not tenable; the price level will increase, causing the LM curve to shift up and to the left, leading the LR curve to shift up. Compared with the initial situation, output is unchanged, the price level is higher, and the real interest rate is higher.

Figure 14.4

Figure 14.5

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(b) If the Fed raises its target for the real interest rate to keep output stable in response to the shift in the IS curve, it shifts the LR curve up to LR2 (Figure 14.6) The short-run and long-run equilibria both occur at the same point B, at which the real interest rate is higher but output and the price level are unchanged.

Figure 14.6 (c) The increase in the expected inflation rate causes the real interest rate to decline, if the Fed keeps the nominal interest rate unchanged, causing the LR curve to shift down (Figure 14.7). The shortrun equilibrium occurs at point B, with a higher level of output and lower real interest rate. In the long run (Figure 14.8), the equilibrium must occur at the intersection of the FE line and the IS curve, so the existing real interest rate is not tenable; the price level will increase, causing the LM curve to shift up and to the left, leading the LR curve to shift up, with the equilibrium again occurring at point A. Compared with the initial situation, output is unchanged, the price level is higher, and the real interest rate is unchanged.

Figure 14.7

Figure 14.8

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(d) If the Fed raises its target for the nominal interest rate to keep the real interest rate unchanged in response to the increase in the expected inflation rate, then there is no shift in the LR curve (Figure 14.9). The short-run and long-run equilibria both occur at the same point as the initial equilibrium A, with no change in output, the real interest rate, or the price level.

Figure 14.9 4.

Governments have policies against negotiating with hostage-taking terrorists, because if they negotiate with some terrorists, more terrorists will take hostages in the future. Then they cannot credibly say they will not negotiate with the next set of terrorists. If the government commits to never negotiate with terrorists, then there is no gain to the terrorists for taking hostages, so there will be less terrorism. This example is like that of monetary rules. If you want to stop hostage taking, you must have a credible commitment not to negotiate. Similarly, a central bank that wants to stop inflation must have a credible commitment not to increase money-supply growth once inflation expectations have been set. If governments have negotiated with terrorists in the past, they cannot say they will not negotiate with the next set of terrorists, or the outcome is likely to be many dead hostages. Similarly, if a central bank has used unexpected inflation to expand the economy in the past, it cannot credibly say that it will not do so in the future. Consequently, an attempt to reduce money-supply growth won’t be believed, and the output costs of disinflation will be high.

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Answers to Textbook Problems

Review Questions 1. The major sources of government outlays are government purchases, transfer payments, and net interest payments. The major sources of government revenues are personal taxes, contributions for social insurance, indirect business taxes, and corporate taxes. The federal government’s outlays and revenues differ from those of state and local governments in that: (1) most spending on nondefense goods and services is done by state and local governments; (2) the federal government spends far more on transfers than on nonmilitary goods and services; (3) the federal government makes grants in aid to state and local governments; (4) the federal government is a large payer of net interest, while state and local governments are net recipients of interest payments; and (5) most of the federal government’s revenues come from personal taxes and contributions for social insurance, while state and local governments rely more heavily on indirect business taxes (sales taxes). 2. The overall budget deficit equals the primary budget deficit plus net interest payments. Both concepts are useful. The overall deficit tells how much the government must borrow currently to pay for its outlays. The primary deficit tells whether current revenues are sufficient to pay for current programs. Net interest payments are ignored in the primary deficit because they are due to the borrowing for expenditures in the past. The concept of the current deficit is the same as that of the overall deficit, but counting government expenditures instead of outlays; that is, not counting government investment as a current expenditure. The idea is that government investment provides capital goods for the future, so should not be counted as current spending in calculating the deficit. So, the overall deficit, the primary deficit, and the current deficit all measure very different things conceptually. Which one should be used depends on the purpose for which an analyst is using the measure. 3. The government deficit is the change in the government debt. A large change in the debt-GDP ratio can be caused by: (1) a high deficit relative to GDP, and (2) a slow growth rate of nominal GDP. 4. Fiscal policy affects the macroeconomy in three ways: (1) aggregate demand effects, (2) government capital formation, and (3) incentive effects. The aggregate demand channel affects the macroeconomy because expansionary fiscal policy shifts the IS curve up and to the right, causing the AD curve to shift up and to the right as well. Both classicals and Keynesians agree that an increase in government spending shifts the IS and AD curves. There is disagreement about the effects of tax changes, however. Classicals generally believe in the Ricardian equivalence proposition, so that the IS and AD curves do not shift. Keynesians reject the Ricardian equivalence proposition and believe that the IS and AD curves do shift in response to tax changes. The formation of government capital affects the macroeconomy. The quantity and quality of public infrastructure, such as roads, schools, sewer and water systems, and hospitals, are important determinants of the growth rate of the economy. In addition, human capital formation, especially through education programs, affects the productivity of the labor force in the future. Fiscal policy also has incentive effects that influence the macroeconomy. Tax policies influence economic behavior. Capital income taxes affect people’s decisions to save and invest, while labor income taxes affect people’s labor-supply decisions.

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5. An automatic stabilizer is a provision in the budget that causes government spending to rise or taxes to fall automatically (without legislative action) when GDP falls. An example is unemployment insurance. The advantage of automatic stabilizers over legislated changes in spending and taxes is that they occur quickly, while legislation takes a long time to put in place. 6. An example would be no tax on income below $15,000, then a tax at 20% on income above $15,000. Someone with income of $30,000 would pay taxes of .20($30,000 − $15,000) = $3000. The average tax rate is 10%, while the marginal tax rate is 20%. The average tax rate most directly affects how wealthy a person feels, while the marginal tax rate affects the reward for working an extra hour. 7. Increasing the tax rate increases distortions by more than reducing the tax rate (by the same amount) reduces distortions. Varying between a high and low tax rate leads to a greater average distortion than keeping the tax rate constant at a medium level. 8. Government debt is a potential burden on future generations in two ways. First, if tax rates must be raised in the future to pay off the debt, then the economy will operate less efficiently in the future because of the increased distortions from the higher tax rates. Second, government deficits may reduce national saving, so the economy accumulates less capital and future output will be lower. Or if the government borrows from abroad, future citizens will face the burden of making interest payments to foreigners. In either case, the future standard of living will be lower. However, government deficits caused by (lump-sum) tax cuts do not reduce national saving if the Ricardian equivalence proposition is valid. This occurs because the tax cut does not cause consumption to rise, so there is no change in national saving. 9. Ricardian equivalence might not hold if people face borrowing constraints, if they are shortsighted, if they fail to leave bequests, or if taxes aren’t lump sum. 10. The inflation tax, or seignorage, arises when the government raises revenue by printing money. The inflation tax is equal to the inflation rate times the real money supply in an all-currency economy in which the money multiplier equals 1. (More generally, the inflation tax collected by the government equals the inflation rate multiplied by the monetary base.) The government collects the inflation tax by printing money to purchase goods and services. The tax is paid by anyone who holds money, because the purchasing power of his or her money is eroded by inflation. The government cannot always increase its real revenues from the inflation tax by increasing money growth and inflation, because a high enough inflation rate causes the real money supply to fall enough that seignorage revenue begins to fall when inflation increases.

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Numerical Problems 1.

The following table shows the categories of the budget: Outlays Purchases of goods and services Transfer payments Grants in aid Net interest paid Total Outlays

Central Government

Provincial Governments

Combined Governments

200

150

350

100 100 90 490

50 0 −30 170

150 100 60 660

Taxes Grants in aid Total receipts

450 0 450

100 100 200

550 100 650

Deficit Primary deficit

40 −50

−30 0

10 −50

Receipts

To calculate net interest paid in this table: The central government has debt of 1000 and the nominal interest rate is 10%, so it pays 1000 × 0.10 = 100 in interest on its debt. Of this amount, since provincial governments hold debt of 200, they get 200 × 0.10 = 20 in interest, while the private sector gets the other 80 in interest payments. The central government receives 10 in interest, so its net interest payments are 100 − 10 = 90. Provincial governments receive 20 in interest from the central government and 10 in interest from the private sector, so their net interest payments are −30. The deficit is total outlays minus total receipts. The primary deficit is the deficit minus net interest payments. 2.

In the year in which the transfer is made, both the deficit and the primary deficit increase by $1 billion. In the next year, the deficit increases by the amount of the increased interest payments, which total $1 billion times the nominal interest rate, or $1 billion × 0.10 = $100 million. The primary deficit is unchanged. In the following year, the government debt has increased by $1100 million ($1 billion due to the initial debt, plus $100 million of interest from the past year). So the deficit is higher by the amount $1100 million × 0.10 = $110 million. Again the primary deficit is unchanged.

3. Deficit = G + TR + INT − T = 1800 + (800 − 0.05Y) + 100 − (1000 + 0.1Y) = 1700 − 0.15Y. The full-employment budget deficit is the deficit that would occur if the economy were at full employment. Full-employment output is 10,000, so the full-employment deficit is 1700 − (0.15 × 10,000) = 200. (a) When Y = 12,000, the deficit is 1700 − (0.15 × 12,000) = −100. This is smaller than the fullemployment deficit of 200. (b) When Y = 10,000, the deficit is 200 (as calculated above), which is equal to the full-employment deficit, since output is at its full-employment level.

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(c) When Y = 8000, the deficit is 1700 − (0.15 × 8000) = 500. This is larger than the fullemployment deficit of 200. In general, the full-employment deficit is unaffected by the state of the economy, while the actual deficit rises relative to the full-employment deficit in recessions and falls relative to the fullemployment deficit in expansions. 4.

(a) In this situation, someone earning income Y between $8000 and $20,000 pays a total tax of T = 0.25 (Y − $8000), while someone earning between $20,000 and $30,000 pays tax of T = $3000 + 0.30 (Y − $20,000). Someone with income of $16,000 then pays tax of 0.25($16,000 − $8000) = $2000. This gives an average tax rate of $2000/$16,000 = 12.5%, while the marginal tax rate is 25%. Someone with income of $30,000 then pays tax of $3000 + 0.30($30,000 − $20,000) = $6000. This gives an average tax rate of $6000/$30,000 = 20%, while the marginal tax rate is 30%. (b) In this situation, someone earning income Y between $6000 and $20,000 pays a total tax of T = 0.20 (Y − $6000), while someone earning between $20,000 and $30,000 pays tax of T = $2800 + 0.30 (Y − $20,000). Someone with income of $16,000 then pays tax of .20($16,000 − $6000) = $2000. This gives an average tax rate of $2000/$16,000 = 12.5%, while the marginal tax rate is 20%. Someone with income of $30,000 then pays tax of $2800 + .30($30,000 − $20,000) = $5800. This gives an average tax rate of $5800/$30,000 = 19.33%, while the marginal tax rate is 30%. (c) The person making $16,000 has the same average tax rate, but a lower marginal tax rate, so there’s no income effect, just a substitution effect toward increased labor supply. The person making $30,000 faces the same marginal tax rate, so there’s no substitution effect, but has a lower average tax rate, so the income effect tends to reduce labor supply.

5. If workers value their leisure at 90 goods per day, then 90 goods per day must be the equilibrium value of the after-tax real wage. (a) The after-tax real wage equals (1 − t) × pre-tax real wage; so 90 = (1 − 0) × pre-tax real wage; so the pre-tax real-wage = 90. Setting the pre-tax real wage equal to the marginal product of labor gives 90 = 250 − N, or N = 160. Output is Y = 250N − 0.5N2 = (250 × 160) − (0.5 × 1602) = 27,200. The after-tax real wage equals (1 − t) × pre-tax real wage; so 90 = (1 − 0) × pre-tax real wage; so the pre-tax real-wage = 90. (b) The after-tax real wage equals (1 − t) × pre-tax real wage; so 90 = (1 − 0.25) × pre-tax real wage; so the pre-tax real-wage = 90/0.75 = 120. Setting the pre-tax real wage equal to the marginal product of labor gives 120 = 250 − N, or N = 130. Output is Y = (250 × 130) − (0.5 × 1302) = 24,050. The cost of the distortion in terms of lost output is 27,200 − 24,050 = 3150. (c) The after-tax real wage equals (1 − t) × pre-tax real wage; so 90 = (1 − 0.5) × pre-tax real wage; so the pre-tax real-wage = 90/0.5 = 180. Setting the pre-tax real wage equal to the marginal product of labor gives 180 = 250 − N, or N = 70. Output is Y = (250 × 70) − (0.5 × 702) = 15,050. The cost of the distortion in terms of lost output is 27,200 − 15,050 = 12,150, for changing the tax rate from 0% to 50%. Doubling the tax rate from 25% to 50% makes the distortion nearly four times as big. This suggests that taxes should be smoothed over time, since high tax rates increase the distortion more than proportionately.

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6.

(a) To find the largest nominal deficit that the government can run without raising the debt-GDP ratio, use Eq. (15.4) and set the change in the debt-GDP ratio equal to zero. The equation is: Change in debt–GDP ratio = deficit/nominal GDP − [(total debt/nominal GDP) × growth rate of nominal GDP]. Plugging in the values of the known variables and setting the change in the debtGDP ratio equal to zero gives: 0 = (deficit/nominal GDP) − [(1000/nominal GDP) × 0.10]. Multiplying both sides of the equation by nominal GDP eliminates that term from the equation, leaving 0 = deficit − 100. This has the solution: deficit = 100. (b) Since the debt-GDP ratio is initially 0.6, and nominal GDP is initially 10,000, then debt must initially be 6,000. If real GDP is initially 5,000 and remains constant, then with inflation of 5%, nominal GDP must increase 5% to 10,500. The equation is: Change in debt–GDP ratio = deficit/nominal GDP − [(total debt/nominal GDP) × growth rate of nominal GDP]. Plugging in the values of the known variables and setting the change in the debt-GDP ratio equal to zero gives: 0 = (deficit/10,000) − [(6,000/10,000) × 0.05], so deficit = 300.

7.

(a) The debt-GDP ratio is .10 at the start. After n years it is .10(1.07/1.05)n. After one year it is .102, after two years it is .104, after five years it is .110, and after ten years it is .121. If after n years the debt-GDP ratio is 10, we want to find n such that .10(1.07/1.05)n ≥ 10. Taking logarithms of both sides of this equation and solving shows that the debt-GDP ratio exceeds 10 after 245 years. So the government must run a primary surplus at some point, as the public won’t continue to buy government bonds forever. (b) Now, after n years the debt-GDP ratio is .10(1.07/1.08)n. After one year it is .099, after two years it is .098, after five years it is .095, and after ten years it is .091. The debt-GDP ratio is declining over time, so it will never exceed 10, and the government can roll over its debt forever. The crucial difference from part (a) is that here the growth rate of GDP exceeds the interest rate.

8.

L = 0.2Y − 500i = 0.2Y − 500r − 500π. With Y = 1000, L = 200 − 500r − 500π. (a) When r = 0.04, equating real money supply to money demand gives: M/P = L = 200 − (500 × 0.04) − 500π = 180 − 500π. Real seignorage revenue R = πM/P = 180π − 500π 2. The following table shows seignorage revenue (R) for inflation rates between 0 and 0.30. These values are plotted in Figure 15.3.

Figure 15.3

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Chapter 15

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π

R

π

R

π

R

0.00 0.02 0.04 0.06 0.08 0.10

0.0 3.4 6.4 9.0 11.2 13.0

0.12 0.14 0.16 0.18 0.20

14.4 15.4 16.0 16.2 16.0

0.22 0.24 0.26 0.28 0.30

15.4 14.4 13.0 11.2 9.0

357

(b) Seignorage is maximized at π = 0.18. (c) The maximum amount of seignorage revenue is 16.2. (d) When r = 0.08, equating real money supply to money demand gives: M/P = L = 200 − (500 × 0.08) − 500π = 160 − 500π. Real seignorage revenue R = πM/P = 160π − 500π 2. The following table shows seignorage revenue (R) for inflation rates between 0 and 0.30. These values are plotted in Figure 15.4.

Figure 15.4

π

R

0.00 0.02 0.04 0.06 0.08 0.10

0.0 3.0 5.6 7.8 9.6 11.0

π 0.12 0.14 0.16 0.18 0.20

R 12.0 12.6 12.8 12.6 12.0

π 0.22 0.24 0.26 0.28 0.30

R 11.0 9.6 7.8 5.6 3.0

The maximum seignorage of 12.8 is attained when π = 0.16. 9.

(a) The monetary base is growing at a 10% rate, so it increases by 0.1 × $250 = $25. The nominal value of seignorage over the year is $25. (b) Deposit holders pay the inflation tax on their non-interest-bearing deposits of $600 × 0.10 = $60. This amount is received by banks. Banks pay the inflation tax on their non-interest-bearing reserves of $50 × 0.10 = $5. Currency holders pay the inflation tax on their non-interest-bearing currency of $200 × 0.10 = $20. Overall, deposit holders pay an inflation tax of $60, banks pay an inflation tax of −$60 + $5 = −$55, and currency holders pay an inflation tax of $20. The total inflation tax is $60 − $55 + $20 = $25.

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(c) If deposit holders get the market rate of interest on their accounts, and the market rate of interest rises with inflation, then deposit holders pay no inflation tax to banks. In this case the inflation tax is borne entirely by banks ($5) and currency holders ($20).

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359

Analytical Problems 1.

The main reason for having a system of grants in aid from the federal government to state and local governments is that there are nationwide benefits to education, transportation, and welfare programs, but these programs are most efficiently administered at the state and local level. Since the benefits are nationwide, the programs should be paid for at the national level. However, since it takes local knowledge to provide the programs at the right level, state and local governments should decide the best way to provide the services. The advantage of such a system is that the national government can identify the external effects, that is, the features that make these programs have nationwide benefits, and provide appropriate funding to pay for those benefits. The disadvantage of such a system is that the administration of the programs may become politicized. The grants may go to the regions with the most powerful politicians rather than the regions with the greatest needs and external benefits.

2.

This program has very bad incentive effects. For income (y) below $10,000, a person gets a transfer equal to $10,000 − y. So for every dollar of income a person earns, he or she loses a dollar of transfers. This is like having a marginal tax rate of 100%! The program makes it unlikely that a person with low-income opportunities would want to work at all. A program with a better incentive effect would be to provide a subsidy to labor income. For example, suppose the program said that it would subsidize labor income at a 25% rate. If a person worked 2000 hours per year at a wage of $4 per hour, to get labor income of $8000, the subsidy would increase the person’s wage by 25% to $5 per hour, so he or she would earn $10,000 per year. Unlike the first program, which increased the effective marginal tax rate on labor income to 100%, this program increases the after-tax real wage rate by 25%, encouraging work effort. The advantage of this system is that it increases the effective after-tax real wage rate, so there is a substitution effect toward greater work effort. The disadvantages are that (1) there is an income effect toward lower work effort; and (2) if the program is cut off at a particular income level, then the effective marginal tax rate suddenly rises once people reach that level. This means there is a kink in the budget constraint, so people are likely to choose the point at which the kink occurs; and (3) it does not offer much help to those most in need: the unemployable and those with only very small potential income.

3.

(a) Begin with Eq. (15.4): Change in debt–GDP ratio = deficit/nominal GDP − [(total debt/nominal GDP) × growth rate of nominal GDP]. To make things easier, replace the words with symbols, where the debt-GDP ratio = B/PY, with debt = B, nominal GDP = PY, let i = nominal interest rate, and the primary deficit is Bp. Then Eq. (15.4) is ∆(B/PY) = ∆B/PY − [(B/PY) × (∆PY/PY)]. In symbols, the equation that the nominal deficit equals the nominal primary deficit plus nominal interest payments on government debt is ∆B = ∆Bp + iB. Substitute this expression into Eq. (15.4) and do some algebra: ∆(B/PY) = ∆B/PY − [(B/PY) × (∆PY/PY)] = (∆B p + iB)/PY − [(B/PY) × (∆PY/PY)] = ∆B p/PY + (B/PY × i) − [(B/PY) × (∆PY/PY)] = ∆B p/PY − [(B/PY) × (∆PY/PY − i)].

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(b) If the primary deficit is zero, then ∆Bp/PY = 0, so the equation above is: ∆(B/PY) = − [(B/PY) × (∆PY/PY − i)] = (B/PY) × (i − ∆PY/PY) Thus changes to the debt-GDP ratio depend on whether the nominal interest rate is larger or smaller than the growth rate of nominal GDP. 4.

A balanced-budget amendment might prove useful if the government otherwise had a tendency to run a perpetual budget deficit. The amendment would provide a mechanism for fiscal discipline, forcing policymakers to balance the budget. But there could be significant disadvantages, since fiscal policy wouldn’t be as flexible. In particular, automatic stabilizers kick in during a recession to increase spending and reduce taxes, creating a budget deficit but stimulating the economy; however, these effects would have to be offset if the budget were to be balanced. Also, instead of smoothing taxes over time, the government would have to raise taxes when times were bad and incomes were low and reduce taxes when times were good and incomes were high, thus creating distortions to the economy. Finally, a balanced-budget amendment would fail to recognize that capital formation would help future generations, so deficit financing that’s paid off by taxes on future generations would be appropriate.

Hyperinflation in the United States Although extreme inflations have not occurred for a very long time in the United States, they are not completely absent from U.S. history. Before declaring independence from Great Britain, the British colonies that would eventually become the United States issued their own money. In the first half of the eighteenth century, several colonies (including South Carolina and the New England colonies as a group) experienced very significant inflations. A more widespread inflation began in 1776, when the Continental Congress started issuing large amounts of currency to help pay for the war against England (the individual colonies were simultaneously printing their own moneys as quickly as possible). The amount of Continental currency put into circulation went from $6,000,000 in 1775 to $124,800,000 in 1779, and average prices increased more than one hundred-fold between the signing of the Declaration of Independence and the end of the Revolutionary War. The Continental currency’s precipitous decline in value gave rise to a common expression, “not worth a continental.” Another severe inflationary episode (on what is now American soil, although not involving the government of the United States) occurred in the Confederacy during the Civil War. 1 The Confederacy found it very difficult to collect taxes, due to lack of cooperation from the individual Confederate states, the inroads of the invading Union forces, and a lack of experienced and reliable tax collectors. (In one incident, when agents of the Confederate Treasury attempted to contact the state collector in Arkansas, A. B. Greenwood, they were informed that “Mr. Greenwood fled with his property from the state to avoid capture by the enemy and has settled in Texas.” [cited in Lerner, p. 165].) Tax evasion was widespread, and up to October 1864 less than 5% of all revenue entering the Confederate Treasury came from taxes. In a desperate attempt to pay its bills, the Confederate government printed large quantities of paper money. As the war continued, even the printing of money became a problem, as sufficient paper and engravings for new bills became ever harder to find. At one point the Confederate government began paying 6 cents on the dollar for counterfeit notes, which were in wide circulation. The counterfeit notes were then stamped “valid” and reissued as legitimate money. In April 1865, when Robert E. Lee surrendered to Ulysses Grant at Appomattox Courthouse, Virginia, prices in the Southern states were ninety-two times their level at the beginning of the war. 1

For an account, see Eugene M. Lerner, “Inflation in the Confederacy, 1861−65,” in Milton Friedman, ed., Studies in the Quantity Theory of Money, Chicago: University of Chicago Press, 1956.

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