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# Exercícios resolvidos, macroeconomia Olivier Blanchard

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Resolução dos exercícios da 5º edição em inglês.

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### Exercícios resolvidos, macroeconomia Olivier Blanchard

2. 2. 143 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. control has been important in managing the pace of the transition and in protecting property rights 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: 1.318/1.195=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 6 recessions (according to the traditional definition) since 1960, but 8 recessions according the NBER recession dating. Seasonally-adjusted annual percentage growth rates of GDP (in chained 2000 dollars) are given below. 1969:4 -1.9 1981:4 -4.9 1970:1 -0.6 1982:1 -6.4 1974:3 -3.8 1990:4 -3.5 1974:4 -1.6 1991:1 -1.9 1975:1 -4.8 2008:3 -2.7 1980:2 -7.9 2008:4 -5.4 1980:3 -0.7 2009:1 -6.4 2009:2 -0.7 With respect to the note on 2001, the growth rates for 2001 are given below. 2001:1 -1.3% 2001:2 2.6%
3. 3. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 144 2001:3 -1.1% 2001:4 1.4% The other NBER recession was dated April 1960 to February 1961. Real growth rates are as follows. 1960:2 -1.9% 1960:3 0.7% 1960:4 -5.0% 1961:1 2.4% 7. a-b.% point increase in the unemployment rate for the 6 traditional recessions 1969-70 0.7 1981-82 1.1 1974-75 3.1 1990-91 0.9 1980 0.6 2008-09 3.7 The unemployment rate increased by 1.5 percentage points between January 2001 and December 2001. CHAPTER 2 Quick Check 1. a. True. b. 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. c. False. d. True. e. False. The level of the CPI means nothing. The rate of change of the CPI is one measure of inflation. f. Uncertain. Which index is better depends on what we are trying to measure—inflation faced by consumers or by the economy as a whole. g. False. The underground economy is large, but by far the majority of the measured unemployed in Spain are not employed in the underground economy. 2. 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. 3. 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.
4. 4. 145 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 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. 4. 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%. 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. 5. 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. 6. 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.
5. 5. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 146 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 ultra- sounds 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. 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 took several years after the recession for the labor market to recover. CHAPTER 3 Quick Check 1. a. True. b. False. Government spending excluding transfers was 19% of GDP. c. False. The propensity to consume must be less than one for our model to make sense. d. True. e. False. f. False. The increase in equilibrium output is one times the multiplier. g. False. 2. a. Y=160+0.6(Y-100)+150+150 Y=1000
6. 6. 147 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. b. YD=Y-T=1000-100=900 c. C=160+0.6(900)=700 3. 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. c. Private saving=Y-C-T=900-160-0.6(800)-100=160. Public saving =T-G=-10. National 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. 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. 5. 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. 6. a. Y=[1/(1-c1+c1t1)][c0-c1t0+I+G] b. T = t0 + t1[1/(1-c1+c1t1)][c0-c1t0+I+G]
7. 7. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 148 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. 7. 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 propensity to consume for the economy as a whole. 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 low- income taxpayers. 8. 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. 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. 10. Answers will vary depending on when students visit the website. CHAPTER 4 Quick Check 1. a. False.
8. 8. 149 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. b. False. c. 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. d. True. e. False. f. False. g. True. h. True. 2. 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. 3. 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 4. 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.
9. 9. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 150 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. c. \$8 is withdrawn on each trip to the bank. Money holdings are \$8, \$4, \$8, and \$4. 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. 8. 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. 9. 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. CHAPTER 5 Quick Check 1. a. True. b. True. c. False.
10. 10. 151 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. d. False. The balanced budget multiplier is positive (it equals one), so the IS curve shifts right. e. False. f. 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). g. True. 2. a. Y=[1/(1-c1)][c0-c1T+I+G] The multiplier is 1/(1-c1). 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).
11. 11. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 152 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<b2d1/d2. 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). 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.
12. 12. 153 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. d. The increase in 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. 7. 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). 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. 8. 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. 9. a. The IS curve shifts left. Output and the interest rate fall. 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 intended federal funds rate by 25 basis points. Subsequent changes in federal funds rate over the period 1993-2000 are given below.
13. 13. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 154 Changes in the Intended Federal Funds Rate September 4, 1992 3 March 25, 1997 5.5 February 4, 1994 3.25 September 29, 1998 5.25 March 22, 1994 3.5 October 15, 1998 5 April 18, 1994 3.75 November 17, 1998 4.75 May 17, 1994 4.25 June 30, 1999 5 August 16, 1994 4.75 August 24, 1999 5.25 November 15, 1994 5.5 November 16, 1999 5.5 February 1, 1995 6 February 2, 2000 5.75 July 6, 1995 5.75 March 21, 2000 6 December 19, 1995 5.5 May 16, 2000 6.5 January 31, 1996 5.25 d. In real terms, investment was 11.9% of GDP in 1992 and increased every year over the period to reach 17.6% of GDP in 2000. e. Over the period 1993-2000, the average annual growth rate of GDP per person was 2.6%. Over the period first four years of the period, the average annual growth rate was 2%; over the second four years, the average annual growth rate was 3.2%. 11. a. Growth was negative in 2000:III, 2001:I, and 2001:III. 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. CHAPTER 6 Quick Check 1. a. False. The participation rate has increased over time. b. False. c. False. d. True. e. False. f. Uncertain/False. The degree of bargaining power depends on the nature of the job and the employee’s skills.
14. 14. 155 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. g. True. h. False. 2. 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 1/0.45 or 2.2 months. d. (3+2.8+1.4+1.4)/(122+6.2)=7%. e. new workers: 0.4/(3+1.4)=9%. 3. a. W/P=1/(1+)=1/1.05=0.952 b. Wage setting: u=1-W/P=1-0.952=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 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. 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. 5. 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.
15. 15. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 156 6. 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. 7. a. EatIn EatOut Population 100 Population 100 Labor Force 75 Labor Force 100 Employment 50 Employment 75 Unemployment 25 Unemployment 25 Unemployment Rate 33% Unemployment Rate 25% Participation Rate 75% Participation Rate 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 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 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 value- added, 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 = 3% b. 55% c. second month: (0.55)2 =30%; sixth month: (0.55)6 = 3% d. 1996: 17% 2000: 11% 1997: 16% 2001: 12% 1998: 14% 2002: 18% 1999: 12% 2003: 22%
16. 16. 157 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 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. CHAPTER 7 Quick Check 1. a. True. b. True. In the AS relation, if P=Pe , Y=Yn. Note that Pe must be known to graph the AS curve. c. 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. d. 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. e. True. f. False. Fiscal policy affects the interest rate in the medium run and therefore affects investment. g. 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. 2. 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. 3. a. SR: short run WS: wage-setting curve MR: medium run PS: price-setting curve WS PS AS AD LM IS b. i P 4. 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 WS PS AS AD IS LM SR up no change up no change no change up MR same as SR no change up further no change no change up further Y i P SR falls rises rises MR falls further rises further rises further
17. 17. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 158 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 WS PS AS AD LM IS b-c. In the medium run, consumption must lower than its original level because disposable income is unchanged, but consumer confidence is lower. 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. IS LM AD AS SR left down left no change MR same as SR down further same as SR down Y i P SR falls falls falls MR back to original Yn falls further falls further C I Private S SR falls ambiguous ambiguous MR Increases from SR but still lower than original level rises (above original level) rises (above original level)
19. 19. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 160 9. 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, but after-tax income rises. c. In our model, the real wage depends only on 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/a F(u,z)x(1-a)/a c. The AS curve slopes up in Y-P space. d. If P= Pe , then 1=(1+)1/a F(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.
20. 20. 161 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 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, short- run 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. 13. a. 1959:IV – 1969:IV 53.1% 1969:IV – 1979:IV 38.1% 1979:IV – 1989:IV 34.9% 1989:IV – 1999:IV 38.6% 1999:IV – 2009:IV 19.5% 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. 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. 1959:IV – 1969:IV 34.0% 1969:IV – 1979:IV 24.4% 1979:IV – 1989:IV 22.8% 1989:IV – 1999:IV 22.7% 1999:IV – 2009:IV 8.7% CHAPTER 8 Quick Check 1. a. True. b. False. c. False. d. True. e. False. f. 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.
21. 21. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 162 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. 3. a. un=0.1/2 =5% b. πt =0.1-2(0.03) = 4% every year beginning with year t. c. πe t= 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. f. Inflation expectations will again be forever wrong. This is unlikely. 4. a. 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%. 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%; πt+3 = 16% d. As indexation increases, inflation becomes more sensitive to the difference between the unemployment rate and the natural rate. 6. 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. 7. a. =1: uu=6%; =2: uu=3%
22. 22. 163 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 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 8. a-d. 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%. 9. The relationships imply a lower natural rate in the more recent period. CHAPTER 9 Quick Check 1. a. False. The unemployment rate rises when output growth is less than the normal rate and falls when output growth is greater than the normal rate. b. True. c. True. d. 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. e. False. In the medium run, inflation equals adjusted money growth, which is the difference between nominal money growth and output growth. f. True. g. Uncertain. In principle, the statement is true, but nominal rigidities may make even fully credible policy costly. h. True. i. True. 2. 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%) 3. a. un= 5%
23. 23. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 164 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. π u gyt gmt t-1: 8% 5% 3% 11% t: 4% 9% -7% -3% t+1: 4% 5% 13% 17% t+2: 4% 5% 3% 7% t+3: 4% 5% 3% 7% 4. 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. 5. a. Inflation will start increasing. b. It should let unemployment increase to its new, higher, natural rate. Dig Deeper 6. 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. 7. a. πt-πt-1= -(ut-.05) ut- ut-1= -0.4(gmt-πt-.03)
24. 24. 165 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. b. Assuming gm,t-1=13%, πt-1= 10%, ut-1=5%, and beginning in year t, gm=3%, the economy evolves as follows. π u t: 7.1% 7.9% t+1: 3.1% 9.1% t+2: -0.7% 8.8% t+3: -3.2% 7.5% t+4: -4.1% 5.9% t+5: -3.5% 4.4% t+6: -2.1% 3.6% t+7: -0.5% 3.4% t+8: 0.8% 3.7% t+9: 1.5% 4.3% t+10: 1.6% 4.9% c. 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. d. u=5% and π=0% in the medium run. Explore Further 8. 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. 9. a. Yes. b. The levels of employment and unemployment can both rise if the participation rate increases. CHAPTER 10 Quick Check 1. a. True. b. False. c. False.
25. 25. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 166 d. False. e. True. f. False. g. True. 2. The table should read as follows. Food Transportation Services Price Quantity Price Quantity Mexico 5 pesos 400 20 pesos 200 United States \$1 1,000 \$2 2,000 a. U.S. consumption per person = \$1(1000) + \$2(2,000)=\$5000 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 3. 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.
26. 26. 167 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. Dig Deeper 4. 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. 5. 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. a. Japan tended to converge to the United States in the earlier period, but not in the recent periods. b. Had Japan and the United States maintained their growth rates from the earlier period, Japan would have surpassed the United States in output per person some time ago. Instead, output per person remains substantially higher in the United States. per person (\$34,875) was substantially higher than Japanese real output per person (\$24,037). 7. a. There was substantial convergence for the France, Belgium, and Italy until the last two decades. Since then, the standard of living of these countries relative to the U.S. standard of living has fallen somewhat. b. Argentina, Chad, Madagascar, and Venezuela have not converged to the United States. In fact, they have grown steadily poorer relative to the United States. 8. Real GDP per Capita (\$2005), PPP adjusted Source: Alan Heston, Robert Summers and Bettina Aten, Penn World Table (PWT) Version 6.3, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania, August 2009.
27. 27. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 168 a. 10 Richest Countries (in the data sample) in 1970 Kuwait 97813.29 Qatar 79230.89 Brunei 58050.13 Libya 37391.52 Palau 28583.66 Bermuda 26084.11 Switzerland 24605.51 Luxembourg 22906.31 Saudi Arabia 22273.17 Bahrain 21409.55 b. 10 Richest Countries (in the data sample) in 2007 Qatar 88292.58 Luxembourg 77783.50 United Arab Emirates 51346.98 Brunei 50575.44 Macao 50543.23 Bermuda 48868.23 Norway 48392.99 Singapore 44618.95 Hong Kong 43121.49 United States 42886.92 c-d. Equatorial Guinea has grown the most (1393%) over the period, with China (using the PWT preferred version 2) second at 889%. (Note that using the PWT China version 1, which more closely mirrors Chinese official statistics, China’s growth over the period is 1414%.) Liberia has grown the least (-79%). There are 162 countries with observations for both 1970 and 2007. 31 of these countries had negative growth over the period. CHAPTER 11 Quick Check 1. a. True, in a closed economy, and if saving includes public and private saving. b. False. c. 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 steady- state 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.
29. 29. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 170 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. 7. 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 f. Y/N =(s/)1/2 g. Y/N = 2 h. Y/N = 21/2 8. 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 Y/N t 1.00 1.00 t+1 0.90 0.97 t+2 0.82 0.93 t+3 0.75 0.91 9. 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 2008, the national saving rate was approximately 12.6%. In steady state, K/N = (0.126/0.075)2 =2.82, and Y/N=(3.25)1/2 =1.68. b. For fiscal year 2008, the budget deficit (including the off budget items) was 3.2% of GDP. (We’ll use the fiscal year budget deficit with the calendar year saving rate.) Eliminating the deficit increases the national saving rate to 15.8% (12.6% + 3.2%). As a
31. 31. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 172 Dig Deeper 4. 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. 5. 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 inflation=20% 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. 6. a. i. K/(AN) = (s/(+gA+gN))2 = 1 ii. Y/(AN)= (K/AN)1/2 =1 iii. gY/(AN) = 0 iv. gY/N = gA=4% v. gY = gA+gN=6% b. i. K/(AN) = (s/(+gA+gN))2 = 0.64 ii. Y/(AN)= (K/AN)1/2 =0.8 iii. gY/(AN) = 0 iv. gY/N = gA=8% v. 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.
32. 32. 173 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. c. i. K/(AN) = (s/(+gA+gN))2 = 0.64 ii. Y/(AN)= (K/AN)1/2 =0.8 iii. gY/(AN) = 0 iv. gY/N = gA=4% v. gY = gA+gN=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. 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, then 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 be higher 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. gY – gN gA gK – gN U.S. 1.8% 2.0% 1.4% France 3.2% 3.1% 3.4% Japan 4.2% 3.8% 5.0% UK 2.4% 2.6% 2.0%
33. 33. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 174 CHAPTER 13 Quick Check 1. a. 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. b. False. c. True. d. True. e. True. f. True. g. False. 2. 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. 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 to 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.
34. 34. 175 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 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). 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. 7. 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. MC=W/MPL so W/P=MPL/(1+) d. Labor demand slopes down. As N increases, the MPL falls, so W/P falls. e. An improvement in technology increases the MPL, so the labor demand curve shifts right. The real wage increases when technology improves. 8. 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. a. Projections for job decline from 2008-2018 Some examples: Stock clerks and order fillers – technological change Electrical and electronic equipment assemblers – perhaps foreign competition b. Projections for job growth from 2008-2018 Some examples: Home health aides – aging of the population Computer software engineers, applications – technological change c. More of occupations that are forecast to grow require degrees as opposed to on-the-job training.
35. 35. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 176 d. Many occupations that are forecast to decline require only short-term on-the-job training. 10. 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; 2008: \$8:30 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. CHAPTER 14 Quick Check 1. a. True. b. True. c. True. d. False. e. True. f. False. g. True. h. True. The nominal interest rate is always positive. i. False. The real interest rate can be negative. 2. 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. 3. a. exact: r = (1+.04)/(1+.02)-1 = 1.96%; approximation: r .04-.02 = 2% b. 3.60%; 4% c. 5.48%; 8% 4. 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.
36. 36. 177 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. d. Answers will vary. 5. 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/(1+i)] - \$z. 10 years: \$575.90; 20 years: \$836.49; 30 years: \$936.96; 60 years: \$996.39 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 one- for-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.
37. 37. Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 178 c. Output increases. The nominal interest rate is higher than in Figure 14-4. 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 14-4. 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. CHAPTER 15 Quick Check 1. a. False. b. True. c. True. d. False. e. True. f. True. g. False. h. Uncertain/False. Some of the increase in the stock market was probably justified. But most economists believe that there was a bubble in the stock market as well. A stock market correction followed. 2. 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% 3. 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% 4. a. The LM curve shifts down unexpectedly. There isan 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.
38. 38. 179 Copyright © 2009 Pearson Education, Inc. Publishing as Prentice Hall. 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 it Dig Deeper 5. 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. 6. 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. 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