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1.(a)S d –6000 4000r 0.8Y. (b) When Y 10,000, r 0.05. When Y 10,200, r .03. (c) When G 2400, desired saving becomes S d –6400 4000r 0.8Y. S d is now 400 less for any given r and Y. Setting S d I d, we get 8000r 8800 – 0.8Y. Similarly, using the equation that goods supplied equals goods demanded gives the same anwer. At Y 10,000, r 0.10. The market-clearing real interest rate increases from 0.05 to 0.10. Thus the IS curve shifts up and to the right from IS1 to IS2 in Figure 9.19. Figure 9.19 2.(a) Setting MS=MD: r –0.02 (Y/100,000). When Y 8000, r 0.06. When Y 9000, r 0.07. These points are plotted as line LMa in Figure 9.20. Figure 9.20 (b) M 6600, r –0.05 (Y/100,000). When Y 8000, r 0.03. When Y 9000, r 0.04. The LM curve is shifted down and to the right from LMa to LMb in Figure 9.20, since the same level of Y gives a lower r at equilibrium. (c)Setting MS=MD: r – 0.03 (Y/100,000). When Y 8000, r 0.05. When Y 9000, r 0.06. The LM curve is shifted down and to the right from LMa to LMc in Figure 9.20, since there is a higher real interest rate for every given level of output. The LM curve shifts down and to the right by one percentage point (the increase in e ) because for any given Y, the same nominal interest rate clears the asset market. With an unchanged nominal interest rate, the increase in e is matched by an equal decrease in r. 3. (a) Similar to quesiton2: use S d Y – C d – G and S d I d for the IS curve so Y (960 2.5G) – 2500r. When G 196, this is Y 1450 – 2500r. the LM curve: Setting money demand equal to money supply so Y 19,780/P 50 500 r. With full-employment output of 1000 solving for r gives r 0.18. Using Y 1000 and r 0.18 solving for P gives P 23. Plugging these results into the consumption and investment equations gives C 694 and I 110. (b) With G 216, r .20, P 23.27, C 684, and I 100. 4. (a) First, look at labor market equilibrium. Labor supply is NS 55 10(1 – t)w. Labor demand (ND) comes from the equation w 5A – (0.005A ND). Substituting the latter equation into the former, and equating labor supply and labor demand gives N 100. Using this in either the labor supply or labor demand equation then gives w 9. Using N in the production function gives Y 950. (b) Next, look at goods market equilibrium and the IS curve. S d Y – C d – G and S d I d gives So r (542.5 G)/450 – 0.004/3Y. When G 50, this is r 1.317 – 0.004/3 Y. With full-employment output of 950, r 0.05. C 654 and I 246. (c) Next, look at asset market equilibrium and the LM curve. Setting money demand equal to money supply r r [0.5Y – (5 9150/P)]/250. With Y 950 and r 0.05, solving for P gives P 20. (d) With G 72.5, r 1.367 – 0.004/3 Y. With Y 950, r .10, P 20.56, C 644, I 233.5. The real wage, employment, and output are unaffected by the change. 5. The IS curve is found by setting Setting S d I d. Desired saving is S d Y – C d – G Y – [1275 0.5(Y –T) – 200r] – G. gives Y – [1275 0.5(Y – T) – 200r] – G 900 –200r, or Y 4350 – 800r 2G – T. The LM curve is M/P L 0.5Y – 200i 0.5Y – 200(r ) 0.5Y – 200r. (a) T G 450, M 9000. The IS curve gives Y 4800 – 800r. The LM curve gives 9000/P 0.5Y – 200r. To find the aggregate demand curve, LM: 9000/P 0.5Y – 200r. Multiplying by 4 gives 36,000/P 2Y – 800r. Rearranging gives 800r 2Y – 36,000/P. IS: Y 4800 – 800r. Rearranging gives 800r 4800 – Y. Setting the right-hand sides of these two equations to each other (since both equal 800r) gives: 2Y – (36,000/P) 4800 – Y, or 3Y 4800 (36,000/P), or Y 1600 (12,000/P); this is the AD curve. With Y 4600 at full employment, the AD curve gives 4600 1600 (12,000/P), or P 4. From the IS curve Y 4800 – 800r, so 4600 4800 – 800r, or 800r 200, so r 0.25. Consumption is C 1275 0.5(Y – T) – 200r 1275 0.5(4600 – 450) – (200 × 0.25) 3300. Investment is I 900 – 200r 900 – (200 × 0.25) 850. (b) Following the same steps as above, with M 4500 the aggregate demand curve AD: Y 1600 (6000/P). With Y 4600, this gives P 2. Nothing has changed in the IS equation, so it still gives r 0.25. And nothing has changed in either the consumption or investment equations, so we still get C 3300 and I 850. Money is neutral here, as no real variables are affected and the price level changes in proportion to the money supply. (c) T G 330, M 9000. The IS curve is Y 4350 – 800r 2G – T 4350 – 800r (2 330) – 330 4680 – 800r. LM: 36,000/P 2Y – 800r, or 800r 2Y – 36,000/P. IS: Y 4680 – 800r, or 800r 4680 – Y. AD: 2Y – (36,000/P) 4680 – Y, or (36,000/P) 4680 3Y, or Y 1560 (12,000/P). With Y 4600 at full employment, the AD curve gives 4600 1560 (12,000/P), or P 3.95. From the IS curve, Y 4680 – 800r, so 4600 4680 – 800r, or 800r 80, so r 0.10. Consumption is C 1275 0.5(Y – T) – 200r 1275 0.5(4600 – 330) – (200 0.10) 3390. Investment is I 900 – 200r 900 – (200 0.10) 880. 6. (a) A 2, f1 5, f2 0.005, n0 55, nw 10, c0 300, cY 0.8, cr 200, t0 20, t 0.5, i0 258.5, ir 250, l0 0, lY 0.5, lr 250. (b) These values are all calculated directly, using the equations in the Appendix. They should match the results in Numerical Problem 4, above. (c) See the answer to part b. Analytical Problems 1. (a) The increase in desired investment shifts the IS curve up and to the right, as shown in Figure 9.21. The price level rises, shifting the LM curve up and to the left to restore equilibrium. Since the real interest rate rises, consumption declines. In summary, there is no change in the real wage, employment, or output; there is a rise in the real interest rate, the price level, and investment; and there is a decline in consumption. Figure 9.21 (b) The rise in expected inflation shifts the LM curve down and to the right, as shown in Figure 9.22. The price level rises, shifting the LM curve up and to the left to restore equilibrium. Since the real interest rate is unchanged, consumption and investment are unchanged. In summary, there is no change in the real wage, employment, output, the real interest rate, consumption, or investment; and there is a rise in the price level. Figure 9.22 (c) The increase in labor supply is shown as a shift in the labor supply curve in Figure 9.23 (a). This leads to a decline in the real wage rate and an increase in employment. The rise in employment causes an increase in output, shifting the FE line to the right in Figure 9.23 (b). To restore equilibrium, the price level must decline, shifting the LM curve down and to the right. Since output increases and the real interest rate declines, consumption and investment increase. In summary, the real wage, the real interest rate, and the price level decline; and employment, output, consumption, and investment rise. Figure 9.23 (d) The reduction in the demand for money gives results identical to those in part (b). 2. The increase in the price of oil reduces the marginal product of labor, causing the labor demand curve to shift to the left from ND1 to ND2 in Figure 9.24. Since households’ expected future incomes decline, labor supply increases, shifting the labor supply curve from NS1 to NS2 (but by assumption, the shift to the left in labor demand is larger than the shift to the right in labor supply). At equilibrium, there is a reduced real wage and lower employment. The productivity shock results in a shift to the left of the full-employment line from FE1 to FE2 in Figure 9.25, as both employment and productivity decline. Because the shock is permanent, it reduces future output and reduces the future marginal product of capital, both of which result in a downward shift of the IS curve. The new equilibrium is located at the intersection of the new IS curve and the new FE line. If, as shown in the figure, this intersection lies above and to the left of the original LM curve, the price level will increase and shift the LM curve upward (from LM1 to LM2) to pass through the new equilibrium point. The result is an increase in the price level, but an ambiguous effect on the real interest rate. Since output is lower, consumption is lower. Since the effect on the real interest rate is ambiguous, the effect on saving and investment are ambiguous as well, though the fall in the future marginal product of capital would tend to reduce investment. Figure 9.24 Figure 9.25 The result is different from that of a temporary supply shock; when the shock is temporary there is no impact on future output or the marginal product of capital, so the IS curve does not shift. In that case the price level increases to shift the LM curve up and to the left from LM1 to LM2 in Figure 9.26 to restore equilibrium. In that case, the real interest rate unambiguously increases. Under a permanent shock, the IS curve shifts down and to the left, so the rise in the real interest rate is less than in the case of a temporary shock, and the real interest rate can even decline. Figure 9.26 3. (a) The decrease in expected inflation increases real money demand, shifting the LM curve up, as shown in Figure 9.27. The real interest rate rises and output declines. Figure 9.27 (b) The increase in desired consumption shifts the IS curve up and to the right, as shown in Figure 9.28. This causes the real interest rate and output to rise. Figure 9.28 (c) The increase in government purchases shifts the IS curve up and to the right, with the same result as in part (b). (The FE line also shifts, as the increase in government expenditures reduces people’s wealth and leads them to increase labor supply, but this shift will not affect the short-run equilibrium, as the economy will be off the FE line.) (d) If Ricardian equivalence holds, the increase in taxes has no effect on either the IS or LM curves, so there is no change in either the real interest rate or output. If Ricardian equivalence doesn’t hold, so that the increase in taxes reduces consumption spending, the IS curve shifts down and to the left, as shown in Figure 9.29. Both the real interest rate and output decline. Figure 9.29 (e) An increase in the expected future marginal productivity of capital shifts the IS curve up and to the right, with the same result as in part (b). 4. The change in Eq. (9.B.10) has no effect on employment, the real wage, or output. The only effect this has is on the term IS, which is now IS [1 – (1 – t)cY – iY]/(cr ir). The real interest rate and price level are still determined by Eqs. (9.B.22) and (9.B.23), respectively. 5. The change in the money demand function affects only the equation determining the price level, Eq. (9.B.23). It is now P M/[l0 lY Y – lr(IS – IS Y e – im)] CH10 Numerical Problems 1. (a) Labor supply is given by the equation NS 45 0.1w. Before the shock, labor demand is determined by the equation w 1.0(100 – N). Setting labor supply equal to labor demand by substituting the labor demand equation into the labor supply equation gives N 45 0.1 w 45 [0.1 1.0(100 – N)] 45 10 – 0.1N, or 1.1 N 55, so N 50. Then w 1.0(100 – N) 50. Output is Y 1.0[(100 50) – (0.5 502)] 3750. After the shock, repeating the above steps gives N 45 0.1 w 45 [0.1 1.1(100 – N)] 45 11 – 0.11N, or 1.11 N 56, so N 50.45. Then w 1.1(100 – N) 54.505. Output is Y 1.1[(100 50.45) – (0.5 50.452)] 4150. (b) Now NS 10 0.8w. Before the shock, N 10 0.8 w 10 [0.8 1.0(100 – N)] 10 80 – 0.8N, or 1.8 N 90, so N 50. Then w 1.0(100 – N) 50. Output is Y 1.0[(100 50) – (0.5 502)] 3750. After the shock, N 10 0.8 w 10 [0.8 1.1(100 – N)] 10 88 – 0.88N, or 1.88 N 98, so N 52.13. Then w 1.1(100 – N) 52.66. Output is Y 1.1[(100 52.13) – (0.5 52.132)] 4240. (c) If the real wage is only slightly procyclical, then a flat labor supply curve, as in part (b) is necessary, rather than a steep labor supply curve as in part (a). Figure 10.4 illustrates the difference in slopes of the two labor supply curves. When labor demand increases from ND1 to ND2, the real wage rises a lot (from w1a to w2a) with a steep labor supply curve, but the real wage rises only a little bit (from w1b to w2b) if the labor supply curve is fairly flat. A calibrated RBC model would fit the facts better if the labor supply curve were fairly flat, that is, labor supply is sensitive to the real wage, as in part (b). Figure 10.4 2. The IS curve gives Y C I G 600 0.5(Y – T) – 50r 450 – 50r G 1050 – 100r 0.5Y – 0.5T G, or 0.5Y 1050 – 100r – 0.5T G, or Y 2100 – 200r – T 2G. The LM curve gives M/P L 0.5Y – 100i 0.5Y – 100(r ) 0.5Y – 100(r 0.05) 0.5Y – 100r – 5. (a) M 4320, G T 150. The IS curve is Y 2100 – 200r – T 2G 2100 – 200r – 150 (2 150) 2250 – 200r. Output must be at its full-employment level of 2210. From the IS curve, 2210 2250 – 200r, or 200r 40, so r 0.20. Using this in the LM curve to find the price level gives M/P 0.5Y – 100r – 5, or 4320/P (0.5 2210) – (100 0.20) – 5, so P 4320/(1105 – 20 – 5) 4320/1080 4. Then consumption is C 600 0.5(Y – T) – 50r 600 0.5(2210 – 150) – (50 0.20) 600 1030 – 10 1620. Investment is I 450 – 50r 450 – (50 0.20) 440. (b) When M increases to 4752, nothing in the IS curve is affected, so Y and r are the same as in part (a), as are C and I. The LM curve becomes 4752/P 1080, or P 4.4. No real variables are affected, and the price level rises 10% just as the money supply did, so money is neutral. (c) When G T 190, the IS curve shifts. It becomes Y 2100 – 200r – T 2G 2100 – 200r – 190 (2 190) 2290 – 200r. With Y 2210, this gives 2210 2290 – 200r, or 200r 80, so r 0.40. From the LM curve, 4320/P 0.5Y – 100r – 5 (0.5 2210) – (100 0.40) – 5 1105 – 40 – 5 1060, so P 4320/1060 4.075. C 600 0.5(Y – T) – 50r 600 0.5(2210 – 190) – (50 0.40) 600 1010 – 20 1590. I 450 – 50r 450 – (50 0.40) 430. Fiscal policy is not neutral since the change in policy has real effects on the interest rate, consumption, and investment. 3. The IS curve is found by setting desired saving equal to desired investment. Desired saving is S d Y – C d – G Y – [250 0.5(Y – T) – 500r] – G. Setting Sd Id gives Y – [250 0.5(Y– T) – 500r] – G 250 – 500r, or Y 1000 – 2000r 2G – T. The LM curve is M/P L 0.5Y – 500i 0.5Y – 500(r e) 0.5Y – 500r. (a) T G 200, M 7650. The IS curve gives Y 1000 – 2000r 2G – T 1000 – 2000r (2 200) – 200 1200 – 2000r. The LM curve gives 7650/P 0.5Y – 500r. To find the aggregate demand curve, eliminate r in the two equations by multiplying the LM curve through by 4 and rearrange the resulting equation and the IS curve. LM: 7650/P 0.5Y – 500r. Multiplying by 4 gives 30,600/P 2Y – 2000r. Rearranging gives 2000r 2Y – 30,600/P. IS: Y 1200 – 2000r. Rearranging gives 2000r 1200 – Y. Setting the right-hand sides of these two equations to each other (since both equal 2000r) gives: 2Y – (30,600/P) 1200 – Y, or 3Y 1200 (30,600/P), or Y 400 (10,200/P); this is the AD curve. With Y 1000 at full employment, the AD curve gives 1000 400 (10,200/P), or P 17. From the IS curve Y 1200 – 2000r, so 1000 1200 – 2000r, or 2000r 200, so r 0.10. Consumption is C 250 0.5(Y – T) – 500r 250 0.5(1000 – 200) – (500 0.10) 600. Investment is I 250 – 500r 250 – (500 0.10) 200. (b) Following the same steps as above, with M 9000 instead of 7650, gives the aggregate demand curve AD: Y 400 (12,000/P). With Y 1000, this gives P 20. Nothing has changed in the IS equation, so it still gives r 0.10. And nothing has changed in either the consumption or investment equations, so we still get C 600 and I 200. Money is neutral here, as no real variables are affected and the price level changes in proportion to the money supply. (c) T G 300, M 7650. The IS curve is Y 1000 – 2000r 2G – T 1000 – 2000r (2 300) – 300 1300 – 2000r. IS: Y 1300 – 2000r, or 2000r 1300 – Y. LM: 30,600/P 2Y – 2000r, or 2000r 2Y – 30,600/P. AD: 2Y – (30,600/P) 1300 – Y, or (30,600/P) 1300 3Y, or Y 433 1/3 (10,200/P). With Y 1000 at full employment, the AD curve gives 1000 433 1/3 (10,200/P), or P 18. From the IS curve, Y 1300 – 2000r, so 1000 1300 – 2000r, or 2000r 300, so r 0.15. Consumption is C 250 0.5(Y – T) – 500r 250 0.5(1000 – 300) – (500 0.15) 525. Investment is I 250 – 500r 250 – (500 0.15) 175. 4. AD: Y 300 30(M/P), AS: Y 500 10(P – Pe), M 400. (a) P e 60. Setting AD AS to eliminate Y, we get 300 30(M/P) 500 10(P – P e ). Plugging in the values of M and P e gives 300 (30 400/P) 500 10(P – 60), or 300 (12,000/P) 500 10P – 600, or 400 (12,000/P) 10P. Multiplying this equation through by P/10 gives 40P 1200 P 2, or P 2 – 40P – 1200 0. This can be factored into (P – 60)(P 20) 0. P can’t be negative, so the only solution to this equation is P 60. At this equilibrium P P e, so Y 500, and the economy is at full-employment output. (b) With an unanticipated increase in the money supply to M 700, the expected price level is unchanged at Pe 60. The aggregate demand curve is Y 300 30(M/P) 300 (30 700/P) 300 (21,000/P). The aggregate supply curve is Y 500 10(P – Pe) 500 10(P – 60) 10P – 100. Setting AD AS to eliminate Y gives 300 (21,000/P) 10P – 100, or 400 (21,000/P) 10P, or P – 40 – (2100/P) 0. Multiplying through by P gives P2 – 40P – 2100 0. This can be factored as (P – 70)(P 30) 0, which has the positive solution P 70. From the AD curve, Y 300 (21,000/P) 300 (21,000/70) 600. (c) When M 700 and is anticipated, P Pe. Then the AD curve is Y 300 (21,000/P) and the AS curve is Y 500. Setting AD AS gives 500 300 (21,000/P), which has the solution P 105. 5. (a) To find the Solow residual, use the equation for the production function, dividing through to solve for A: A Y/K 0.3N 0.7. Assuming there’s no change in utilization rates, this is the measured Solow residual. Given that equation, plugging in the values for Y, K, and N, gives the Solow residual as 1.435 in 2006 and 1.507 in 2007. The growth rate of the Solow residual is [(1.507/1.435) – 1] 100% 5.0%. (b) With no change in utilization rates, the growth rate of the Solow residual equals the growth rate of productivity (A), 5.0%. (c) With a change in utilization rates, the production function is modified, as shown in Eq. (10.2). Now productivity is measured as A Y/(uKK) 0.3(uNN) 0.7 but the Solow residual is still measured as in part (a). Setting uN 1 in year 2006 and 1.03 in year 2007, we calculate the value of A as 1.435 in 2006 (as in part a), and 1.476 in 2007. This is an increase in productivity of [(1.476/1.435) –1] 100% 2.9%, significantly less than the 5.0% increase in the Solow residual. (d) Setting uN 1 in year 2006 and 1.03 in year 2007, and uK 1 in year 2006 and 1.03 in year 2007, we calculate the value of A as 1.435 in 2006 (as in part a), and 1.463 in 2007. This is an increase in productivity of [(1.463/1.435) – 1] 100% 2.0%, again significantly less than the 5.0% increase in the Solow residual. This problem illustrates the idea that the measured Solow residual grows faster than productivity when the utilization rates of capital and labor increase. 6. An example is shown in Figure 10.5. There are several long cycles in output. Figure 10.5 7. (a) With an unemployment rate of 5%, there are initially 5 million unemployed and 95 million employed. Since 1% of the employed become unemployed, 95 million .01 950,000 move from employment to unemployment each month. Since 19% of the unemployed become employed, 5 million .19 950,000 from unemployment each month. Since the same number move from employed to unemployed as the number moving from unemployed to employed, the unemployment rate remains 5% in February and March. (b) Note: All amounts are in millions. April: Employed (E) to Unemployed (U): 95 .03 2.85. U to E is 5 .19 .95. So U 5 2.85 – .95 6.9. The unemployment rate (u) 6.9%. May: E to U: 93.1 .01 .931. U to E is 6.9 .19 1.311. So U 6.9 .931 – 1.311 6.52 and u 6.52%. June: E to U: 93.48 .01 .9348. U to E is 6.52 .19 1.2388. So U 6.52 .9348 – 1.2388 6.216 and u 6.216%. July: E to U: 93.784 .01 .93784. U to E is 6.216 .19 1.18104. So U 6.216 .93784 – 1.18104 5.9728 and u 5.9728%. 8. (a) IS 2.47, IS 0.0004, LM 0, LM 0.001, lr 500, b 100. (b) Y [2.47 88,950/(P 500)]/(.0004 .001) (2.47 177.9/P)/.0014 (c) Y 6000 100P – 2915 3085 100P; use this in the AD curve to eliminate Y. 3085 100P (2.47 177.9/P)/.0014; multiply through by P and .0014 to get 4.319P .14P 2 2.47P 177.9, or .14P 2 1.849P – 177.9 0; use quadratic formula: P 29.65. Y 3085 100P 6050. (d) Long run: Y 6000; 6000 (2.47 177.9/P)/.0014, so P 30. Analytical Problems 1. (a) The increase in MPK f leaves aggregate supply unchanged, since expected future labor income and expected future wages are unchanged. But aggregate demand increases, because firms increase investment, shifting the IS curve up and to the right. There is no shift in either the LM curve or the FE line. Figure 10.6(a) shows that the increase in aggregate demand causes no change in output, since the AS curve is vertical, but the price level increases. Figure 10.6(b) shows the shift up and to the right of the IS curve from IS 1 to IS 2. To get the economy to equilibrium, the price level rises so that the LM curve shifts from LM 1 to LM 2. The real interest rate increases as a result. In the labor market, there is no change in labor demand or supply, so employment and output are unchanged. Since the real interest rate rises, saving increases and consumption declines. Since investment equals saving, investment also rises. Figure 10.6 (b) The misperceptions theory gets a different result. As shown in Figure 10.7, the shift in the aggregate demand curve from AD1 to AD2 increases both output and the price level as the economy moves along the short-run aggregate supply curve SRAS. The difference in this result compared to the result in part (a) comes from producers misperceiving the change in the price level as a change in relative prices, and increasing their labor demand and output. Figure 10.7 2. (a) In the case of a permanent increase in government purchases, the income effect on labor supply, which arises because the present value of taxes increases to pay for the added government spending, is much higher than in the case of a temporary increase in government spending. So workers increase their labor supply more when the government spending change is permanent than when it is temporary. (b) Desired national saving is unaffected by the change in government spending if the change in consumption is just equal to the change in taxes, so there is no shift in the saving curve. If investment is also unaffected by the change in government spending, then the IS curve does not shift. (c) Figure 10.8 shows the effect of the increase in government purchases on the economy. The FE line shifts to the right from FE1 to FE2 due to the increase in labor supply. To restore equilibrium, the price level must decline to shift the LM curve from LM 1 to LM 2. So output rises and the real interest rate declines. Figure 10.8 If consumption falls less than the increase in government purchases, the IS curve shifts up and to the right from IS1 to IS2 in Figure 10.9. As a result of the shift in the IS curve, the real interest rate and the price level will fall by less than in the case in which current consumption falls by 100, and in fact, the real interest rate and the price level may even rise if the IS curve shifts by a lot, as shown in the figure. Figure 10.9 3. The temporary increase in government purchases causes an income effect that increases workers’ labor supply. This results in an increase in the full-employment level of output from FE1 to FE2 in Figure 10.10. The increase in government purchases also shifts the IS curve up and to the right from IS1 to IS2, as it reduces national saving. Assuming that the shift up of the IS curve is so large that it intersects the LM curve to the right of the FE line, the price level must rise to get back to equilibrium at full employment, by shifting the LM curve up and to the left from LM1 to LM2. The result is an increase in output and the real interest rate. Figure 10.10 Figure 10.11 shows the impact on the labor market. Labor supply shifts from NS1 to NS2, leading to a decline in the real wage and a rise in employment. Average labor productivity declines, since employment rises while capital is fixed. Investment declines, since the real interest rate rises. Figure 10.11 To summarize, in response to a temporary increase in government purchases, output, the real interest rate, the price level, and employment rise, while average labor productivity and investment decline. (a) The business cycle fact is that employment is procyclical. The model is consistent with this fact, since employment rises when government purchases rise, causing output to rise. (b) The business cycle fact is that the real wage is mildly procyclical. The model is inconsistent with this fact, since it shows a decline in the real wage when government purchases rise and output rises. (c) The business cycle fact is that average labor productivity is procyclical. The model is inconsistent with this fact, since it shows a decline in average labor productivity when government purchases rise and output rises. (d) The business cycle fact is that investment is procyclical. The model is not consistent with this fact, as investment falls when government purchases rise and output rises. (e) The business cycle fact is that the price level is procyclical. The model is consistent with this fact, as the price level rises when government purchases increase and output increases. 4. (a) An increase in expected future output increases money demand, so the LM curve shifts up and to the left. As shown in Figure 10.12, the LM curve shifts from LM1 to LM2. General equilibrium in the economy can be restored by shifting the LM curve from LM2 to LM3, which occurs as the price level declines Figure 10.12 (b) If the Fed wants to stabilize the price level, then it increases the money supply in response to the increase in money demand, so that the LM curve shifts from LM2 to LM3 without a decline in the price level. This represents reverse causation, because the rise in future output causes the current money supply to increase. It might appear that the rise in the current money supply caused the rise in future output because of this timing, but in fact the reverse is true. 5. The temporary wage tax has a small income effect but a large substitution effect, so labor supply is reduced. As Figure 10.13 shows, this increases the (pretax) real wage rate and reduces employment. The reduction in employment shifts the FE line from FE1 to FE2 in Figure 10.14, while the increase in government purchases shifts the IS curve from IS1 to IS2. To restore equilibrium, where IS, LM, and FE intersect, the price level must rise, so that the LM curve shifts from LM1 to LM2. The result is an increase in the real interest rate and a decline in output. Figure 10.13 Figure 10.14 CH8 Analytical Problems 1. Figure 8.8 illustrates the business cycle. The current NBER method picks peaks and troughs in the level of aggregate economic activity, which are points on the figure where the slope of the line is zero. These are shown in Figure 8.8 as P1 (at the peak of the cycle) and T1 (at the trough of the cycle). However, the older method picks peaks and troughs in detrended economic activity. This means the peaks and troughs occur at points that are the farthest away from the trend line, which means those points at which the slope of the line showing aggregate economic activity is the same as the slope of the trend line. These points are shown in Figure 8.8 as P2 and T2. Note that the point P2 occurs before P1, meaning that peaks in detrended economic activity are earlier than peaks in the level of economic activity. Note also that the point T2 occurs later than T1, which means that troughs in detrended economic activity are later than troughs in the level of economic activity. Since under the old method, troughs occur later and peaks occur earlier, contractions appear to be longer and expansions appear to be shorter using the pre-1927 method than using the current method. Thus the fact that after World War II expansions were longer and contractions were shorter than before World War I is somewhat illusory, since it’s based on two different accounting mechanisms. If expansions and contractions were in fact equally long in both periods, the change in accounting method would mean that our official dating of the business cycle would show longer expansions and shorter contractions after World War II than before World War I. Figure 8.8 2. Expenditure on durable goods is more sensitive to the business cycle than expenditure on nondurable goods and services, because people can more easily change the timing of their expenditure on durables. When economic activity is weak, and people face the danger of losing their jobs, they avoid making durable goods purchases. Instead, they may drive their cars a little longer before buying new ones, get the old washing machine repaired instead of buying a new one, and put off buying new furniture until a new expansion indicates greater income security. So in a recession, durable purchases decline a lot, but when an expansion begins, durable purchases pick up substantially. The exception was in the business cycle that began in March 2001, when very low interest rates supported expenditures on durable goods. 3. (a) In symbols, let A average labor productivity, Y output, and H total hours worked. By definition, A Y/H, so in growth terms, A/A Y/Y – H/H. Since all three are procyclical, they all move in the same direction over the business cycle. If total hours worked varied more than output in an expansion, then H/H would be greater than Y/Y, so that A/A would be negative, and average labor productivity would be countercyclical. So it must be the case that output varies more than total hours worked in an expansion. A similar argument holds in a contraction. (b) That average labor productivity is procyclical helps explain why the Okun’s Law coefficient is 2, not 1. A one-percentage point increase in unemployment is approximately a one percent fall in employment. Thus, if there were no change in average labor productivity, we might expect the percentage fall in output to equal the number of percentage points that the unemployment rate rises. But since average labor productivity moves in the same direction as output, it magnifies the output effect of a given amount of unemployment. 4. Figure 8.9 illustrates the effects of a demand shock. The economy begins in equilibrium at point A, where the LRAS, SRAS, and AD curves intersect. The demand shock shifts the aggregate demand curve to the left to AD. In the short run, the equilibrium is at point B, where AD intersects SRAS. This is a point at which output has declined (a recession), but the price level is unchanged. Over time, the short-run aggregate supply curve shifts down to SRAS, restoring long-run equilibrium at point C. At this point, output is back at its full-employment level and the price level has declined. Thus the result of a demand shock on the price level is that the price level is unchanged in the short run and declines in the long run. Since the 1973–1975 recession was one in which the price level rose sharply, it must not have been due to a demand shock. Figure 8.9 Figure 8.10 illustrates the effects of a supply shock. The economy begins in equilibrium at point A, where the LRAS, SRAS, and AD curves intersect. The supply shock shifts the long-run aggregate supply curve to the left to LRAS. The new equilibrium is at point B, where AD intersects LRAS. This is a point at which output has declined (a recession), but the price level has risen. This matches what happened in the 1973–1975 recession. Thus we conclude that the 1973–1975 recession was the result of a supply shock, not a demand shock. Figure 8.10 5. Growth that is “too rapid” most likely refers to a situation in which the aggregate demand curve has shifted to the right and, in the short run, intersects the SRAS curve at a level of output that’s greater than the full-employment level of output (Figure 8.11). This situation is associated with inflation because, in the long run, prices will rise, shifting the SRAS curve up to intersect with the LRAS and AD curves. The shock that is implicitly assumed to be hitting the economy is an aggregate demand shock, since that’s the only shock that increases output in the short run and inflation in the long run. Figure 8.11

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