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ANSWERS TO END-OF-CHAPTER PROBLEMS CHAPTER 1 Quick Check 1. a. True. b. True. c. True. d. Uncertain. It is true that the growth of output per worker increased in the mid-1990s, but economists disagree about the degree to which this increase in growth will persist. The growth of output per worker fluctuates a great deal from year to year, which makes it difficult to draw inferences from the data. e. True. f. False. The European “unemployment miracle” refers to the low rate of unemployment in Europe in the 1960s. g. False. The slump was triggered by the collapse of the Japanese stock market. h. False. 2. a. 1960-2000 1994-2000 2001-2004 US 3.2% 3.9% 2.45% EU 3.1% 2.3% 2.3% Japan 4.7% 1.4% 2.3% Growth rates in all three regions are lower in the most recent period than over the period 1960-2004. However, compared to the period 1994-2000, U.S. growth is lower in the most recent period, Japanese growth is higher, and European growth is unchanged. b. Answers will vary. 3. a. Low unemployment might lead to an increase in inflation. b. Tax cuts may have been useful to stimulate the U.S. economy during the 2001 recession. However, the tax cuts were permanent. The recession is over and the deficit remains high. c. Although labor market rigidities may be important, it is also important to consider that these rigidities may not be excessive, and that high unemployment may arise from flawed macroeconomic policies. d. Although poor regulation of the financial system may be contributing to the length of Japans slump, most economists believe that the collapse in Japanese asset prices triggered the economic downturn. Moreover, tightening regulation would likely involve more pain in the short run since some banks and firms would be forced to close. e. 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 4. This is a discussion question, so answers will vary. Based on the discussion in the text, there are clear similarities in the policy responses of the U.S. and Japanese governments. Central banks in both countries reduced interest rates, and governments in both countries tried to stimulate the economy with lower taxes. Government spending also increased in both countries; explicitly for economic stimulus in Japan, and as part of foreign and security policy in the United States. As for the differences, the text leaves the implication that Japanese banking system is less efficient than the U.S. banking system, which perhaps allows for easier recovery in the United States. There is also an allusion to the liquidity trap in Japan, since interest rates are zero. However, the mechanics of the liquidity trap are not discussed in detail until Chapter 22. 5. a. 10 years: (1.01)101.10 or 10 % higher; 20 years: 22% higher; 50 years: 64% higher b. 22%; 49%; 169% higher c. Take output per worker as a measure of the standard of living. 10 years: 1.22/1.1 1.11, so the standard of living would be about 11% higher; 20 years: 22% higher; 50 years: 64% higher d. No. Labor productivity growth fluctuates a lot from year to year. The last few years may represent good luck. Some economists believe there has been a lasting change in the U.S. economy that will lead to continued high productivity growth in the future, but we cannot be certain. 6. China overtakes the United States in 2044, or 41 years from 2003 The problem asks students to find the answer by using a spreadsheet. Algebraically, 11(1.03)t=1.6(1.08)t 11/1.6 = (1.08/1.03)t t = ln(11/1.6)/ln(1.08/1.03) 40.7 yrs Explore Further 7. a-c. As of June 2005, there have been 5 recessions since 1960. The numbers are seasonally- adjusted annual percentage growth rates of GDP in chained 2000 dollars. 1969:4 -1.9 1980:2 -7.8 1 1970:1 -0.7 1980:3 -0.7 1974:3 -3.8 1981:4 -4.9 1974:4 -1.6 1982:1 -6.4 1975:1 -4.8 1990.4 -3.0 1991:1 -2.0 8. a-b. % point increase in unemployment rate for the 5 recessions 1969-70 0.7 1981-82 1.1 1974-75 3.1 1990-91 0.9 1980 0.9 Jan. 2001 Jan. 2002 1.5 CHAPTER 2 Quick Check 1. a. False. b. Uncertain. True for nominal GDP, false for real GDP. c. True. d. True. e. False. The level of the CPI means nothing. Its rate of change tells us about inflation. f. Uncertain. Which index is better depends on what we are trying to measureinflation faced by consumers or by the economy as a whole. 2. a. no change: intermediate good 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. $1,000,000, the value of the silver necklaces. b. 1st Stage: $300,000. 2nd Stage: $1,000,00- $300,000=$700,000. GDP: $300,000+$700,000=$1,000,000. c. Wages: $200,000 + $250,000=$450,000. Profits: ($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. 2003 GDP: 10*$2,000+4*$1,000+1000*$1=$25,000 2004 GDP: 12*$3,000+6*$500+1000*$1=$40,000 Nominal GDP has increased by 60%. b. 2003 real (2003) GDP: $25,000 2004 real (2003) GDP: 12*$2,000+6*$1,000+1000*$1=$31,000 Real (2003) GDP has increased by 24%. c. 2003 real (2004) GDP: 10*$3,000+4*$500+1,000*$1=$33,000 2004 real (2004) GDP: $40,000. Real (2004) 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. 2003 base year: Deflator(2003)=1; Deflator(2004)=$40,000/$31,000=1.29 Inflation=29% b. 2004 base year: Deflator(2003)=$25,000/$33,000=0.76; Deflator(2004)=1 Inflation=(1-0.76)/0.76=.32=32% c. Analogous to 4d. 6. a. 2003 real GDP = 10*$2,500 + 4*$750 + 1000*$1 = $29,000 2004 real GDP = 12*$2,500 + 6*$750 + 1000*$1 = $35,500 b. (35,500-29,000)/29,000 = .224 = 22.4% c. Deflator in 2003=$25,000/$29,000=.862 Deflator in 2004=$40,000/$35,500=1.127 Inflation = (1.13 -.86)/.86 = .307 = 30.7%. 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 due to constant improvements in medical technology. b. 10%. c. The quality-adjusted price of checkups is 5% higher. The remaining 10% of the price increase reflects a quality improvement. d. We need to know the price of checkups using the old method in the year the new ultrasound information is introduced. Even without this information, we can say that the quality-adjusted price increase of checkups is less than 15%, since there has been some quality improvement. 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. True GDP should increase by less than $22 because by working for an extra hour, you are no longer producing the work of cooking within the house. Since cooking within the house is a final service, it should count as part of GDP. Unfortunately, it is hard to measure the value of work within the home, which is 2 why measured GDP does not include it. If we assume, for this problem, that the value of home cooking is equal to the value of restaurant cooking, and that eating out simply replaces home cooking, then working late increases true GDP by only the value of the work, in this case $12. 9. a. As of revisions through June 2005, there were 3 quarters of negative growth during the period 1999-2002. The numbers are seasonally-adjusted annual percentage growth rates of GDP in chained 2000 dollars. 2000:3 -0.5 2001:1 -0.5 2001:3 -1.4 b. The unemployment rose in 2001 and continued to rise until mid- 2003, when it began to fall. Unemployment is not the whole story because discouraged workers may leave the labor force and thus not be counted as unemployed. The participation rate fell over 2001, and continued to all (albeit more slowly and with substantial monthly variation) over the period. c. Although we graph employment against time in this problem (since the book does not use logarithms), the result would be similar if we used a logarithmic scale. From the graph, employment growth was negative over 2001. Then, employment growth continued at roughly the same rate (perhaps lower, as would be clear with a logarithmic scale) as before the recession. In other words, employment did not rapidly catch up to its previous trajectory. Indeed, as of June 2005, the graph is consistent with a permanent, negative effect on employment. The employment to population ratio fell by about 1.5 percentage points over 2001 and continued to fall until August, 2003, when it leveled off and then rose slightly. d. Clearly, the labor market recovered much more slowly than GDP. CHAPTER 3 Quick Check 1. a. True. b. False. Government spending without transfers was 19% of GDP. c. False. The propensity to consume must be less than one for our model to be well defined. d. True. e. False. f. False. The increase in output is one times the multiplier. g. False. 2. a. Y=160+0.6*(Y-100)+150+150 Y=1000 b. YD=Y-T=1000-100=900 c. C=160+0.6*(900)=700 3. a. Equilibrium output is 1000. Total demand=C+I+G=700+150+150=1000. Total demand equals production. This is the equilibrium condition used to solve for output. b. Output falls by: 40*multiplier = 40/.4=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 (or in short, saving) equals private plus public saving, or 150. National saving equals investment. This statement is mathematically equivalent to the equilibrium condition that total demand equals production. Thus, national saving equals investment is an alternative statement of the equilibrium condition. Dig Deeper 4. a. Y increases by 1/(1-c1) b. Y decreases by c1/(1- c1) c. The answers differ because government spending affects demand directly, but taxes affect demand 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 on 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. 3 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. So, output tends to vary less, and 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 c. Both Y and T decrease. d. If G is cut, Y decreases even more, so the balanced budget reinforces (or amplifies) the effect of the fall in consumer confidence. 7. a. Disposable income and hence consumption both increase for any level of Y, so the ZZ curve shifts up, and equilibrium output increases. b. There is no effect on equilibrium output, since T does not change. c. Presumably, equilibrium output increases. The fall in consumption from the tax increase is smaller in magnitude than the increase in consumption from the transfer increase, because of the difference in the propensities to consume. So, demand and equilibrium output increase. d. People with high wealth probably have a lower propensity to consume than people with low wealth. At the extreme, those in poverty may spend most of any additional dollar on basic needs. Since wealth and income are usually related, people with high income probably have a lower propensity to consume than people with low income. Therefore, tax cuts are likely to be more effective at stimulating output when they are directed toward people with low income, who are likely to spend more of the extra disposable income. 8. a. Y= c0 + c1(Y-T) + b0+b1Y + G Y=1/(1- c1- b1)*c0 - c1T + b0 + G b. The multiplier is 1/(1- c1- b1), and increases with b1. Allowing investment to depend on output increases the multiplier. Intuitively, an increase in autonomous spending now has a multiplier effect through two channels, consumption and investment, so the multiplier increases. For the multiplier to be positive, we need c1+ b11. If this inequality were reversed, the economy would not have a well-defined equilibrium. One extra unit of autonomous spending would lead to a greater than one unit increase in spending (consumption plus investment) in every round of the multiplier, so the economy would explode into infinite output. c. Equilibrium output increases. Investment increases by more than the increase in business confidence, since the increase in output also leads investment to increase. In equilibrium, national saving equals investment. If investment increases in equilibrium, then so does national saving. 9. Answers will vary depending upon when the website is accessed. CHAPTER 4 Quick Check 1. a. False. b. False. c. True. d. False. e. False. f. True. 2. a. i=0.05: Money demand = $18,000 i=0.10: Money demand = $15,000 b. Money demand decreases when the interest rate increases because bonds, which pay interest, become more attractive. For the same reason, bond demand increases. c. The demand for money falls by 50%. d. The demand for money falls by 50%. e. A 1% increase (decrease) in income leads to a 1% increase (decrease) in money demand. This effect is independent of the interest rate. 3. a. i=100/$PB 1; i 33%; 18%; 5% when $PB =$75; $85; $95. b. When the price increases, 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) An increase in the interest rate of 10% increases bond demand 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. 4 d. When people earn more income, this does not change their wealth right away. Thus, they increase their demand for money and decrease their demand for bonds. 6. An increase in the interest rate makes the purchase of bonds more attractive because it reduces their price. A purchaser of a bond can receive the same nominal payment for a lower price. 7. a. $16 is withdrawn on each trip to the bank. Money holdingsday one: $16; day two: $12; day three: $8; day four: $4. b. Average money holding is ($16+$12+$8+$4)/4=$10. c. $8 dollar withdrawals. Money holdings of $8; $4; $8; $4. d, Average money holdings is $6. e. $16 dollar withdrawals; money holdings of $0; $0; $0; $16. f. Average money holding is $4. g. Based on these answers, ATMs and credit cards have reduced money demand. 8. a. velocity=1/(M/$Y)=1/L(i) b. Velocity increased from 3.7 to 9.1 between 1960 and 2003. c. ATMS and credit cards reduced L(i) so velocity increased. 9. a. Demand for central bank money=0.1*$5,000b*(.8-4i) b. $100 b = 0.1*$5,000b*(.8-4i) i=15% c. M=(1/.1)*$100 b=$1,000 b M= Md at the interest derived in part (b). d. If H increases to $300 b, the interest rate falls to 5%. e. The interest rate falls to 5%, since when H equals $300 b, M=(1/.1)*$300 b=$3,000 b. 10. The ratio of currency to total money (the parameter c in the text) would rise, leading to a fall in the money multiplier. Explore Further 11. Answers will vary depending upon when the website is accessed. CHAPTER 5 Quick Check 1. a. True. b. True. c. False. d. False. The balanced budget multiplier is positive (it equals one), so the IS curve shifts right. e. False. f. Uncertain. An increase in G leads to an increase in Y (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*M/P)/d2 +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 is big if b1 is big, b2 is small, d1 is small, and/or d2 is big, i.e., if investment is very sensitive to Y, investment is not very sensitive to i, money demand is not very sensitive to Y, money demand is very sensitive to i. 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 2c: Y=1/(1-c1-b1+ b2d1/d2)*c0-c1T+ b0+(b2*M/P)/d2 +G c. From the LM relation: i= Y*d1/d2 (M/P)/d2 To obtain the equilibrium interest rate, substitut
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