Macroeconomics (ANSWER KEY TO CHAPTER PROBLEMS) by Olivier Blanchard

135

ANSWERS TO END-OF-CHAPTER PROBLEMS CHAPTER 1 Quick Check 1. a. b. c. d.

True. True. False. False/uncertain. The rate of growth was higher during the decade beginning in 1996 than during the previous two decades, but it is probably unrealistic to expect productivity to continue to grow at such a fast pace. e. False. There are problems with the statistics, but the consensus is that growth in China has been high. f. False. The European “unemployment miracle” refers to the relatively low European unemployment rate in the 1960s and the early 1970s. g. True. h. True.

2. a. More flexible labor market institutions may lead to lower unemployment, but there are questions about how precisely to restructure these institutions. The United Kingdom has restructured its labor market institutions to resemble more closely U.S. institutions and now has a lower unemployment rate than before the restructuring. On the other hand, Denmark and the Netherlands have relatively low unemployment rates while maintaining relatively generous social insurance programs for workers. In addition, some economists argue that tight monetary policy has at least something to do with the high unemployment rates in Europe. b. Although the Euro will remove obstacles to free trade between European countries, each country will be forced to give up its own monetary policy.

Dig Deeper 3. a. The Chinese government has encouraged foreign firms to produce in China. Since foreign firms are typically more productive than Chinese firms, the presence of foreign firms has lead to an increase in Chinese productivity. The Chinese government has also encouraged joint ventures between foreign and Chinese firms. These joint ventures allow Chinese firms to learn from more productive foreign firms. b. The recent increase in U.S. productivity growth has been a result of the development and widespread use of information technologies. c. The United States is a technological leader. Much of U.S. productivity growth is related to the development of new technologies. China is involved in technological catch-up. Much of Chinese productivity growth is related to adopting existing technologies developed abroad. d. It’s not clear to what extent China provides a model for other developing countries. High investment seems a good strategy for countries with little capital, and encouraging foreign firms to produce (and participate in joint ventures) at home seems a good strategy for countries trying to improve productivity. On the other hand, the degree to which China’s centralized political control has been important in managing the pace of the transition and in protecting property rights Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall.

136 of foreign firms remains open to question. 4. a. 10 years: (1.018)10=1.195 or 19.5 % higher 20 years: 42.9% higher 50 years: 144% higher b. 10 years: 31.8 % higher 20 years: 73.7 % higher 50 years: 297.8% higher c. Take output per worker as a measure of the standard of living. 10 years: 1.195/1.318=1.103, so the standard of living would be 10.3% higher; 20 years: 21.6 % higher 50 years: 63% higher d. No. Labor productivity growth fluctuates a lot from year to year. The last few years may represent good luck. It is too soon to tell whether there has been a change in the trend observed since 1970. 5. a.

13.2(1.034)t=2.8(1.088)t t = ln(13.2/2.8)/[ln(1.088/1.034)] t ≈ 30.5 yrs This answer can be confirmed with a spreadsheet, for students unfamiliar with the use of logarithms.

b. No. At current growth rates, Chinese output will exceed U.S. output within 31 years, but Chinese output per person (the Chinese standard of living) will still be less than U.S. output per person.

Explore Further 6. a/c. As of February 2008, there had been 5 recessions (according to the traditional definition) since 1960. Seasonally-adjusted annual percentage growth rates of GDP (in chained 2000 dollars) are given below. 1969:4 1970:1

-1.9 -0.7

1981:4 1982:1

-4.9 -6.4

1974:3 1974:4 1975:1

-3.8 -1.6 -4.7

1990:4 1991:1

-3.0 -2.0

1980:2 1980:3

-7.8 -0.7

With respect to the note on 2001, the growth rates for 2001 are given below. 2001:1 2001:2 2001:3 2001:4

-0.5% 1.2% -1.4% 1.6%

Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall.

137 7. a-b. % point increase in the unemployment rate for the 5 recessions 1969-70 0.7 1981-82 1.1 1974-75 3.1 1990-91 0.9 1980 0.6 The unemployment rate increased by 1.5 percentage points between January 2001 and January 2002.

CHAPTER 2 Quick Check 1.

a. b. c. d. e. f. g.

2.

3.

4.

True. True/Uncertain. Real GDP increased by a factor of 25; nominal GDP increased by a factor of 21. Real GDP per person increased by a factor of 4. False. True. False. The level of the CPI means nothing. The rate of change of the CPI is one measure of inflation. Uncertain. Which index is better depends on what we are trying to measure—inflation faced by consumers or by the economy as a whole. False. The underground economy is large, but by far the majority of the measured unemployed in Spain are not employed in the underground economy.

a.

No change. This transaction is a purchase of intermediate goods.

b.

+$100: personal consumption expenditures

c.

+$200 million: gross private domestic fixed investment

d.

+$200 million: net exports

e.

No change. The jet was already counted when it was produced, i.e., presumably when Delta (or some other airline) bought it new as an investment.

a.

The value of final goods =$1,000,000, the value of the silver necklaces.

b.

1st Stage: $300,000. 2nd Stage: $1,000,00-$300,000=$700,000. GDP: $300,000+$700,000=$1,000,000.

c.

Wages: $200,000 + $250,000=$450,000. Profit: ($300,000-$200,000)+($1,000,000-$250,000-300,000) =$100,000+$450,000=$550,000. GDP: $450,000+$550,000=$1,000,000.

a.

2006 GDP: 10($2,000)+4($1,000)+1000($1)=$25,000 2007 GDP: 12($3,000)+6($500)+1000($1)=$40,000 Nominal GDP has increased by 60%.


138

5.

6.

b.

2006 real (2006) GDP: $25,000 2007 real (2006) GDP: 12($2,000)+6($1,000)+1000($1)=$31,000 Real (2006) GDP has increased by 24%.

c.

2006 real (2007) GDP: 10($3,000)+4($500)+1,000($1)=$33,000 2007 real (2007) GDP: $40,000. Real (2007) GDP has increased by 21.2%.

d.

The answers measure real GDP growth in different units. Neither answer is incorrect, just as measurement in inches is not more or less correct than measurement in centimeters.

a.

2006 base year: Deflator(2006)=1; Deflator(2007)=$40,000/$31,000=1.29 Inflation=29%

b.

2007 base year: Deflator(2006)=$25,000/$33,000=0.76; Deflator(2007)=1 Inflation=(1-0.76)/0.76=.32=32%

c.

Analogous to 4d.

a.

2006 real GDP = 10($2,500) + 4($750) + 1000($1) = $29,000 2007 real GDP = 12($2,500) + 6($750) + 1000($1) = $35,500

b.

(35,500-29,000)/29,000 = .224 = 22.4%

c.

Deflator in 2006=$25,000/$29,000=.86 Deflator in 2007=$40,000/$35,500=1.13 Inflation = (1.13 -.86)/.86 = .31 = 31%.

d.

Yes, see appendix for further discussion.

Dig Deeper 7.

a.

The quality of a routine checkup improves over time. Checkups now may include EKGs, for example. Medical services are particularly affected by this problem since there are continual improvements in medical technology.

b.

The new method represents a 10% quality increase.

c.

There is a 5% true price increase. The other 10% represents a quality increase. The quality-adjusted price of checkups using the new method is only 5% higher than checkups using the old method last year.

d.

You need to know the relative value of pregnancy checkups with and without ultrasounds in the year the new method is introduced. Still, since everyone chooses the new method, we can say that the quality-adjusted price of checkups has risen by less than 15%. Some of the observed 15% increase represents an increase in quality.


139 8.

a.

Measured GDP increases by $10+$12=$22. (Strictly, this involves mixing the final goods and income approaches to GDP. Assume here that the $12 per hour of work creates a final good worth $12.)

b.

No. The true value of your decision to work should be less than $22. If you choose to work, the economy produces the value of your work plus a takeout meal. If you choose not to work, presumably the economy produces a home-cooked meal. The extra output arising from your choice to work is the value of your work plus any difference in value between takeout and home-cooked meals. In fact, however, the value of home-cooked meals is not counted in GDP. (Of course, there are other details. For example, the value of groceries used to produce home-cooked meals would be counted in GDP. Putting such details aside, however, the basic point is clear.)

Explore Further 9.

a.

Quarters 2000:III, 2001:I, and 2001:III had negative growth.

b.

The unemployment rate increased after 2000, peaked in 2003, and then began to fall. The participation rate fell steadily over the period—from 67.1% in 2000 to 66% in 2004. Presumably, workers unable to find jobs became discouraged and left the labor force.

c.

Employment growth slowed after 2000. Employment actually fell in 2001. The employment-to-population ratio fell between 2000 and 2004.

d.

It several years after the recession for the labor market to recover.


a. b. c. d. e. f. g.

True. False. Government spending excluding transfers was 19% of GDP. False. The propensity to consume must be less than one for our model to make sense. True. False. False. The increase in output is one times the multiplier. False.

2.

a.

Y=160+0.6(Y-100)+150+150 Y=1000

b.

YD=Y-T=1000-100=900

c.

C=160+0.6(900)=700

a.

Equilibrium output is 1000. Total demand=C+I+G=700+150+150=1000. Total demand equals production. We used this equilibrium condition to solve for output.

b.

Output falls by (40 times the multiplier) = 40/(1-.6)=100. So, equilibrium output is now 900. Total demand=C+I+G=160+0.6(800)+150+110=900. Again, total demand equals production.

3.


140 c.

Private saving=Y-C-T=900-160-0.6(800)-100=160. Public saving =T-G=-10. National saving (or in short, saving) equals private plus public saving, or 150. National saving equals investment. This statement is mathematically equivalent to the equilibrium condition, total demand equals production. In other words, there is an alternative (and equivalent) equilibrium condition: national saving equals investment.

Dig Deeper 4.

5.

6.

7.

a.

Y increases by 1/(1-c1)

b.

Y decreases by c1/(1-c1)

c.

The answers differ because spending affects demand directly, but taxes affect demand indirectly through consumption, and the propensity to consume is less than one.

d.

The change in Y equals 1/(1-c1) - c1/(1- c1)=1. Balanced budget changes in G and T are not macroeconomically neutral.

e.

The propensity to consume has no effect because the balanced budget tax increase aborts the multiplier process. Y and T both increase by one unit, so disposable income, and hence consumption, do not change.

a.

Y=c0+c1YD+I+G implies Y=[1/(1-c1+c1t1)][c0-c1t0+I+G]

b.

The multiplier=1/(1-c1+c1t1)<1/(1-c1), so the economy responds less to changes in autonomous spending when t1 is positive. After a positive change in autonomous spending, the increase in total taxes (because of the increase in income) tends to lessen the increase in output. After a negative change in autonomous spending, the fall in total taxes tends to lessen the decrease in output.

c.

Because of the automatic effect of taxes on the economy, the economy responds less to changes in autonomous spending than in the case where taxes are independent of income. Since output tends to vary less (to be more stable), fiscal policy is called an automatic stabilizer.

a.

Y=[1/(1-c1+c1t1)][c0-c1t0+I+G]

b.

T = t0 + t1[1/(1-c1+c1t1)][c0-c1t0+I+G]

c.

Both Y and T decrease.

d.

If G is cut, Y decreases even more. A balanced budget requirement amplifies the effect of the decline in c0. Therefore, such a requirement is destabilizing.

a.

In the diagram representing goods market equilibrium, the ZZ line shifts up. Output increases.

b.

There is no effect on the diagram or on output.

c.

The ZZ line shifts up and output increases. Effectively, the income transfer increases the


141 propensity to consume for the economy as a whole.

8.

d.

The propensity to consume is likely to be higher for low-income taxpayers. Therefore, tax cuts will be more effective at stimulating output if they are directed toward lowincome taxpayers.

a.

Y=C+I+G Y=[1/(1-c1-b1)]*[c0-c1T+b0+G]

b.

Including the b1Y term in the investment equation increases the multiplier. Increases in autonomous spending now create a multiplier effect through two channels: consumption and investment. For the multiplier to be positive, the condition c1+b1<1 is required.

c.

Output increases by b0 times the multiplier. Investment increases by the change in b0 plus b1 times the change in output. The change in business confidence leads to an increase in output, which induces an additional increase in investment. Since investment increases, and saving equals investment, saving must also increase. The increase in output leads to an increase in saving.

Explore Further 9.

10.

a.

Output will fall.

b.

Since output falls, investment will also fall. Public saving will not change. Private saving will fall, since investment falls, and investment equals saving. Since output and consumer confidence fall, consumption will also fall.

c.

Output, investment, and private saving would have risen.

d.

Clearly this logic is faulty. When output is low, what is needed is an attempt by consumers to spend more. This will lead to an increase in output, and therefore—somewhat paradoxically—to an increase in private saving. Note, however, that with a linear consumption function, the private saving rate (private saving divided by output) will fall when c0 rises.

Answers will vary depending on when students visit the website.


a. b. c.

d. e. f. g. h.

False. False. False. Money demand describes the portfolio decision to hold wealth in the form of money rather than in the form of bonds. The interest rate on bonds is relevant to this decision. True. False. False. True. True.


142 2.

3.

4.

a.

i=0.05: money demand = $18,000 i=0.10: money demand = $15,000

b.

Money demand decreases when the interest rate increases because bonds, which pay interest, become more attractive.

c.

The demand for money falls by 50%.

d.

The demand for money falls by 50%.

e.

A 1% increase (decrease) in income leads to a 1% increase (decrease) in money demand. This effect is independent of the interest rate.

a.

i=100/$PB –1; i=33%; 18%; 5% when $PB =$75; $85; $95.

b.

When the bond price rises, the interest rate falls.

c.

$PB =100/(1.08) ≈ $93

a.

$20=MD=$100(.25-i) i=5%

b.

M=$100(.25-.15) M=$10

Dig Deeper 5.

a.

BD = 50,000 - 60,000 (.35-i) If the interest rate increases by 10 percentage points, bond demand increases by $6,000.

b.

An increase in wealth increases bond demand, but has no effect on money demand, which depends on income (a proxy for transactions demand).

c.

An increase in income increases money demand, but decreases bond demand, since we implicitly hold wealth constant.

d.

First of all, the use of “money” in this statement is colloquial. “Income” should be substituted for “money.” Second, when people earn more income, their wealth does not change right away. Thus, they increase their demand for money and decrease their demand for bonds.

6.

Essentially, the reduction in the price of the bond makes it more attractive. A bond promises fixed nominal payments. The opportunity to receive these fixed payments at a lower price makes a bond more attractive.

7.

a.

$16 is withdrawn on each trip to the bank. Money holdings are $16 on day one; $12 on day two; $8 on day three; and $4 on day four.

b.

Average money holdings are ($16+$12+$8+$4)/4=$10.


143 c.

$8 is withdrawn on each trip to the bank. Money holdings are $8, $4, $8, and $4.

8.

9.

d.

Average money holdings are $6.

e.

$16 is withdrawn on each trip to the bank. Money holdings are $0, $0, $0, and $16.

f.

Average money holdings are $4.

g.

Based on these answers, ATMs and credit cards have reduced money demand.

a.

All money is in checking accounts, so demand for central bank money equals demand for reserves. Therefore, demand for central bank money=0.1($Y)(.8-4i).

b.

$100B = 0.1($5,000B)(.8-4i) i=15%

c.

Since the public holds no currency, money multiplier = 1/reserve ratio = 1/.1=10. M=(10)$100B=$1,000B M= Md at the interest derived in part (b).

d.

If H increases to $300B the interest rate falls to 5%.

e.

The interest rate falls to 5%, since when H equals $300B, M=(10)$300B=$3,000B.

The money multiplier is 1/[c+(1-c)], where c is the ratio of currency to deposits and  is the ratio of reserves to deposits. When c increases, as in the Great Depression, the money multiplier falls.

Explore Further 10.

Answers will vary depending on when students visit the FOMC website.


a. b. c. d. e. f.

g. 2.

a.

True. True. False. False. The balanced budget multiplier is positive (it equals one), so the IS curve shifts right. False. Uncertain. An increase in government spending leads to an increase in output (which tends to increase investment), but also to an increase in the interest rate (which tends to reduce investment). True. Y=[1/(1-c1)][c0-c1T+I+G] The multiplier is 1/(1-c1).


144 b.

Y=[1/(1-c1-b1)][c0-c1T+b0-b2i+G] The multiplier is 1/(1-c1-b1). Since the multiplier is larger than the multiplier in part (a), the effect of a change in autonomous spending is bigger than in part (a). An increase in autonomous spending now leads to an increase in investment as well as consumption.

c.

Substituting for the interest rate in the answer to part (b), Y=[1/(1-c1-b1+b2d1/d2)][c0-c1T+b0+(b2/d2)(M/P)+G]. The multiplier is 1/(1-c1-b1+b2d1/d2).

d.

The multiplier is greater (less) than the multiplier in part (a) if (b1-b2d1/d2) is greater (less) than zero. The multiplier as measured in part (c) measures the marginal effect of an increase in autonomous spending on equilibrium output. As such, the multiplier is the sum of two effects: a direct effect of output on demand and an indirect effect of output on demand via the interest rate. The direct effect is equivalent to the horizontal shift of the IS curve. The indirect effect depends on the slope of the LM curve (since the equilibrium moves along the LM curve in response to a shift of the IS curve) and the effect of the interest rate on investment demand. The direct effect is captured by the sum c1+b1, which measures the marginal effect of an increase in output on the sum of consumption and investment demand. As this sum increases, the multiplier gets larger. The indirect effect is captured by the expression b2d1/d2 and tends to reduce the size of the multiplier. The ratio d1/d2 is the slope of the LM curve, and the parameter b2 measures the marginal effect of an increase in the interest rate on investment. Note that the slope of the LM curve becomes larger as money demand becomes more sensitive to income (i.e., as d1 increases) and becomes smaller as money demand becomes more sensitive to the interest rate (i.e., as d2 increases).

3.

a.

The IS curve shifts left. Output and the interest rate fall. The effect on investment is ambiguous because the output and interest rate effects work in opposite directions: the fall in output tends to reduce investment, but the fall in the interest rate tends to increase it.

b.

From the answer to 2(c), Y=[1/(1-c1-b1+b2d1/d2)][c0-c1T+b0+(b2/d2)(M/P)+G].

c

From the LM relation, i=Y(d1/d2)–(M/P)/d2. To obtain the equilibrium interest rate, substitute for equilibrium Y from part (b).

d.

I= b0+b1Y-b2i=b0+(b1-b2d1/d2)Y+(b2/d2)(M/P) To obtain equilibrium investment, substitute for equilibrium Y from part (b).

e.

From part (b), holding M/P constant, equilibrium Y decreases by [1/(1-c1-b1+b2d1/d2)] when G decreases by one unit. From part (d), holding M/P constant, I decreases by (b1- b2d1/d2)/(1-c1-b1+b2d1/d2) when G decreases by one unit. So, if G decreases by one unit, investment will increase when b1
f.

A fall in G leads to a fall in output (which tends to reduce investment) and to a fall in the interest rate (which tends to increase investment). Therefore, for investment to increase, the output effect (b1) must be smaller than the interest rate effect (b2d1/d2).


145 Note that the interest rate is the product of two factors: (i) d1/d2, the slope of the LM curve, which gives the effect of a one-unit change in equilibrium output on the interest rate, and (ii) b2, which gives the effect of a one-unit change in the equilibrium interest rate on investment. 4.

a.

Y=C+I+G=200+.25(Y-200)+150+.25Y-1000i+250 Y=1100-2000i

b.

M/P=1600=2Y-8000i i=Y/4000-1/5

c.

Substituting from part (b) into part (a) gives Y=1000.

d.

Substituting from part (c) into part (b) gives i=5%.

e.

C=400; I=350; G=250; C+I+G=1000

f.

Y=1040; i=3%; C=410; I=380. A monetary expansion reduces the interest rate and increases output. Consumption increases because output increases. Investment increases because output increases and the interest rate decreases.

g.

Y=1200; i=10%; C=450; I=350. A fiscal expansion increases output and the interest rate. Consumption increases because output increases. Investment is affected in two ways: the increase in output tends to increase investment, and the increase in the interest rate tends to reduce investment. In this example, these two effects exactly offset one another, and investment does not change.

Dig Deeper 5.

Firms deciding how to use their own funds will compare the return on bonds to the return on investment. When the interest rate on bonds increases, bonds become more attractive, and firms are more likely to use their funds to purchase bonds, rather than to finance investment projects.

6.

a.

If the interest rate were negative, people would hold only money, and not bonds. Money would be a better store of value than bonds.

b.

See hint.

c.

See hint.

d.

The increase the money supply has little effect on the interest rate. If the interest rate is actually zero, than the increase in the money supply literally has no effect.

e.

No. If there is no effect on the interest rate, which affects investment, monetary policy cannot affect output.

a.

The reduction in T shifts the IS curve to the right. The increase in M shifts the LM curve down. Output increases.

b.

The Clinton-Greenspan policy mix was (loosely) contractionary fiscal policy (IS left) and expansionary monetary policy (LM down).

7.


146

8.

9.

c.

In 2001, there was a recession, which was triggered by a fall in investment spending following the decline in the stock market. The events of September 11, which came after the recession had begun, had only a limited effect. In fact, the economy had positive growth in the fourth quarter of 2001. The expansionary monetary and fiscal policies tended to weaken the recession, but the policies came too late to avoid a recession.

a.

Increase G (or reduce T), which shifts the IS curve to the right, and increase M, which shifts the LM curve down.

b.

Reduce G (or increase T), which shifts the IS curve to the left, and increase M, which shifts the LM curve down. The interest rate falls. Investment increases, since the interest rate falls while output remains constant. The IS curve shifts left. Output and the interest rate fall.

a. b.

Consumption falls. The change in investment is ambiguous: the fall in output tends to reduce investment, but the fall in the interest rate tends to increase investment. The change in private saving equals the change in investment. So, private saving could rise or fall in response to a fall in consumer confidence.

Explore Further 10.

a.

The fall in G and the increase in T shift the IS curve to the left. The increase in M shifts the LM curve down. The interest rate falls, and investment increases.

b.

Receipts rose, outlays fell, and the budget deficit fell.

c.

On September 4, 1992, the FOMC reduced the federal funds rate by 25 basis points. Subsequent changes in federal funds rate over the period 1993-2000 are given below. Changes in the Federal Funds Rate September 4, 1992 3 February 4, 1994 3.25 March 22, 1994 3.5 April 18, 1994 3.75 May 17, 1994 4.25 August 16, 1994 4.75 November 15, 1994 5.5 February 1, 1995 6 July 6, 1995 5.75 December 19, 1995 5.5 January 31, 1996 5.25

11.

March 25, 1997 September 29, 1998 October 15, 1998 November 17, 1998 June 30, 1999 August 24, 1999 November 16, 1999 February 2, 2000 March 21, 2000 May 16, 2000

5.5 5.25 5 4.75 5 5.25 5.5 5.75 6 6.5

d.

Investment was 12.1% of GDP in 1992 and increased every year over the period to reach 17.7% of GDP in 2000.

e.

Over the period 1993-2000, the average annual growth rate of GDP per person was 2.49%. Over the period first four years of the period, the average annual growth rate was 1.98%; over the second four years, the average annual growth rate was 3%.

a.

Growth was negative in 2000:III, 2001:I, and 2001:III.


147 b.

Investment had a bigger percentage change, and unlike consumption, growth in investment was negative for every quarter in 2000 and 2001, except 2000:II. Overall investment was generally more variable than nonresidential fixed investment in 2000 and 2001. Moreover, nonresidential fixed investment had positive growth during 2000, but negative growth in 2001.

c.

Investment had a substantially larger decline in its contribution to growth in 2000 and 2001. The proximate cause of the recession of 2001 was a fall in investment demand.

d.

Investment fell in the last two quarters of 2001, but began growing again in the first quarter of 2001. Consumption growth was slow for the first three quarters of 2001, but grew rapidly in the fourth quarter. As mentioned in the text, the Fed reduced the federal funds rate several times during the fourth quarter of 2001. Moreover, automobile manufacturers offered large discounts. These actions may have helped to generate strong consumer spending. In any event, it is clear that the events of September 11 did not cause the recession of 2001. The recession had started well before these events.


2.

3.

a. b. c. d. e. f. g. h.

False. The participation rate has increased over time. False. False. True. False. Uncertain/False. The degree of bargaining power depends on the nature of the job and the employee’s skills. True. False.

a.

(Monthly hires + monthly separations)/monthly employment =(4.4+4.6)/122=7%

b.

1.4/6.2=23%

c.

(1.4+1.4)/6.2=45%. Duration is 1/.37 or 2.2 months.

d.

(3+2.8+1.4+1.4)/57.3=15%.

e.

new workers: 0.4/(3+1.4)=9%.

a.

W/P=1/(1+)=1/1.05=.952

b.

Wage setting: u=1-W/P=4.8%

c.

W/P=1/1.1=.91; u=1-.91=9%. The increase in the markup lowers the real wage. Algebraically, from the wage-setting equation, the unemployment rate must rise for the real wage to fall. So the natural rate increases. Intuitively, an increase in the markup implies more market power for firms, and therefore less production, since firms will use


148 their market power to increase the price of goods by reducing supply. Less production implies less demand for labor, so the natural rate rises.

Dig Deeper 4.

5.

6.

7.

a.

Answers will vary.

b-c.

Most likely, the difference between your actual wage and your reservation wage will be higher for the job you will have ten years later.

d.

The later job is more likely to require training, which means you will be costly to replace, and will probably be a much harder job to monitor, which means you may need an incentive to work hard. Efficiency wage theory suggests that your employer will be willing to pay a lot more than your reservation wage for the later job, to make the job valuable to you, so you will stay at it and work hard.

a.

The computer network administrator has more bargaining power. She is much harder to replace.

b.

The rate of unemployment is the most important indicator of labor market conditions. When the rate of unemployment increases, it becomes easier for firms to find replacements, and worker bargaining power falls.

c.

In our model, the real wage is always given by the price-setting relation: W/P=1/(1+). Since the price-setting relation depends on the actual price level and not the expected one, this relation holds in the short run and the medium run of our model

a.

When the unemployment rate is very low, it is very difficult for firms to find workers to hire and very easy for workers to find jobs. As a result, the bargaining power of workers is very high when the unemployment rate is very low. Therefore, the wage gets very high as the unemployment rate gets very low.

b.

Presumably, the real wage would grow without bound as the unemployment rate approached zero. Since a worker could always find a job, there would be nothing to constrain aggressive wage bargaining. At any positive rate of unemployment, however, there is some constraint on worker bargaining power.

a.

EatIn Population Labor Force Employment Unemployment Unemployment Rate Participation Rate

100 75 50 25 33% 75%

Eat out Population Labor Force Employment Unemployment Unemployment Rate Participation Rate

100 100 75 25 25% 100%

b.

The measured labor force and participation rate rise. Measured employment rises. Measured unemployment does not change, but the measured unemployment rate falls. Measured GDP will rises.

c.

To adjust the labor market statistics, you would have to estimate the number of workers informally employed at home and add them to the measured employed. To the extent that workers employed informally at home were measured as unemployed, you


149 would have to reduce measured unemployment accordingly. To the extent that workers employed informally at home were considered out of the labor force, counting these workers as employed would increase the size of the labor force. To adjust the GDP statistics, you would have to estimate the value-added of final goods produced at home. You could make comparisons to similar goods produced outside the home, or make comparisons to workers involved in similar industries outside the home, estimate the relevant wage and hours worked, and calculate value-added as the cost of labor, as is done for government services. In either case, you need to calculate valueadded, since intermediate goods—groceries, cleaning supplies, child care supplies, and so on—involved in the production of at-home goods are already counted in GDP as final goods in the formal sector.

Explore Further 8.

a.

55%; (0.55)2= 30%; (0.55)6 = 2%

b.

55%

c.

second month: (0.55)2=30%; sixth month: (0.55)6 = 2%

d.

Average proportion 27 weeks or more over 1990-1999= 16.1% 1996: 17% 2000: 11% 1997: 16% 2001: 12% 1998: 14% 2002: 18% 1999: 12% 2003: 22% The long-term unemployed exit unemployment less frequently than the average unemployed worker.

9.

a-b.

Answers will depend on when the page is accessed.

c.

The decline in unemployment does not equal the increase in employment, because the labor force is not constant.


a. b. c. d. e. f. g.

True. True. In the AS relation, if P=Pe, Y=Yn. Note that Pe must be known to graph the AS curve. False. The AD curve slopes down because an increase in P leads to a fall in M/P, so the nominal interest rate increases, and I and Y fall. False. There are changes in autonomous expenditure and supply shocks, both of which cause output to deviate from the natural level in the short run. True. False. Fiscal policy affects the interest rate in the medium run and therefore affects investment. False. The natural level of output changes in response to a permanent supply shock (other than a change in Pe). The price level changes in the medium run in response to either a demand or a supply shock.


150 2.

3.

a.

IS shifts right, and LM shifts up. AD shifts right, and AS shifts up.

b.

Y returns to its unchanged natural level. The interest rate and the price level increase.

a.

SR: short run MR: medium run

SR MR

WS: wage-setting curve PS: price-setting curve

WS up

PS AS AD no up no change change same no up no as SR change further WS PS AS AD LM change IS

IS no change no change

LM up up further

b. i SR MR

4.

YP falls falls further

i rises rises further

P rises rises further

a.

Money is neutral in the sense that the nominal money supply has no effect on output or the interest rate in the medium run. Output returns to its natural level. The interest rate is determined by the position of the IS curve and the natural level of output. Despite the neutrality of money in the medium run, an increase in the money supply will increase output and reduce the interest rate in the short run. Therefore, expansionary monetary policy can be used to speed up the economy's return to the natural level of output when output is low.

b.

In the medium run, fiscal policy affects the interest rate and investment, so fiscal policy is not considered neutral.

c.

False. Labor market policies, such as the degree of unemployment insurance, can affect the natural level of output.

Dig Deeper 5.

a.

SR: short run MR: medium run SR MR

IS left

LM down

AD left

AS no change same down same down WS as SRPS further AS ADas SRLM IS


151 b-c. SR MR

SR MR

Y falls back to original Yn

i falls falls further

P falls falls further

C falls back to original level

I ambiguous rises (above original level)

Private S ambiguous rises (above original level)

The short-run change in investment is ambiguous, because the interest rate falls, which tends to increase investment, but output also falls, which tends to reduce investment. In the medium run, investment must rise (as compared to its short-run and original levels), because the interest rate falls but output returns to its original level. Since the budget deficit does not change in this problem, the change in private saving equals the change in investment. It is possible that private saving will fall in the short run, but private saving must rise (above its short-run and original levels) in the medium run. 6.

7.

a.

Open answer. Firms may be so pessimistic about sales that they do not want to borrow at any interest rate.

b.

The IS curve is vertical; the interest rate does not affect equilibrium output.

c.

The LM curve is unaffected.

d.

The AD curve is vertical; the price level does not affect equilibrium output.

e.

The increase in z reduces the natural level of output and shifts the AS curve up. Since the AD curve is vertical, equilibrium output does not change, but the price level increases. Note that output is above its natural level.

f.

Since Y>Yn, P>Pe. Therefore, Pe rises and theAS curve shifts up. In fact, the AS curve shifts up forever, and the price level increases forever. Output does not change; it remains above its natural level forever.

a.

The LM has a flat segment at i=0 and then slopes up.

b.

The IS slopes down as before. There is no flat segment at i=0. Arguably, the IS curve is undefined for nominal interest rates below zero.


152

8.

9.

c.

As P falls, M/P rises, and the nominal interest rate falls. Eventually, when P falls far enough, the nominal interest reaches zero. The AD curve slopes down until P reaches the level consistent with i=0. For levels of P below this threshold, the AD curve is vertical.

d.

There is no effect on output in the short run or the medium run. Since the money stock does not affect the interest rate, it does not affect output.

a.

The AD curve shifts left in the short run. Output and the price level fall in the short run. In the medium run, the expected price level falls, and AS shifts right, returning the economy to the original natural level of output, but at a lower price level.

b.

The unemployment rate rises in the short run, but returns to its original level (the natural rate, which is unchanged) in the medium run.

c.

The Fed should increase the money supply, which shifts the AD curve right. A monetary expansion of the proper size exactly offsets the effect of the decline in business confidence on the AD curve. The net effect is that the AD curve does not move in the short run or medium run, and neither does the AS curve.

d.

Under the policy option in part (c), output and the price level are higher in the short run. In the medium run, output is the same in parts (a) and (c), but the price level is higher in part (c).

e.

The unemployment rate is lower in the short run in part (c). In the medium run, the unemployment rate is the same in parts (b) and (c).

a.

The AS curve shifts up in the short run and shifts up further in the medium run. Output falls in the short run and falls further in the medium run. The price level rises in the short run and rises further in the medium run.

b.

The unemployment rate rises in the short run and rises further in the medium run.

c.

The Fed could increase the money supply in the short run and shift the AD curve to the right. The AS curve would shift up over time.

d.

Output and the price level are higher in the short run in part (c). Output is the same in the medium run in parts (a) and (c), but the price level is higher in part (c).

e.

The unemployment rate in the short run is lower in part (c), but the same in the medium run in parts (a) and (c).

10.

The Fed’s job is not so easy. It has to distinguish changes in the actual rate of unemployment from changes in the natural rate of unemployment. The Fed can use monetary policy to keep the unemployment rate near the natural rate, but it cannot affect the natural rate.

11.

a.

The unemployment rate rises in the short run and rises further in the medium run. The real wage falls immediately to its new medium-run level.

b.

The unemployment rate falls in the short run but returns to the original natural rate in the medium run. The real wage is unaffected. However, after tax income rises.


153 c.

In our model, the real wage depends only upon the markup. A fall in the markup increases the real wage. Policy measures that improve product market competition—for example, more vigorous anti-trust enforcement—could increase the real wage.

d.

The fall in income taxes tended to increase the after-tax real wage. The increase in oil prices tended to reduce the after-tax real wage. Intuitively, the immediate effect of an oil price increase is to reduce the real wage by increasing gas prices. Thus, the increase in gas prices tends to absorb the extra after-tax income provided by the tax cut.

Explore Further 12.

a.

P=(1+)(Pe)a(F(u,z))a(PE)1-a

b.

P=(1+)(Pe)a(F(u,z))a(Px)1-a P= Pe(1+)1/aF(u,z)x(1-a)/a

13.

c.

The AS curve slopes up in Y-P space.

d.

If P= Pe, then 1=(1+)1/aF(u,z)x(1-a)/a. An increase in x implies that F must fall to maintain the equality. F falls when u rises. So, an increase in the relative price of energy resources leads to an increase in the natural rate of unemployment.

e.

The AS curve shifts up in the short run and shifts up further in the medium run. The unemployment rate and the price level rise in the short run and rise further in the medium run. Output falls in the short run and falls further in the medium run.

f.

An increase in the relative price of energy resources causes the AS curve to shift up in the short run. If Pe remains constant, the AS curve will not shift further after the initial, shortrun shift. In order for Pe to remain constant, wage setters must be expecting the Fed to reduce the money supply, thereby shifting the AD curve left. This monetary policy moves output to its new, lower natural level right away, and maintains the original price level, so there will be no price adjustment in the transition to the new medium-run equilibrium.

a.

1959:IV – 1969:IV 1969:IV – 1979:IV 1979:IV – 1989:IV 1989:IV – 1999:IV 1999:IV – 2007:IV

b.

The 70s, 80s, and 90s look remarkably similar. The 60s had by far the highest growth. Clearly, the first decade of the 21st century will have the lowest growth.

52.9% 38.2% 35.1% 37.6% 20.7%

Note, although the problem did not ask for the growth rates of GDP per person, the ranking of the decades would be similar. The growth rates of GDP per person are given below.


154 1959:IV – 1969:IV 1969:IV – 1979:IV 1979:IV – 1989:IV 1989:IV – 1999:IV 1999:IV – 2007:IV

34.4% 24.0% 23.0% 21.8% 11.7%


a. b. c. d. e. f.

True. False. False. True. False. True.

2.

a.

No. In the 1970s, we experienced high inflation and high unemployment. The expectations-augmented Phillips curve is a relationship between inflation and unemployment conditional on the natural rate and inflation expectations. Given inflation expectations, when the natural rate of unemployment increases (i.e., when there is an increase in z or ), there is also an increase in both the actual unemployment rate and the inflation rate. In addition, increases in inflation expectations imply higher inflation for any level of unemployment. In the 1970s, both the natural rate and expected inflation increased, so both unemployment and inflation were relatively high. Note that increases in inflation expectations also tend to increase the unemployment rate in the short run from the supply side—think of an increase in the expected price level, given last period’s price, in the AD-AS framework. However, increases in inflation expectations may tend to increase short run output from the demand side, because of the real interest rate effect. The real interest rate is introduced in Chapter 14.

3.

b.

No. The expectations-augmented Phillips curve implies that maintaining a rate of unemployment below the natural rate requires not merely high inflation but increasing inflation. This is because inflation expectations continue to adjust to actual inflation.

a.

un=0.1/2 =5%

b.

πt =0.1-2(0.03) = 4% every year beginning with year t.

c.

πet= 0 and πt=4% forever. Inflation expectations will be forever wrong. This is unlikely.

d.

 might increase because inflation expectations adapt to persistently positive inflation. The increase in  has no effect on un.

e.

π5= π 4+0.1-2(0.03)=4%+4%=8% For t>5, π t= 8% + (t - 5)(4%). So, π 10=28%; π 15=48%. Inflation increases by four percentage points every year.


155 4.

f. a.

Inflation expectations will again be forever wrong. This is unlikely. A higher cost of production means a higher markup of the price level over wages. In the simple model of the text, the markup reflects all nonwage components of the price of a good.

b.

un=(0.08+0.1)/2 The natural rate of unemployment increases from 5% to 6% as  increases from 20% to 40%.

Dig Deeper 5.

a.

un=01./2=.05 π t = π t-1 - 2(ut - .05) = π t-1 + 2%=2% π t = 2%; π t+1 = 4%; π t+2 = 6%; π t+3 = 8%.

6.

7.

b.

π t = 0.5 π t + 0.5 π t-1 - 2(ut - .05) or, π t = π t-1 - 4(ut - .05)

c.

π t = 4%; π t+1 = 8%; π t+2 = 12%; π t+3 = 16%

d.

As indexation increases, inflation becomes more sensitive to the difference between the unemployment rate and the natural rate.

a.

Yes. The average rate of unemployment was lower in the 1990s. Indeed, even though the unemployment rate was at a historical low, inflation rose very little.

b.

The natural rate of unemployment probably decreased.

a.

=1: uu=6%; =2: uu=3% As wages become more flexible, more of the effect of supply shocks (changes in  and z) is transmitted to changes in wages and less to changes in the natural rate of unemployment.

b.

=1: uu=9%; =2: uu=4.5% In an environment with more wage flexibility (higher ), the natural rate of unemployment rises less in response to an increase in the price of oil.

Explore Further As of 2006, the equation that seems to fit well is πt – πt-1 = 4.4% –0.73ut, which implies a natural rate of approximately 6%.

8.

a-d.

9.

The relationships imply a lower natural rate in the more recent period.


a. b. c.

False. The unemployment rate rises when output growth is less than the normal rate and rises when output growth is greater than the normal rate. True. True.


156 d.

e. f. g. h. i. 2.

3.

False. The Phillips curve relates the change in inflation to the difference between the unemployment rate and the natural rate. Okun’s law relates the change in the unemployment rate to the difference between output growth and the normal rate. The aggregate demand relation equates inflation to real money growth. It is true that the aggregate demand relation implies that inflation equals adjusted money growth, which is the difference between money growth and output, but this is only a relation between inflation and output growth conditional on money growth. False. In the medium run, inflation equals adjusted money growth, which is the difference between nominal money growth and output growth. True. Uncertain. In principle, the statement is true, but nominal rigidities may make even fully credible policy costly. True. True.

a.

The unemployment rate will increase by 1% per year when g=0.5%. Absent output growth, productivity growth tends to increase the unemployment rate, since fewer workers are required to produce a given quantity of goods. Absent output growth, labor force growth also tends to increase the unemployment rate, since more workers are competing for the same number of jobs. Therefore, unemployment will increase unless the growth rate exceeds the sum of productivity growth and labor force growth.

b.

For the unemployment rate to decrease by 0.5% per year for the next four years, output must grow at 4.25% per year for each of the next four years.

c.

Okun’s law is likely to become ut-ut-1=-0.4*(gyt-5%)

a.

un= 5%

b.

Assume the economy has been at the natural rate of unemployment for two years (this year and last year). Then, gyt = 3%; gmt = gyt + πt = 11%.

c. t-1: t: t+1: t+2: t+3: 4.

π 8% 4% 4% 4% 4%

u 5% 9% 5% 5% 5%

gyt 3% -7% 13% 3% 3%

gmt 11% -3% 17% 7% 7%

a.

See text for full answer. Gradualism reduces the need for large policy swings, with effects that are difficult to predict, but immediate reduction may be more credible and encourage rapid, favorable changes in inflation expectations. Nevertheless, the staggering of wage decisions suggests that a gradual disinflation—as long as it is credible—is the option consistent with no change in the unemployment rate.

b.

The answer is not clear. Based in Ball's evidence, a fast disinflation probably results in a lower sacrifice ratio, depending on the features listed in part (c).

c.

Relevant features include the degree of indexation, the nature of the wage-setting process, and the initial rate of inflation.


157 5.

a.

Inflation will start increasing.

b.

It should let unemployment increase to its new, higher, natural rate.

Dig Deeper 6.

7.

a.

sacrifice ratio=1

b.

πt = 11%; πt+1 = 10%; πt+2 = 9%; πt+3 = 8%; πt+4 = 7%; . . . ; πt+9 = 2%

c.

10 years; sacrifice ratio= (10 point years of excess unemployment)/(10 percentage point reduction in inflation)=1

d.

πt = 8.5%; πt+1 = 5.9%; πt+2 = 3.9%; πt+3 = 2.4%; πt+4 = 1.3% Less than 5 years are required. sacrifice ratio=5/(12-1.3)=0.47 The sacrifice ratio is lower because people are somewhat forward-looking and incorporate the target inflation rate into their expectations.

e.

The central bank can let the unemployment rate return to the natural rate beginning at time t+1. The ex post sacrifice ratio from this scenario = (1 point year of excess unemployment)/(10 point reduction of inflation) = 0.1

f.

Take measures to enhance credibility.

a.

πt-πt-1= -(ut-.05) ut- ut-1= -0.4(gmt-πt-.03)

b.

Assuming gm,t-1=13%, πt-1= 10%, ut-1=5%, and beginning in year t, gm=3%, the economy evolves as follows.

t: t+1: t+2: t+3: t+4: t+5: t+6: t+7: t+8: t+9: t+10: c.

π 7.1% 3.1% -0.7% -3.2% -4.1% -3.5% -2.1% -0.5% 0.8% 1.5% 1.6%

u 7.9% 9.1% 8.8% 7.5% 5.9% 4.4% 3.6% 3.4% 3.7% 4.3% 4.9%

Inflation does not decline smoothly. In the early years, the large unemployment rates (relative to the natural rate) reduce inflation to negative values. In this example, money growth equals the normal growth rate of output, so negative inflation drives real money growth (and hence output growth) above the normal output growth rate, and unemployment falls. Eventually, when unemployment falls below the natural rate, inflation begins to increase again. These cycles continue, with decreasing amplitude.


158 d.

u=5% and π=0% in the medium run.

Explore Further 8.

9.

a.

Yes.

b.

The unemployment rate increased from 5.7% in January 2002 to 6.3% in June 2003.

c.

Although growth was positive, it well below the normal rate of 3% for most of the period. Therefore, growth was too low to prevent the unemployment rate from rising.

d.

Employment fell.

e.

Yes.

f.

Productivity grew.

a.

Actually, according to non-seasonally adjusted data, the level of unemployment fell in five months of 2001, although it rose over the entire year. Nevertheless, in several months in which the level of unemployment rose (e.g., July), the level of employment also rose, which is the point of the problem.

b.

The levels of employment and unemployment can both rise if the participation rate increases.


a. b. c. d. e. f. g.

True. True. False. False. True. False. True.

2.

The table should read as follows. Transportation Food

Mexico United States

a.

Services

Price

Quantity

Price

Quantity

5 pesos

400

20 pesos

200

$1

1,000

$2

2,000

U.S. consumption per person = $1(1000) + $2(2,000)=$5000


159

3.

b.

Mexican consumption per person=5(400) pesos + 2(2000) pesos = 6000 pesos

c.

From the U.S. point of view, the exchange rate (E)=10 pesos/$. Mexican consumption per person in dollars = 6000 pesos/E=$600

d.

Mexican consumption per person ($PPP)=$1(400)+$2(200)=$800

e.

Mexican standard of living relative to the United States Exchange rate method: 600/5000 =0.12 PPP method: 800/5000=0.16

a.

Y=63

b.

Y doubles.

c.

Yes.

d.

Y/N=(K/N)1/2

e.

K/N=4 implies Y/N=2. K/N=8 implies Y/N=2.83. Output less than doubles.

f.

No.

g.

No. In part (f), we are essentially looking at what happens to output when we increase capital only, not capital and labor in equal proportion. There are decreasing returns to capital.

h.

Yes.

Dig Deeper 4.

5.

a.

Y/Y = .5 (K/K) growth rate of output = 1/2 growth rate of capital

b.

4% per year

c.

K/Y increases.

d.

No. Since capital is growing faster than output, the saving rate will have to increase to maintain the same pace. Eventually, the required saving will exceed output. Capital must grow faster than output because there are decreasing returns to capital in the production function.

Even though the United States was making the most important technical advances, the other countries were growing faster because they were importing technologies previously developed in the United States. In other words, they were reducing their technological gap with the United States.

Explore Further 6.

The figures on GDP per person are chained ($2000) PPP numbers.


160 a.

Version 6.2 of the Penn World Table through 2003 yields the following average growth rates.

U.S. Japan b.

7.

1974-2003 1.97% 1.98%

1991-2003 1.97% 0.80%

Had the United States and Japan maintained the growth rates they achieved over the period 1951 to 1973, Japanese real output per person would have surpassed U.S. output per person by 2003. Instead, in 2003 U.S. real output per person ($34,875) was substantially higher than Japanese real output per person ($24,037).

The figures on GDP per person are chained ($2000) PPP numbers. a. There was substantial convergence for the France, Belgium, and Italy through 1991. Since then, the standard of living of these countries relative to the U.S. standard of living has fallen somewhat. b.

8.

1951-1973 2.19% 4.70%

Argentina, Chad, Madagascar, and Venezuela have not converged to the United States. In fact, they have grown steadily poorer relative to the United States.

The figures on GDP per person are chained ($2000) PPP numbers. a. 10 Richest Countries in 1970 Qatar $66, 763 Kuwait $64,914 Brunei $30,749 Bermuda $21,492 Switzerland $21,111 United States $17,321 Bahamas $16,911 Luxembourg $16,806 Denmark $16,584 Sweden $15,785 b.

10 Richest Countries in 2003 Luxembourg $49,262 Qatar $36,157 Bermuda $35,738 United Arab Emirates $35,658 United States $34,875 Norway $34,011 Macao $30,420 Switzerland $28,792 Ireland $28,248 Denmark $27,970


161 c.

10 Richest Countries in 1970: Proportional Increase in the Standard of Living 1970-2003 Luxembourg 2.93 United States 2.01 Denmark 1.69 Bermuda 1.66 Sweden 1.66 Switzerland 1.36 Bahamas 1.09 Brunei 0.85 Qatar 0.54 Kuwait 0.40

d.

The dataset includes 152 countries with observations for both 1970 and 2003. biggest proportional increase in standard of living: smallest proportional increase in standard of living: fraction with negative growth:

China 9.94 Liberia 0.17 18/152=18%


a. b. c.

d. e.

f.

True, if saving includes public and private saving. False. True. In the model without depreciation, there is no steady state. A constant saving rate produces a positive but declining rate of growth. In the infinite-time limit, the growth rate equals zero. Output per worker rises forever without bound. In the model with depreciation, if the economy begins with a level of capital per worker below the steadystate level, a constant saving rate also produces a positive but declining rate of growth, with a limit of zero. In this case, however, output per worker approaches a fixed number, defined by the steady-state condition of the Solow model. Note that depreciation is not needed to define a steady state if the model includes labor force growth or technological progress. Uncertain. See the discussion of the golden-rule saving rate. Uncertain/False. It is likely the U.S. rate is below the golden rule rate and that transforming Social Security to a pay-as-you-go system would ultimately increase the U.S. saving rate. These premises imply that such a transformation would increase U.S. consumption in the future, but not necessarily in the present. Indeed, if the only effect of such a transformation is to increase the saving rate, we know that consumption per worker will fall in the short run. Moreover, moving to a pay-as-you-go system requires transition costs. If these costs are borrowed, then the reduction in public saving will offset the increase in private saving during the transition. If these costs are not borrowed, then transitional generations must suffer either a reduction in promised benefits or an increase in taxes to finance their own retirement (at least to some degree) in addition to the retirement of a previous generation. Thus, whether the U.S. “should” move to a payas-you-go system depends on the likely resolution of intergenerational distributional issues and your view about the equity of such a resolution. Uncertain. The U.S. capital stock is below the golden rule, but that does not necessarily


162

h.

imply that there should be tax breaks for saving. Even if the tax breaks were effective in stimulating saving, the increase in future consumption would come at the cost of current consumption. False. Even if you accept the premise (that educational investment increases output, as would be implied by the Mankiw, Romer, Weil paper), it does not necessarily follow that countries should increase educational saving, since future increases in output will come at the expense of current consumption. Of course, there are other arguments for subsidizing education, particularly for low-income households.

2.

Disagree. An increase in the saving rate does not affect growth in the long run, but does increase growth in the short run. In addition, an increase in the saving rate leads to an increase in the longrun level of output per worker. Finally, since the evidence suggests that the U.S. saving rate is below the golden-rule rate, an increase in the saving rate would increase steady-state consumption per worker.

3.

Assume that the economy begins in steady state. One decade after an increase in the saving rate, the growth rate of output per worker will be higher than it was in its initial steady state. Five decades after an increase in the saving rate, the growth rate of output per worker will be close to its value in the initial steady state (this value is zero in the absence of technological progress). The level of output per worker will be higher, however, than it was in the initial steady state.

Dig Deeper 4.

a.

This would likely lead to a higher saving rate, so output per worker and output per person will be higher in the long run.

b.

Treat an increase in female participation as a one-time increase in employed labor. In this case, an increase in female participation would have no effect on the level of output per worker, but would lead to a higher level of output per person, since a greater fraction of the population is employed.

5.

A transformation to a fully funded system leads to an increase in the saving rate. Ignoring any short-run transition costs, in the long run an increase in the saving rate leads to a higher level of output per worker, but has no effect on the growth rate of output per worker.

6.

a.

K/N=(s/(2))2; Y/N=s/(4)

b.

C/N=(1-s)Y/N=s(1-s)/(4)

c-e.

Y/N increases with s. C/N increases until s=0.5, then decreases.

a.

Yes.

b.

Yes.

c.

Yes.

d.

Y/N = (K/N)1/3

e.

In steady state, sY//N = K/N, which, given the production function in part (d), implies K/N=(s/)3/2

7.


163

8.

f.

Y/N =(s/)1/2

g.

Y/N = 2

h.

Y/N = 21/2

a.

Substituting from problem 7 part (e) implies K/N=1.

b.

Substituting from problem 7 part (f), Y/N=1.

c.

K/N=0.35; Y/N=0.71

d.

K/N 1.00 0.90 0.80 0.71

t t+1 t+2 t+3 9.

Y/N 1.00 0.97 0.93 0.89

b.

K/N = (0.15/.075)2 = 4 Y/N= (4)1/2=2

c.

K/N=(0.2/0.075)2 =7.11 Y/N=(7.11)1/2=2.67 Capital per worker and output per worker increase.

Explore Further 10.

a.

For 2006, the national saving rate was approximately 14.1%. In steady state, K/N = (0.141/0.075)2 =3.56, and Y/N=(3.25)1/2 =1.89.

b.

For 2006, the budget deficit (including the off budget items) was 1.9% of GDP. Eliminating the deficit increases the national saving rate to 16% (14.1% + 1.9%). As a result, in steady state, K/N = (0.16/.075)2=4.55, and Y/N=(4.55)1/2 =2.13. Steady-state output per worker increases by 12.7%.


a. b. c. d. e.

f. g. h.

True. True. False. In steady state, there is no growth of output per effective worker. True. False. The steady-state rate of growth of output per effective worker is zero. A higher saving rate leads to higher steady-state level of capital per effective worker, but has no effect on the steady-state rate of growth of output per effective worker. True. False. False/Uncertain. Even pessimists about technological progress typically argue that the rate of progress will decline, not that it will be zero. Strictly, however, the truth of this statement is uncertain, because we cannot predict the future.


164 2.

3.

a.

Most technological progress seems to come from R&D activities. See discussion on fertility and appropriability in Chapter 12.2.

b.

This proposal would probably lead to lower growth in poorer countries, but higher growth in rich countries.

c.

This proposal would lead to an increase in R&D spending. If fertility did not fall, there would be an increase in the rates of technological progress and output growth.

d.

Presumably, this proposal would lead to a (small) decrease in the fertility of applied research and therefore to a (small) decrease in growth.

e.

This proposal would reduce in the appropriability of drug research. Presumably, there would be a reduction in the development of new drugs, a reduction in the rate of technological progress, and a reduction in the growth rate.

a.

The economic leaders typically achieve technological progress by generating new ideas through research and development.

b.

Developing countries can import technology from the economic leaders by copying this technology or by receiving a transfer of technology as a result of joint ventures with firms headquartered in the economic leaders. Even in the absence of technology transfer, foreign direct investment can increase technological progress in the host country by substituting more productive foreign production techniques for less efficient domestic ones.

c.

Poor patent protection may facilitate a more rapid adoption of new technologies in developing countries. The costs of such a policy are relatively small, since developing countries generate relatively few new technologies.

Dig Deeper 4.

5.

a.

The growth rate of output per worker falls in the short run and continues to fall over time. In the long run, the growth rate approaches a new steady state with a permanently lower (but still positive) growth rate. Output per worker continues to rise over time, just at a slower rate.

b.

A permanent reduction in the saving rate has no affect on the steady-state growth rate of output per worker. The growth rate of output per worker falls (but remains positive) in the short run but in the long run it approaches its original steady-state rate.

a.

Nominal GDP Year 1: 10(100)+10(200)=3000 Year 2: 12(100)+12(230)=3960

b.

Year 2 Real GDP (Year 1 Prices)=10(100)+10(230)=3300 growth rate of real GDP=3300/3000 – 1 = 10%

c.

GDP deflator Year 1=1; Year 2=3960/3300=1.2


165 inflation=20%

6.

d.

Real GDP/Worker Year 1 = 3000/100=30; Year 2 = 3300/110=30 Labor productivity growth is zero.

e.

Year 2 Real GDP (Year 1 Prices)=10(100)+13(230)=3990 output growth=3990/3000 – 1 = 33%.

f.

GDP deflator Year 1=1; Year 2=3960/3990=0.992 inflation=0.992/1 – 1 = -0.8%

g.

Real GDP/worker=36.3 in year 2. Labor productivity growth is 36.3/30=21%.

h.

This statement is true, assuming there is progress in the banking services sector.

a.

i. ii. iii. iv. v.

K/(AN) = (s/(+gA+gN))2 = 1 Y/(AN)= (K/AN)1/2=1 gY/(AN) = 0 gY/N = gA=4% gY = gA+gN=6%

b.

i. ii. iii. iv. v.

K/(AN) = (s/(+gA+gN))2 = 0.64 Y/(AN)= (K/AN)1/2=0.8 gY/(AN) = 0 gY/N = gA=8% gY = gA+gN=10%

An increase in the rate of technological progress reduces the steady-state levels of capital and output per effective worker, but increases the rate of growth of output per worker. c.

i. ii. iii. iv. v.

K/(AN) = (s/(+gA+gN))2 = 0.64 Y/(AN)= (K/AN)1/2=0.8 gY/(AN) = 0 gY/N = gA=4% gY = gA+gN=10%

(K/(AN)) = (4/5)2; (Y/(AN)) = (4/5); gY/(AN) = 0; gY/N = 4%; gY = 10% People are better off in case a. Given any set of initial values, the level of technology is the same in cases (a) and (c), but the level of capital per effective worker is higher at every point in time in case (a). Thus, since Y/N=AY/(AN)=A(K/(AN))1/2=A1/2(K/N)1/2, output per worker is always higher in case (a). 7.

a.

Probably affects A. Think of climate.

b.

Affects H and possibly A, if better education improves the fertility of research.


166 c.

Affects A. Strong protection tends to encourage more R&D but also to limit diffusion of technology.

d.

May affect A through diffusion.

e.

May affect K, H, and A. Lower tax rates increase the after-tax return on investment, and thus tend to lead to more accumulation of K and H and to more R&D spending.

f.

If we interpret K as private capital, than infrastructure affects A (e.g., better transportation networks may make the economy more productive by reducing congestion time).

g.

Assuming no technological progress, a reduction in population growth implies an increase in the steady-state level of output per worker. A reduction in population growth leads to an increase in capital per worker. If there is technological progress, there is no steady-state level of output per worker. In this case, however, a reduction in population growth implies that output per worker will increase at every point in time, for any given path of technology. See the answer to problem 6(c).

Explore Further 8.

a.

The quantity gY – gN is the growth rate of output per worker. The quantity gK – gN is the growth rate of capital per worker.

b.

gK – gN = 3(gY – gN) – 2gA

c. U.S. France Japan UK

gY – gN 1.8% 3.2% 4.2% 2.4%

gA 2.0% 3.1% 3.8% 2.6%

gK – gN 1.4% 3.4% 5.0% 2.0%


2.

a. b. c. d. e. f. g.

False. Productivity growth is unrelated to the natural rate of unemployment. If the unemployment rate is constant, employment grows at same rate as the labor force. False. True. True. True. True. False.

a.

u = 1-(1/(1+))(A/Ae)

b.

u = 1-(1/(1+0.05)) = 4.8%

c.

No. Since wages adjust to expected productivity, an increase in productivity eventually leads to equiproportional increases in the real wage implied by wage setting and the real wage implied by price setting, at the original natural rate of unemployment. Thus, equilibrium can be maintained without any change in the natural rate of unemployment.


167 3.

An increase in labor productivity has no effect on the natural rate of unemployment, because the wage ultimately rises to capture the added productivity. The increase in the wage also implies that an increase in labor productivity has no permanent effect on inflation. From the price setting equation, P=(1+)W/A. If the wage (W) increases by the same proportion as productivity (A), the price level will not change.

4.

a.

Reduce the gap, if this leads to an increase in the relative supply of high-skill workers.

b.

Reduce the gap, since it leads to a decrease in the relative supply of low-skill workers.

c.

Reduce the gap, if it leads to an increase in the relative supply of high-skill workers.

d.

Increase the gap, if it leads U.S. firms hire low-skill workers in Central America, since this reduces the relative demand for U.S. low-skill workers.

Dig Deeper 5.

Technological change has led to a reduction in agricultural employment, but evidently has had no effect on the natural rate of unemployment.

6.

a.

P = Pe(1+)(Ae/A)(Y/AL) The new variables are technology variables, A and Ae. An increase in A has two effects. i.

For a given level of Y, an increase in A reduces Y/A, which implies a reduction in N and in increase in u. The increase in u tends to reduce W and therefore to reduce P. This is the effect that tends to increase the actual rate of unemployment in the short run.

ii.

To the extent that Ae lags behind A, Ae/A falls. In effect, workers do not receive as much of an increase in wages as warranted by the increase in productivity. This is the effect that tends to reduce the actual and natural rates of unemployment for a time.

The effects in (i) and (ii) both shift the AS curve down, so output increases in the short run. The effect on short-run unemployment depends on the relative strength of the effects in (i) and (ii).

7.

b.

AS shifts down. Given Ae/A=1, only effect (i) is relevant.

c.

In this case, effects (i) and (ii) from part (a) are relevant. Compared to part (b), the AS curve shifts down further.

a.

W/P=F(1-N/L,z)

b.

Labor supply slopes up. As N increases, u falls for given L, so W/P increases.

c.

W/P=MPL/(1+)

d.

Labor demand slopes down. As N increases, the MPL falls, so W/P falls.


168

8.

e.

An improvement in technology increases the MPL, so the labor demand curve shifts right. The real wage increases when technology improves.

a.

The real wage of high-skill labor increases. The real wage of low-skill labor falls.

b.

Since there is a binding minimum real wage, a fall in labor demand has no effect on the real wage of low-skill workers. Employment of low-skill workers falls, however, and the unemployment rate increases.

c.

Wage inequality will increase by a greater amount in the United States. Unemployment will increase by a greater amount in Europe.

d.

The United States has had a large increase in wage inequality over the past 30 years, and Europe has had a large increase in the unemployment rate.

Explore Further 9.

10.

a.

Projections for job decline from 2006-2016 Some examples: Stock clerks and order fillers – technological change Electrical and electronic equipment assemblers – perhaps foreign competition

b.

Projections for job growth from 2006-2016 Some examples: Home health aides – aging of the population Computer systems analysts – technological change

c.

More occupations that are forecast to grow require degrees as opposed to on-the-job training.

a.

For a given markup, the real wage grows at the rate of technological progress. Clearly, there has been technological progress since 1973.

b.

1973: $8.98; 2006: $8:24

c.

The real wage of low-skill workers has fallen markedly, which suggests that the relative demand for low skill workers has fallen markedly.

d.

Other benefits, particularly health care benefits, might be missing from this calculation.


a. b. c. d. e. f. g.

True. True. True. False. True. False. True.


169

2.

3.

4.

5.

h. i.

True. The nominal interest rate is always positive. False. The real interest rate can be negative.

a.

Real. Nominal profits are likely to move with inflation; real profits are easier to forecast.

b.

Nominal. The payments are nominal.

c.

Nominal. Car lease and car loan payments are usually stated in nominal terms.

a.

exact: r = (1+.04)/(1+.02)-1 = 1.96%; approximation: r .04-.02 = 2%

b.

3.60%; 4%

c.

5.48%; 8%

a.

No. If the nominal interest rate were negative, nobody would hold bonds. Money would be more appealing since it could be used for transactions and would earn zero—as opposed to negative—interest.

b.

Yes. The real interest rate is negative if expected inflation exceeds the nominal interest rate. Even in this case, the real interest rate on bonds (which pay nominal interest) exceeds the real interest rate on money (which does not pay nominal interest) by the nominal interest rate.

c.

A negative real interest rate makes borrowing very attractive and leads to a large demand for investment.

d.

Answers will vary.

a.

The discount rate is the interest rate. So, in case (i), the EPDV is $2,000(1-0.25) under either interest rate, and in case (ii) the EPDV is (1-0.2)$2,000 under either interest rate.

b.

The interest rate does not enter the calculation. Hence, you prefer (ii) to (i) since 20%<25%. Note that the answer to part (a) does not imply that saving will not accumulate. By retirement, the initial investment will have grown by a factor of (1+i) 40 in nominal terms and (1+r)40 in real terms. As long as r is positive, the purchasing power of the initial investment will grow. Moreover, this problem assumes that the tax rate you will pay upon retirement (25%) is higher than the tax rate you pay when you establish the IRA (20%). This assumption may be false for some taxpayers.

6.

a.

$V=$100/0.1=$1000

b.

Since the first payment occurs at the end of the year, $V = $z[1- 1/(1+i)n]/[1-(1+i)] - $z. 10 years: $575.90; 20 years: $836.49; 30 years: $936.96; 60 years: $996.39


170 c.

i = 2%: PV of consol=$5000; 10 years: $816.22; 20 years: $1567.85; 30 years: $2184.44; 60 years: $3445.61 i = 5%: PV of consol=$2000; 10 years: $710.78; 20 years: $1208.53; 30 years: $1514.11; 60 years: $1887.58

7.

a.

The Fisher hypothesis is that in the medium run, changes in inflation are reflected onefor-one in changes in the nominal interest rate. In other words, in the medium run, changes in inflation have no effect on the real interest rate.

b.

Support.

c.

The line should not go through the origin, because the real interest rate is positive: when inflation equals zero, the nominal interest rate is positive.

d.

No. Even if monetary policy does not affect output or the real interest rate in the medium run, it can be used in the short run.

Dig Deeper 8.

a.

The IS shifts right. At the same nominal interest rate, the real interest rate is lower, so output is higher.

b.

The LM curve shifts down because the increase in money growth leads to an increase in the real money stock. The increase in expected inflation has no effect on the LM curve, because money demand depends on the nominal interest rate, not the real interest rate.

c.

Output increases. The nominal interest rate is higher than in Figure 14-5. Whether the nominal interest rate is lower or higher than before the increase in money growth is ambiguous. Thinking in terms of the money market equilibrium, the increase in the nominal money supply tends to reduce the nominal interest rate, but the increase in nominal money demand (because of the increase in output) tends to increase the nominal interest rate.

d.

Output is higher than in Figure 14-5. Reasoning from the IS relation, the real interest rate must be lower, since no exogenous variables in the IS relation have changed. (In other words, while the nominal interest rate may increase relative to Figure 14-5, it increases by less than the increase in expected inflation, so the real interest rate decreases.)

Explore Further 9.

Answers will vary depending upon when the website is accessed.


a. b. c. d. e. f.

False. True. True. False. True. True.


171

2.

3.

4.

g.

False.

h.

Uncertain/False. Some of the increase in the stock market was probably justified. However, most economists believe that there was a bubble in the stock market as well. A stock market correction followed.

a.

(1+i)n=$F/$P 1+i =($F/$P)1/n i =(1000/800)1/3-1 = 7.7%

b.

5.7%

c.

4.1%

The yield is approximately the average of the short-term interest rates over the life of the bond. a.

5%.

b.

5.25%

c.

5.5%

a.

The LM curve shifts down unexpectedly. There is unexpected fall in the interest rate and an unexpected increase in output. Both of these changes lead to an increase in the stock price.

b.

There is no change in the stock price.

c.

The effect on the stock price is ambiguous. Unexpected expansionary fiscal policy means the interest rate is higher than expected (after the expected expansionary monetary policy) but so is output. The interest rate effect tends to reduce the stock price; the output effect to increase them.

Dig Deeper 5.

6.

a.

See Figure 14-5 in Chapter 14.

b.

Initially after the increase, the yield curve will slope down out to one-year maturities, then slope up. After one year, the yield curve will slope up. After three years, the yield curve will be flat.

a.

This question should have read: “Explain why an inverted (downward-sloping) yield curve may indicate that a recession is coming.” An inverted yield curve implies that the expected future interest rate is lower than the current interest rate. These expectations could arise from a belief that the IS curve is going to shift to the left in the future, say because future investment is expected to fall. If the IS curve shifts left in the future, output will fall.

b.

Given the Fisher effect, a steep yield curve probably implies that financial market participants believe that future inflation will be substantially higher than current inflation.


172 7.

Let r be the real interest rate, g the growth rate of dividends, and x the risk premium. The price is given by the following expression. Q=1000/(1 + r + x) + 1000(1 + g)/(1 + r + x)2 + 1000(1 + g)2/(1 + r + x)3 . . . = [1000/(1 + r + x)][1 + (1 + g)/(1 + r + x) + (1 + g)2/(1 + r + x)2 + . . .] = 1000/(r + x - g) a.

$50,000; $20,000

b.

$10,000; $7692.31

c.

$16,666.67; $11,111.11

d.

The stock price increases when the risk premium falls. A fall in the risk premium is like a fall in the real interest rate.

Explore Further 8.

a.

The Fed can reduce the growth rate of money. The nominal interest rate increases in the short run, but falls in the medium run.

b.

Inflation was highest in early 1980. The 12-month inflation rate peaked at 14.6% in March and April of 1980.

d.

A positive spread means that expected future interest rates are higher than current interest rates. A declining spread means that the expected increase in future short-term interest rates is falling. The one-year T-bill rate increased from 7.28% to 12.6% between January 1978 and January 1980, but the spread declined from 0.9 percentage points to –1.46 percentage points over the same period. Financial market participants were not expecting short-term interest rates to continue to increase. Indeed, by the end of the 1970s, the negative spread indicates that short-term interest rates were expected to decline in the future.

e.

There spread declined by almost one percentage point in October 1979. The decline is consistent with expectations of lower inflation in the future.

f.

The one-year interest rate fell.

g.

During the rate cut in the recession, spreads went up, as short-term rates declined. However, long-term rates did not increase, which suggests that inflation expectations did not increase. Instead, the increase in spreads is consistent with the expectation that the anti-inflationary policy would continue with high short-term interest rates after the recession. This is indeed what happened.

9.

Answers will vary.

10.

Answers will vary.


a.

False.


173

2.

3.

4.

b. c. d. e. f. g.

False. False. False. False. True. True.

a.

0.75(1+1.05+1.052)$40,000=$94,575

b.

$194,575

c.

The consumer works for three more years and will be retired for seven years, so there are 10 more years of consumption. So, since the real interest rate is zero, the consumer can consume one-tenth of her total wealth, or 19,457.50, this year.

d.

Consumption could increase by $2,000 annually.

e.

Benefits imply extra annual consumption of 0.6(1.052)$40,000(7/10)=$18,522.

The EPDV of purchasing the machine is /(r+) = $18,000/(r+0.08) a.

Buy. EPDV=$138,462>$100,000

b.

Break-even. EPDV=$100,000

c.

Do not buy. EPDV=$78,261<$100,000

a.

$44,000(1-0.4)36-$40,000(1-0.4)38=$38,400

b.

$44,000(1-0.3)36-$40,000(1-0.3)38=$44,800

Dig Deeper 5.

6.

a.

EPDV of future labor income = $30. Consumption=$10 in all three periods.

b.

youth: -5; middle age: 15; old age: -10

c.

Total saving =n(-5+15-10)=0

d.

0 – 5n + 10n = 5n

a..

youth: 5; middle age: 12.5; old age: 12.5 The consumer cannot borrow against future income when young.

b.

0 + 12.5n - 12.5n = 0

c.

0 + 0 + 12.5n = 12.5n

d.

By allowing people to borrow to consume when young, financial liberalization may lead to less overall accumulation of capital.


174 7.

a.

Expected value of earnings during middle age is 0.5($40,000+$100,000)=$70,000. EPDV of lifetime earnings = $20,000 + $70,000=$90,000. The consumption plan is $30,000 per year. The consumer will save -$10,000 (i.e., the consumer will borrow $10,000) in the first period of life.

b.

In the worst case, the EPDV of lifetime earnings = $60,000. Consumption = $20,000 and saving=0 in the first period of life. Consumption is lower than part (a), and saving is higher.

c.

Consumption in youth is $20,000; in middle age is $50,000; and in old age is $50,000. Consumption will not be constant over the consumer’s lifetime.

d.

The uncertainty leads to higher saving by consumers in the first period of life.

Explore Further 8.

a-c.

Between 1959 and 2006, consumption accounted for 66% of GDP on average and investment for about 13%, so consumption is about five times bigger than investment. Relative to average changes, movements in consumption and investment are of similar magnitude, which implies investment is much more volatile than consumption.

9.

a.

Consumers may be more optimistic about the future (and spend more) when disposable income is higher, so consumer confidence might be positively related to disposable income. However, consumer confidence should depend on expectations about the future, rather than on current variables per se. Hence, there are reasons to think changes in consumer confidence might not always track changes in disposable income.

b.

There appears to be positive relationship between the variables, but it is not tight.

c.

Personal disposable income increased at an annual rate of 11.5% in 2001:III and at an annual rate of 11.6% in 2002:I. Consumer confidence fell in 2001:III but rose in 2002:I. The events of September 11, as well as the ongoing recession, probably played a role in the consumer confidence numbers for 2001:III.


a. b. c. d. e. f. g.

False. False. False. True/Uncertain. Consumers can rely on forecasts by others, but somebody has to do it. False. True. False.

2.

a.

Higher real stock prices led to an increase real wealth directly, which would tend to increase consumption. Moreover, the hype about the New Economy, combined with increasing stock prices, may have led to favorable expectations about future labor income, which would also tend to increase consumption.


175

3.

b.

Subsequent declines in the stock market decreased wealth and may have led consumers to revise (downward) expectations about future labor income, effects that would tend to reduce consumption.

a.

The IS curve shifts right.

b.

The LM curve shifts right.

c.

There are three effects. First, an increase in expected future taxes tends to reduce expected future after-tax income (for any given level of income), and therefore to reduce consumption. This effect tends to shift the IS curve to the left. Second, the increase in future taxes (a deficit reduction program) tends to reduce real interest rates in the future. The fall in the expected future interest rate tends to shift the IS curve to the right. Third, the fall in future real interest rates leads to an increase in investment in the medium run and to an increase in output in the long run. The increase in expected future output tends to shift the IS curve to the right. The net effect on the IS curve is ambiguous. Note that the model of the text has lump sum taxes. In taxes are not lump sum, the tax increase may increase distortions in the economy. These effects tend to reduce output (or the growth rate).

d.

The IS curve shifts to the left.

4.

Rational expectations may be unrealistic, but it does not imply that every consumer has perfect knowledge of the economy. It implies that consumers use the best available information— models, data, and techniques—to assess the future and make decisions. Moreover, consumers do not have to work out the implications of economic models for the future by themselves. They can rely on the predictions of experts on television or in the newspapers. Essentially, rational expectations rules out systematic mistakes on the part of consumers. Thus, although rational expectations may not literally be true, it seems a reasonable benchmark for policy analysis.

5.

The answers below ignore any effect on capital accumulation and output in the long run. Assume the tax cut policy in the future is temporary, so we need only worry about future shortrun effects. a.

The effect on current output is ambiguous. The tax cut in the future will lead to a boom. Output and the real interest rate will increase. The increase in expected future output tends to shift the IS curve to the right; the increase in the expected future real interest rate tends to shift the IS curve to the left. Finally, the fall in expected future taxes tends to increase expected future after-tax income (for any given level of income). This effect tends to shift the IS curve to the right.

b.

This means that the Fed will increase the interest rate in the future (shift the LM curve to the left in the future). The expected interest rate will increase more, which tends to to shift the IS curve to the left, but there is still the effect of lower expected taxes on current consumption. The effect today on output is still ambiguous, but more likely to be negative than in part (a).

c.

Future output will be higher, the future interest rate will not increase, and future taxes will be lower. The IS curve definitely shifts to the right in the current period, and current output increases.


176

Dig Deeper 6.

7.

a-b.

See the discussion in the text.

c.

The gesture seemed to indicate that the Fed supported deficit reduction, and was willing to conduct expansionary monetary policy in the future to offset the direct negative effects on output from spending cuts and tax increases. A belief that the Fed was willing to act in this way would tend to increase expected future output (relative to the case where the Fed did nothing) and to reduce expected future interest rates. Both of these effects would tend to increase output in the short-run.

a.

Future interest rates will tend to rise. Future output will tend to fall. Both effects shift the IS curve to the left in the present. Current output and the current interest rate fall. The yield curve gets steeper on the day of the announcement.

b.

No.

c.

Compared to original expectations, the nominee is expected to follow a more expansionary monetary policy. The yield curve will get flatter on the day of the announcement.

Explore Further 8.

a.

The interest rate will increase in the short run, and increase even further in the medium run. The yield curve will get steeper.

b.

The spread increased over the period. 5-Year Yield minus 3-Month Yield August 2002: 1.64% January 2003: 1.86% August 2003: 2.4% January 2004: 2.22%


a. b. c. d. e. f.

g. 2.

True. False. False. False. False. The statement should read: “Given the definition of the exchange rate adopted in this chapter, if the dollar is the domestic currency and the euro the foreign currency, a nominal exchange rate of 1.10 means that one dollar is worth 1.1 euros.” This statement is True. False.

Domestic Country Balance of Payments ($) Current Account Exports

25


177 Imports

100

Trade Balance Investment Income Received Investment Income Paid Net Investment Income Net Transfers Received Current Account Balance Capital Account Increase in Foreign Holdings of Domestic Assets Increase in Domestic Holdings of Foreign Assets Net Increase in Foreign Holdings Statistical Discrepancy Foreign Country Balance of Payments ($) Current Account Exports Imports Trade Balance Investment Income Received Investment Income Paid Net Investment Income Net Transfers Received Current Account Balance Capital Account Increase in Foreign Holdings of Domestic Assets Increase in Domestic Holdings of Foreign Assets Net Increase in Foreign Holdings Statistical Discrepancy 3.

-75 (=25-100) 0 15 -15 (=0-15) -25 -115 (=-75-15-25)

80 (=65+15) -50 130 (=80-(-50)) -15 (=115-130)

100 25 75 (=100-25) 15 0 15 (=15-0) 25 115 (=75+15+25)

-50 80 (=65+15) -130 (=-50-80) 15 (=130-115)

a.

The nominal return on the U.S. bond is 10,000/(9615.38)–1=4%. The nominal return on the German bond is 6%.

b.

Uncovered interest parity implies that the expected exchange rate is given by E(1+i*)/(1+i)=0.75(1.06)/(1.04)=0.76 Euro/$.

c.

If you expect the dollar to depreciate, purchase the German bond, since it pays a higher interest rate and you expect a capital gain on the currency.

d.

The dollar depreciates by 4%, so the total return on the German bond (in $) is 6% + 4% =10%. Investing in the U.S. bond would have produced a 4% return.

e.

The uncovered interest parity condition is about equality of expected returns, not equality of actual returns.

Dig Deeper 4.

a.

GDP is 15 in each economy. Consumers will spend 5 on each good.


178

5.

b.

Each country has a zero trade balance. Country A exports clothes to Country B, Country B exports cars to Country C, and Country C exports computers to Country A.

c.

No country will have a zero trade balance with any other country.

d.

There is no reason to expect that the United States will have balanced trade with any particular country, even if the United States eliminates its overall trade deficit.

a.

The relative price of domestic goods falls. Relative demand for domestic goods rises. The domestic unemployment rate falls in the short run.

b.

The price of foreign goods in terms of domestic currency is P*/E. A nominal depreciation (a fall in E) increases the price of foreign goods in terms of domestic currency. Therefore, a nominal depreciation tends to increase the CPI.

c.

The real wage falls.

d.

Essentially, a nominal depreciation stimulates output by reducing the domestic real wage, which leads to an increase in domestic employment.

Explore Further 6.

7.

8.

a.

Considering the evidence through May 2008, the yen appreciated from mid-1985 to mid1995, depreciated until mid-1998, appreciated through the end of 1999, depreciated through the end of 2001, appreciated through 2004, depreciated through mid-2007, and then began to appreciate. From a broader perspective, between the January 1979 and May 2008, the yen appreciated by 90%. The yen reached its strongest value against the dollar in mid-1995.

b.

Depreciation of the yen.

c.

The yen appreciated from the end of 2001 to the end of 2004, and again after mid-2007, . This did not help the Japanese recovery.

a.

The sum of world current account balances should be zero. In 2007, the sum was positive, which implies literally that the world as a whole was borrowing. Obviously, this cannot have been true.

b.

In 2007, the United States was the world's biggest borrower by far. The rest of the advanced economies as a whole were lenders, although the Euro area as a borrower. The economies of the Middle East and developing economies in Asia were other large lenders; the economies of central and eastern Europe were large borrowers.

c.

In 2007, the saving of the advanced economies other than the Untied States amounted to only 24% of U.S. borrowing. So, the United States was borrowing heavily from all regions of the world.

d.

The projections in the April 2008 World Economic Outlook suggested no qualitative change in the answers to parts (a) through (c).

a.

World saving essentially equals world investment, as it must logically.


179 b.

In 2007. U.S. saving was 13.6% of GDP, but U.S. investment was 18.8% of GDP. The United States financed the difference by borrowing from abroad. The April 2008 World Economic Outlook projected a gap of similar magnitude for the next two years.


a. b.

f. g.

False. False. An increase in the budget deficit will lead to an increase in the trade deficit, but we can't conclude that from the national income accounting identity. We have to use our model to make that prediction. False. True. False. Econometric evidence suggests that a real depreciation does not lead to an immediate improvement in the trade balance. Typically, the trade balance improves six to twelve months after a real depreciation. only after six to twelve months between only after six to twelve months. True. False.

a.

There is a real appreciation over time. Over time, the trade balance worsens.

b.

The currency depreciates at the rate of -*.

a.

The share of Japanese spending on U.S. goods relative to U.S. GDP is (0.06)(0.11)=0.7%.

b.

U.S. GDP falls by 2(.05)(.007)=0.07%.

c.

U.S. GDP falls by 2(.05)(0.11)=1.1%.

d.

This is an overstatement. The numbers above indicated that even if U.S. exports fall by 5%, the effect is to reduce GDP growth by 1.1%.

c. d. e.

2.

3.

4.

Answers follow the model in the text.

Dig Deeper 5.

a.

The ZZ and NX lines shift up. Domestic output and domestic net exports increase.

b.

Domestic investment will increase because output increases. Assuming taxes are fixed, there is no effect on the deficit.

c.

NX=S-I+T-G. Since the budget deficit is unchanged, and I and NX increase, S must increase.

d.

Except for G and (for our purposes) T, the other variables in equation (19.5) are endogenous. An exogenous shock such as an increase in foreign output can affect all of the endogenous variables simultaneously.


180 6.

7.

a.

There must be a real depreciation.

b.

Y=C+I+G+NX. If NX rises while Y remains constant, C+I+G must fall. The government can reduce G or increase T, which will reduce C.

a.

Y = C + I + G + X – IM Y=c0+c1(Y-T)+d0+d1Y+G+x1Y*-m1Y Y=[1/(1-c1-d1+m1)][c0+c1T+d0+G+x1Y*]

b.

Output increases by the multiplier, which equals 1/(1-c1-d1+m1). The condition 0< m1< c1+d1<1 ensures that the multiplier is defined, positive, and less than one. As compared to the original multiplier, 1/(1+c1), there are two additional parameters: d1, which captures the effect of an additional unit of income on investment, and m1, which captures the effect of an additional unit of income on imports. The investment effect tends to increase the multiplier; the import effect tends to reduce the multiplier.

c.

When government purchases increase by one unit, net exports fall m1Y= m1/(1-c1-d1+m1). Note that the change in output is simply the multiplier.

d.

The larger economy will likely have the smaller value of m1. Larger economies tend to produce a wider variety of goods, and therefore to spend more of additional unit of income on domestic goods than smaller economies do.

e. small economy (m1=0.5) large economy (m1=0.1)

8.

Y 1.1 2

by

NX 0.6 0.2

f.

Fiscal policy has a larger effect on output in the large economy, but a larger effect on net exports in the small economy.

a.

It is convenient to wait to substitute for G until the last step. Y = C + I + G + X – IM = 10 + 0.8(Y - 10) + 10+G + 0.3Y*- 0.3Y Y = [1/(1 - .8 + .3)](12 + G + 0.3Y*) = 2(12 + G + 0.3Y*) = 44 + 0.6Y* When foreign output is fixed, the multiplier is 2 (=1/(1-0.8+0.3)). The closed economy multiplier is 5 (=1/(1-0.8)). In the open economy, some of an increase in autonomous demand falls on foreign goods, so the multiplier is smaller.

b.

Since the countries are identical, Y=Y*=110. Taking into account the endogeneity of foreign income, the multiplier equals [1/(1-0.8 -0.3*0.6 +0.3)]=3.125. The multiplier is higher than the open economy multiplier in part (a) because it takes into account the fact that an increase in domestic income leads to an increase in foreign income (as a result of an increase in domestic imports of foreign goods). The increase in foreign income leads to an increase in domestic exports.

c.

If Y=125, then Y*=44+0.6(125)=119. Using these two facts and the equation Y=2(12+G+0.3Y*) yields 125=24+2G+0.6(119), which implies G=14.8. In the domestic economy, NX=0.3(119)-0.3(125)=-1.8 and T-G=10-14.8=-4.8. In the foreign economy, NX*=1.8 and T*-G*=0.


181 d.

If Y=Y*=125, then 125=24+2G+0.6(125), which implies G=G*=13. In both countries, net exports are zero, but the budget deficit is 3.

e.

In part, fiscal coordination is difficult to achieve because of the benefits of doing nothing and waiting for another economy to undertake a fiscal expansion, as indicated from part (c).

Explore Further 8.

a.

NX=National Saving - I.

b.

As a % of GDP, gross private domestic investment was 3.6 percentage points higher in 2006 than in 1981. Net exports were 5.7 percentage points lower. Therefore, the national income identity implies that national saving fell by 3.6–5.7 = 2.1 percentage points relative to GDP.

c. 1981-1990 1990-2000 2000-2004

Change in Investment (% of GDP) -0.7% 5.1% -0.7%

Change in NX (% of GDP) -0.9% -3.1% -1.7%

Only in the 1990s was the fall in NX matched by an increase in investment. d.

Yes. An increase in investment leads to more capital accumulation and more output in the future, and therefore to a greater ability to repay foreign debt.


a. b. c. d. e. f.

False. True. True. True. Uncertain. If expected appreciation of the yen is greater than or equal to the interest rate in other countries, than foreign investors will hold yen bonds. False. The money stock will change in response to shocks (including policy shocks) so that the home interest rate equals the foreign interest rate.

2.

The appropriate mix is a monetary expansion to lessen the value of the currency (and thereby to improve the trade balance) and a fiscal contraction to prevent output from increasing.

3.

a.

Consumption increases because output increases. Investment increases because output increases and the interest rate falls.

b.

A monetary expansion has an ambiguous effect on net exports. The nominal depreciation tends to increase net exports, but the increase in output tends to reduce net exports.

a.

The IS curve shifts right, because net exports tend to increase. increases.

4.


Domestic output

182 b.

The IS curve shifts right, because the increase in i* tends to create a depreciation of the domestic currency and therefore an increase in net exports. Domestic output increases. The interest parity line also shifts up.

c.

A foreign fiscal expansion is likely to increase Y* and to increase i*. A foreign monetary expansion is likely to increase Y* and to reduce i*.

d.

A foreign fiscal expansion is likely to increase home output. A foreign monetary expansion has an ambiguous effect on home output. The increase in Y* tends to increase home output, but the fall in i* tends to reduce home output.

Dig Deeper 5.

6.

a.

An increase in Y* shifts the IS curve to the right. The incipient rise in the home interest rate creates a monetary expansion as the home central bank purchases foreign exchange to prevent the domestic currency from appreciating. So, the LM curve shifts right. Output and net exports increase.

b.

The interest parity line shifts up, and the LM curve shifts left as the central bank sells foreign exchange to prevent the domestic currency from depreciating. Output falls, which leads to an increase in net exports.

c.

A fiscal expansion in the Leader country, which increases Y* and i*, reduces domestic output, if the effect of Y* on domestic output is small. A monetary expansion in the Leader country, which increases Y* and reduces i*, increases domestic output.

a.

The IS curve shifts to the left. Output falls, the interest rate falls, and the currency depreciates. The currency depreciation tends to increase output by increasing net exports. Therefore, the exchange rate movement dampens the effect of the fall in business confidence.

b.

The IS curve shifts left and the LM curve shifts left (because the money supply falls) as the central bank sells foreign exchange to prevent the domestic currency from appreciating. The fall in output is greater than in part (a).

c.

When the exchange rate is flexible, movements of the exchange rate tend to dampen the output effects of IS shocks. The currency depreciates when the IS curve shifts left and appreciates when the IS curve shifts right.

Explore Further 7.

a.

Et=Eet+1(1+it+x)/(1+i*t+1)

b.

The IS curve slopes down as before, but with the result in part (a) substituted for the nominal exchange rate in the NX function.

c.

The IS curve shifts right, because the fall in the expected exchange rate creates a depreciation (which leads to an increase in net exports) at the original interest rate. The interest parity line shifts left. Output increases, net exports increase, and the currency depreciates.


183

8.

d.

An increase in x tends to increase the value of the domestic currency and therefore to shift the IS curve to the left. According the assumption of the problem, the IS curve returns to its original position. As a result, the combined effect of the increase in the expected exchange rate and the increase in x is no change in output. Since there is no change in output, there is no change in net exports or the exchange rate. The increase in x shifts the interest parity line to the right, back to its original position.

e.

Yes and yes.

a-b.

According to data in The Economist on May 22, 2008, the dollar was expected to appreciate against the pound, the euro, and the renminbi; to depreciate by 1% against the Canadian dollar over 10 years; and to depreciate by 20% over the yen over 10 years.

c.

If significant real depreciation of the dollar is required, the results of part (b) imply that U.S. inflation needs to be consistently lower than foreign inflation by a substantial margin. For example, if real depreciation of 20% against the euro is required over a 10year horizon, U.S. inflation must be 2 percentage points lower than European inflation every year. If the dollar appreciates against the euro, as forecast by uncovered interest parity, U.S. inflation would have to be even lower than European inflation to achieve the needed real depreciation. Differences in annual inflation of this size seem unlikely to happen for an entire decade.

d.

Perhaps the relatively strong demand for dollar assets, irrespective of the interest rate or expected depreciation, has slowed the depreciation of the dollar that might have been expected to result from the enormous U.S. current account deficit.


a. b. c. d. e.

True. Britain returned to the gold standard at too appreciated a parity. True. False. False. False.

2.

b.

The AD curve shifts right in the short run. The AS curve shifts left in the medium run. In the medium run, output is unchanged, but the price level is higher.

c.

Consumption is unchanged in the medium run.

d.

The real exchange rate appreciates, since the price level rises. As a result of the real appreciation, net exports fall in the medium run.

e.

The domestic interest rate equals the foreign interest rate, i*. The nominal interest rate is unaffected by government spending. Since expected inflation is constant, the real interest rate is also unaffected. Investment is unchanged in the medium run.

f.

In a closed economy, an increase in government spending reduces investment in the medium run.


184

3.

4.

g.

The statement is true. Under fixed exchange rates, the interest rate is tied to the foreign interest rate. Since the interest rate does not change, there is no mechanism for government spending to crowd out investment.

a.

The home real interest rate equals the foreign real interest rate minus expected real appreciation of the home currency. When the home currency is expected to appreciate in real terms, foreign bonds must offer a real interest rate higher than the home real interest rate to compensate international portfolio investors for the expected loss in the real value of the foreign currency. When the home currency is expected to depreciate in real terms, home bonds must pay a real interest rate higher than the foreign real interest rate.

b.

According to uncovered interest parity, 10%=6%-expected nominal appreciation, which implies that expected nominal appreciation equals -4% per year. In other words, expected depreciation is 4% per year.

c.

According to real interest parity, 10%-6%=(6%-3%) - expected real appreciation, which implies that expected real appreciation equals -1% per year. Therefore, expected real depreciation is 1% per year.

d.

You would purchase the domestic bond because the foreign bond will pay less interest than the domestic bond, and the domestic currency is expected to gain in value relative to the foreign currency.

a.

The expected exchange rate is E. The home interest rate is i*.

b.

The expected exchange rate is less thanE. The home interest rate is greater than i*.

c.

The domestic interest rate returns to i*, because expected depreciation is zero.

d.

Devaluation per se does not lead to higher interest rates. Fear of devaluation does.

Dig Deeper 5.

6.

a.

The price level rises by 10%.

b.

The real exchange rate is EP/P*. If P rises by 10%, E falls by 10%. There is a 10% depreciation of the currency in nominal terms.

c.

Eet+n falls by 10%.

d.

E falls by 10%.

e.

E falls by more than 10%. By interest parity, i-i* equals expected depreciation. If i falls below i* in the short run, then there is expected appreciation. This can only happen if E falls by more than 10% in the short run. So, E falls by more in the short run than it does in the medium run.

a.

Eet+1 falls.

b.

The UIP curve shifts up. The domestic interest rate must increase to maintain the fixed exchange rate.


185

7.

c.

The money supply falls as the central bank sells foreign exchange to buy its own currency. The LM curve shifts left.

d.

Output falls and the interest rate rises. The government might choose to abandon the fixed exchange rate to avoid the fall in output, even if initially the government had no intention of devaluing. Self-fulfilling crises are possible.

a.

The domestic interest rate equals the foreign interest rate before and after the devaluation.

b.

The expected exchange rate falls toE. The UIP curve shifts up.

c.

The IS curve shifts right, because the devaluation tends to increase net exports. The interest rate would increase with no change in the money supply.

d.

The money supply must increase. The LM curve shifts right.

e.

Output increases.

f.

Fear of further devaluation will increase the expected exchange rate above E and increase the interest rate above i*. These effects will tend to reduce the increase in output. If the initial devaluation creates a strong enough fear of further devaluation, the devaluation could lead to a fall in output.

Explore Further 8.

The answer is given in the comments after part (c). The exchange rate is many times more variable than the interest rate differential.


2.

a. b. c.

d. e.

False. True. Uncertain/False. Even though the unemployment rate declined, it remained high until World War II. Traditional Phillips curve analysis suggests that deflation should have continued. Something more is needed to explain the end of deflation. The text explores several possible explanations. True. False.

a.

The central bank could increase M and shift the LM curve to the right.

b.

Since the unemployment rate is above the natural rate, P>Pe. As a result, Pe falls, the AS curve shifts down, and P falls. In the IS-LM diagram, the fall in P implies an increase in M/P, so the LM curve shifts right.

c.

Expected inflation is likely to fall. The fall in expected inflation tends to increase the real interest rate and shift IS to the left. Output moves further away from the natural level.


186

3.

d.

No. If the Fed does nothing, the economy may not return to the natural level of output, if the effect of the fall in expected inflation is strong enough.

b.

P falls and M/P rises, so the LM curve shifts right. The adjustment mechanism does not work when the nominal interest rate equals zero. As the LM curve shifts right, output does not change.

c.

Monetary policy is ineffective. An increase in M shifts the LM curve to the right, which does not lead to an increase in output when the nominal interest rate equals zero.

d.

Yes. An increase in G or a reduction in T would shift the IS curve to the right. As a result, output would increase.

e.

This is not wise advice. If the economy is in a liquidity trap, the central bank cannot restore output to its natural level.

Dig Deeper 4.

a.

Short-term unemployment has a greater effect on wages. The long-term unemployed may not be searching for employment and may not be very employable.

b.

u=[.05/1.05(1-0.5)]

c.

If =0, 0.4, 0.8, the natural rate =4.8%, 6.0%, 7.9%. Intuitively, if the weight on longterm unemployed were zero instead of 0.5, the wage-setting and price-setting equations would determine the natural short-term rate of unemployment. The long-term unemployed would simply increase the aggregate unemployment rate. Thus, as the proportion of long-term unemployed increased, the natural rate of unemployment would increase. The same kind of reasoning applies here, but the effect is less strong because the weight on long-term unemployed in the wage-setting equation is not zero. In terms of the logic of the labor market, the long-term unemployed put less downward pressure on wages than the short-term unemployed. So, increasing the proportion of long-term unemployed tends to increase the real wage. Effectively, this implies that the labor supply curve (the wage-setting equation) shifts up. If the labor demand curve were downward-sloping, employment would fall as the real wage rose since workers would be less attractive to firms. In this problem, labor demand (the price-setting equation) is flat at a fixed real wage, which implies that all of the adjustment from an increase in the proportion of long-term unemployment takes the form of less employment (and a higher unemployment rate) and none of the adjustment takes the form of a higher real wage.

5.

a.

Higher unemployment implies lower wages given expected prices. This implies lower prices given expected prices. Equivalently, it implies lower inflation given expected inflation, which here equals past inflation.

b.

t - πt-1 = - (uS + uL – un)

c.

πt - πt-1 = - (uS – un)

d.

πt - πt-1 = - [(1 - )ut – un]


187 e.

The curve will shift to up, so that any unemployment rate is associated with a greater increase in the inflation rate.

f.

More overall unemployment is needed to achieve the same decrease in inflation. The cost of disinflation increases.

g.

An increase in the proportion of long-term unemployed tends to imply a larger increase in inflation. In the Great Depression, perhaps the long-term unemployed did not exert much pressure on wages and prices, so deflation ended despite high unemployment.

Explore Further 6.

Answers will vary depending upon when the question is answered.


2.

3.

a. b. c. d. e. f.

True. False. False. False/Uncertain. Incomes policies may be part of a successful stabilization program in some cases, but they don't seem in general to be a prerequisite for stabilization. False. False.

a.

If money growth = 25%, 50%, 75%, seignorage=162.5, 325, 487.5.

b.

In the medium run, if money growth = 25%, 50%, 75%, seignorage=162.5, 200, 112.5. The fall in real money balances associated with higher ongoing inflation reduces the potential for seignorage. Part (a) did not allow for this effect.

a.

This policy would reduce the effect of inflation on real tax revenues.

b.

This policy would reduce the effect of inflation on real tax revenues.

c.

This policy would decrease the effect of inflation on real tax revenues, but would also have other effects. The income tax can tax the rich at a higher rate than the poor, but the sales tax rate is the same for rich and poor.

Dig Deeper 4.

a.

The end to the crisis depends on shifting the composition of taxes away from the inflation tax and toward other taxes. Workers are already paying the inflation tax.

b.

The central bank must make a credible commitment that it will no longer automatically monetize the government debt. Although a currency board would do this, it is a drastic and perhaps unnecessary step.

c.

Price controls may help, but price controls without other policy changes only cause distortions and are a recipe for failure.


188

5.

d.

A recession is not needed, but it may happen. Although nominal rigidities are less important during hyperinflations—a fact that implies that the sacrifice ratio is small—the issue of credibility remains. Unless firms and workers believe in the stabilization program, a severe recession may be the result.

e.

The statement has two components: (i) there is an ongoing fiscal deficit that the government is unable or unwilling to finance from nonmonetary sources, and (ii) the central bank is willing to monetize the debt. The order in which these issues are resolved ultimately depends on the political realities. The fiscal authority could eliminate the deficits. If it does not do so, the central bank could commit not to monetize government debt. However, this could drive the government into default on its bonds.

seignorage=(Y/P)(0.9-∆M/M)(∆M/M) Seignorage is maximized when ∆M/M=45%.

Explore Further 6.

Answers may vary depending upon when the website is accessed, but it is clear that a fall in oil prices would tend to increase the budget deficit in Venezuala. This would create the possibility of a hyperinflation if the government is unwilling or unable to finance itself and the central bank finances the deficit through money creation.


2.

3.

a. b. c. d. e. f.

g.

False. True/Uncertain. False. False. True. Uncertain. It may be wise for a government to commit not to negotiate with hostage takers as a means to deter hijackings, even recognizing that after a hijacking has taken place, there is a strong incentive to negotiate. However, the phrase “under no circumstances” is categorical. There may some circumstances under which a government might wish to violate its commitment. This statement, of course, illustrates the difficulty of precommitment. Can a government really commit not to negotiate, no matter what the circumstances, even if these circumstances may not have been imagined at the time the commitment was made? False.

a.

Inflation will increase in the fourth year.

b.

The President should aim for high unemployment early in the administration, to reduce inflation before the fourth year.

c.

The policies are not likely to achieve the desired the increase in output desired in the fourth year. Since people are forward-looking, expected inflation fourth year will account for the intentions of policymakers. If inflation equals expected inflation, unemployment equals the natural rate.

Answers will vary, but there is some discussion of this issue in the text.


189 4.

New Zealand wants to eliminate fears that the central bank might try to reduce unemployment below the natural rate with expansionary monetary policy and higher inflation. See Chapter 25 for a discussion of inflation targeting.

Dig Deeper 5.

6.

a.

et=0.5(D + R)

b.

The unemployment rate will be less than the natural rate. Inflation will be higher than expected.

c.

The unemployment rate will be greater than the natural rate. Inflation will be lower than expected.

d.

The results fit the evidence in Table 24-1 if one looks at the first two years of each administration, and not just the first year.

e.

The unemployment will equal the natural rate, because π = πe, and there will be high inflation.

The payoffs should be symmetrical, as written below. The table presented in the text leads to the same equilibrium, however. Welfare Cuts Yes

No

Defense

Yes

(R=1, D=1)

(R=-2, D=3)

cuts

No

(R=3, D=-2)

(R=-1, D=-1)

a.

If the Republicans cut military spending, the Democrats get 1 if they cut welfare, but 3 if they do not. So their best response is to vote against welfare cuts. The Republicans will get –2 in this case.

b.

If the Republicans do not cut military spending, the Democrats get –2 if they cut welfare, but –1 if they do not. So their best response is not to cut welfare. The Republicans will get –1 in this case.

c.

Given the answers above, the Republicans will not cut military spending, and the Democrats will not cut welfare. The two parties are locked in a bad equilibrium. They could make a deal: both vote for cuts. If they do, they will both be better off.

Explore Further 7.

Answers will vary.


a.

False.


190 b. c. d. e. f. 2.

3.

4.

False. False. False/Uncertain. Evidence suggests that people have money illusion, when would seem to imply that inflation would distort decision making. False. True. The capital gains tax is not indexed to inflation.

a.

Demand for M1 falls while demand for M2 is unchanged. People shift funds from savings accounts to time deposits.

b.

Demand for M1 increases as people transfer funds from money market funds to checking accounts. Demand for M2 remains unchanged.

c.

There is a shift in the composition of M1 (and consequently M2) as people hold more currency and make fewer trips to the bank while holding smaller checking account balances.

d.

The demand for M2 increases as the benefit of holding government securities falls.

a.

i. r=4%-0%=4%; ii. r=14%-10%=4%

b.

i. r=4%(1-0.25)-0%=3%; ii. r=14%(1-0.25)-10%=10.5%-10%=0.5%

c.

Given the deductibility of nominal mortgage interest payments, inflation is good for homeowners in the United States.

a.

The unemployment rate will remain equal to the natural rate.

b.

It is unlikely that the central bank will be able to hit its target every period. There will be surprises, and there are lags and uncertainty in policymaking.

c.

Changes in the natural rate will make it more difficult for the Fed to hits its target. It will be harder to distinguish changes in the actual rate of unemployment from changes in the natural rate of unemployment.

Dig Deeper 5.

Discussion question.

6.

b.

The IS curve slopes down, and the MP relation slopes up.

c.

An increase in government spending shifts the IS curve right, so output and the real interest rate rise.

d.

The MP relation shifts up. Output falls and the real interest rate increases.

a.

The MP relation shifts up. Output falls and the real interest rate increases.

b.

Since Y
c.

The MP relation shifts down. Output increases and the real interest rate falls.

7.


191 d.

Since Y>Yn, e rises. Inflation tends to move away from its target level. A value of a<1 makes no sense as part of the policy rule, because inflation would tend to move away from its target

Explore Further 8.

Answers will depend upon current Fed policy.


a. b. c. d. e. f. g.

True. False. Uncertain. False. False. False False

2.

a.

Interest payments are 10% of GDP, so the primary surplus is 10%-4%=6%.

b.

Real interest payments are (10%-7%)*100%=3% of GDP. So the inflation-adjusted surplus is 6%-3%=3%.

c.

Assume that last period unemployment was at the natural rate, so there has been a two percentage point increase in the unemployment rate over the last period. By Okun’s law (with a normal growth rate of 3%), output growth is lower by two percentage points. So, output is roughly two percent lower than it would have been. Using the rule of thumb in the text, the surplus is lower by 0.5*2%=1%. So the cyclically-adjusted, inflationadjusted surplus is 2%.

d.

The change in the debt to GDP ratio = (3%-2%)*100% - 3% = -2%. The debt to GDP ratio falls by 2% a year.

e.

In 10 years, the debt to GDP ratio will be 80%.

a.

The new interest rate is 10%+0.5*20%=20%. So assuming that expected depreciation was previously zero, the domestic interest rate increases from 10% to 20%.

b.

The real interest rate increases from 3% to 13%. The high real interest rate is likely to decrease growth.

c.

The official deficit increases from 4% to 14% of GDP. The inflation-adjusted deficit increases from –3% (a surplus) to 7% (a deficit).

d.

The change in the debt ratio = (13%-(-2%))*100%-3%=12%. It goes up very quickly.

e.

In this example, the worries were self-fulfilling.

3.

4.

First, even a temporary deficit leads to an increase in the national debt, and therefore to higher interest payments. This, in turn, implies continued deficits, higher taxes, or lower government


192 spending in the future. Second, the evidence does not support the Ricardian equivalence proposition. Third, if Ricardian equivalence did hold, then government spending would have the same effect on output regardless of whether it was financed by bonds (i.e., with a deficit) taxes. Thus, a deficit, per se, would not be needed to stimulate output. Fourth, war-time economies are already low-unemployment economies. There is no need for further stimulation by using deficits rather than tax finance. The only correct part of the statement is the first sentence. A deficit can be preferable to higher taxes during a war, but not for the reasons stated here.

Dig Deeper 5.

Discussion question. Also see the box on Social Security in Chapter 11 (p. 215).

6.

If financial market participants discount future dividends at the rate of interest on government bonds, then this economy will exhibit Ricardian equivalence. If there is a risk-premium applied to stocks, then this economy will not exhibit Ricardian equivalence. To see why, let τt be the dividend tax rate at time t and consider the pre-dividend stock price under a fixed sequence of expected dividends. $Qt = $Dt(1 - τt) + $Det+1(1 -τt+1)/(1 + i1t)+ . . . = [$Dt + $Det+1/(1 + i1t)+ . . .] - [$Dtτt + $Det+1τt+1/(1 + i1t) + . . .] The second term in brackets is the present discounted value of tax receipts for the government. To finance a given expenditure policy, the government must keep the PDV of tax receipts constant. Thus, for a given sequence of expected dividends, the timing of dividend taxes will not affect the stock price, consumption or investment. As a result, this economy will exhibit Ricardian equivalence. Note that, ex post, dividends will vary from their expected values, so taxes may be adjusted in the future. This new information could affect stock prices. In addition, note that the level of dividend taxes – the PDV of tax receipts – could affect stock prices. If stocks are assessed a risk premium (θ), however, so that they are discounted at rate i + θ, then the timing of dividend taxes will matter, because the government budget constraint will incorporate a different discount rate than the stock market price. As an example, suppose that i=0 forever but θ is positive. In this case, the government can assess taxes at any time with no consequence, but shifting taxes to the future will be favorable to holders of stocks. Since future dividends are uncertain, so are future tax payments – they might not have to be made if dividends turn out to be low. In this scenario, shifting taxes to the future would tend to increase the current stock price, and thus increase consumption and investment (if firms are liquidity constrained). So, Ricardian equivalence is violated.


Macroeconomics (ANSWER KEY TO CHAPTER PROBLEMS) by Olivier Blanchard

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