Respostas Macroeconomia Blanchard - 5ª Edição - Capítulos 2 a 9

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Respostas Blanchard 5 ed
Macroeconomia
Faculdade IBMEC (IBMEC)
61 pag.
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142 
ANSWERS TO END-OF-CHAPTER PROBLEMS 
 
CHAPTER 1 
 
Quick Check 
1. a. True. 
 b. True. 
 c. False. 
 d. 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 
 
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 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% 
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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. 
 
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 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. Theanswers 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. 
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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 
 
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 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] 
 
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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 Further9. 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. 
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 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. 
 
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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. 
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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). 
 
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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. 
 
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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. 
 
 
 
 
 
 
 
 
 
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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. 
 
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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. 
 
 
 
 
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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% 
 
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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 P
e 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 
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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 becausedisposable 
 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) 
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6. 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>P
e. Therefore, Pe rises and the AS 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. 
 
7. a. The LM has a flat segment at i=0 and then slopes up. 
 
b. The IS slopes down as before. 
 
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 supply 
does not affect the interest rate, it does not affect output. 
 
8. 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). 
 
 
 
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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/aF(u,z)x(1-a)/a 
 
 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. 
 
 
 
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161 
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 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 problemdid 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. 
 
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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. 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. 
 
 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%; π t+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% 
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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% 
 
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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 postsacrifice 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) 
 
 
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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. 
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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. 
 
 
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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. 
 
 
 
 
 
 
 
 
 
 
 
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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. 
 
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d. Uncertain. See the discussion of the golden-rule saving rate. 
 
e. Uncertain/False. It is likely that the U.S. rate is below the golden rulerate 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 in addition to the retirement of a 
previous generation. Thus, whether the U.S. “should” move to a pay-as-you-go system 
depends on the likely resolution of intergenerational distributional issues and your view 
about the equity of such a resolution. 
 f. Uncertain. The U.S. capital stock is below the golden rule, but that does not necessarily 
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. 
h. 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 long- 
 run 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 
would 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 would be 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. 
 
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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 
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result, in steady state, K/N = (0.158/.075)2=4.44, and Y/N=(4.55)1/2 =2.11. Steady-state 
output per worker increases by 26%. 
 
CHAPTER 12 
 
Quick Check 
1. a. True. 
 b. True. 
 c. False. In steady state, there is no growth of output per effective worker. 
 d. True. 
 e. 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. 
 f. True. 
 g. False. 
 h. 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. 
 
2. 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, at least for a 
while, 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 the appropriability of drug research. Presumably, there 
would be a reduction in R&D spending on new drugs, a reduction in the rate of 
technological progress, and a reduction in the growth rate. 
 
3. 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. 
 
 
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172 
Dig Deeper 
4. a. The growth rate of output per worker falls in the short runand 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. 
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 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% 
 
 
 
 
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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. 
 
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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