Econ 202 Macroeconomic Analysis 2008 Winter Quarter Prof. Federico Ravenna ANSWER KEY PROBLEM SET 2 CHAPTER 3: PRODUCTIVITY, OUTPUT, AND EMPLOYMENT

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1 Econ 202 Macroeconomic Analysis 2008 Winter Quarter Prof. Federico Ravenna ANSWER KEY PROBLEM SET 2 CHAPTER 3: PRODUCTIVITY, OUTPUT, AND EMPLOYMENT Numerical Problems 6. Since w = 4.5 K 0.5 N -0.5, N -0.5 = 4.5 K 0.5 /w, so N = K/w 2. When K = 25, N = /w 2. a. If t = 0.0, then NS = 100w 2. Setting labor demand equal to labor supply gives /w 2 = 100w 2, so w 4 = , or w = 1.5. Then NS = 100 (1.5) 2 = 225. [Check: N = /1.5 2 = 225.] Y = 45N 0.5 = 45(225) 0.5 = 675. The total after-tax wage income of workers is (1-t) w NS = 1.5 x 225 = b. If t = 0.6, then NS = 100 [(1-0.6) w] 2 = 16w 2. The marginal product of labor is MPN = 22.5 / N 0.5, so N = 100 [(1-0.6) x 22.5 / N 0.5 ] 2, so N 2 = 8100, so N = 90. Then Y = 45N 0.5 = 45(90) 0.5 = Then w = 22.5 / = The total after-tax wage income of workers is (1-t) w NS = 0.4 x 2.37 x 90 = Note that there's a big decline in output and income, although the wage is higher. c. A minimum wage of 2 is binding if the tax rate is zero. Then N = /2 2 = 126.6, NS = 100 x 2 2 = 400. Unemployment is Income of workers is wn = 2 x = 253.2, which is lower than without a minimum wage, because employment has declined so much. Numerical Problems CHAPTER 10: CLASSICAL BUSINESS CYCLE ANALYSIS: MARKET-CLEARING MACROECONOMICS 1. (a) Labor supply is given by the equation NS = w. 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 = w = 45 + [ (100 N)] = N, or 1.1 N = 55, so N = 50. Then w = 1.0(100 N) = 50. Output is Y = 1.0[(100 50) ( )] = 3750.

2 After the shock, repeating the above steps gives N = w = 45 + [ (100 N)] = N, or 1.11 N = 56, so N = Then w = 1.1(100 N) = Output is Y = 1.1[( ) ( )] = (b) Now NS = w. Before the shock, N = w = 10 + [ (100 N)] = N, or 1.8 N = 90, so N = 50. Then w = 1.0(100 N) = 50. Output is Y = 1.0[(100 50) ( )] = After the shock, N = w = 10 + [ (100 N)] = N, or 1.88 N = 98, so N = Then w = 1.1(100 N) = Output is Y = 1.1[( ) ( )] = (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 ND 1 to ND 2, the real wage rises a lot (from w 1 a to w 2 a ) with a steep labor supply curve, but the real wage rises only a little bit (from w 1 b to w 2 b ) 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 CHAPTER 4: CONSUMPTION, SAVING, AND INVESTMENT Numerical Problems 6. a. S d = Y - C d - G = Y - ( r + 0.1Y) = r + 0.9Y b. (1) Using Eq. (4.7): Y = C d + I d + G Y = ( r + 0.1Y) + ( r) = r + 0.1Y So 0.9Y = r At full employment, Y = Solving 0.9 x 6000 = r, we get r = 0.10.

3 (2) Using Eq. (4.8): S d = I d r + 0.9Y = r 0.9Y = r When Y = 6000, r = So we can use either Eq. (4.7) or (4.8) to get to the same result. c. When G = 1440, desired saving becomes S d = Y C d G = Y ( r + 0.1Y) 1440 = r + 0.9Y. S d is now 240 less for any given r and Y; this shows up as a shift in the S d line from S 1 to S 2 in Figure 4.3. Figure 4.3 Setting S d = I d, we get: r + 0.9Y = r 6000r + 0.9Y = 6240 At Y = 6000, this is 6000r = 6240 ( ) = 840, so r = The market-clearing real interest rate increases from 10% to 14%.

4 Analytical Problems 1. (a) As Figure 4.5 shows, the shift to the right in the saving curve from S 1 to S 2 causes saving and investment to increase and the real interest rate to decrease. Figure 4.5 (b) This is really just a transfer from the general population to veterans. The effect on saving depends on whether the marginal propensity to consume (MPC) of veterans differs from that of the general population. If there is no difference in MPCs, there will be no shift of the saving curve; neither investment nor the real interest rate is affected. If the MPC of veterans is higher than the MPC of the general population, then desired national saving declines and the saving curve shifts to the left; the real interest rate rises and investment declines. If the MPC of veterans is lower than that of the general population, the saving curve shifts to the right; the real interest rate declines and investment rises. (c) The investment tax credit encourages investment, shifting the investment curve from I 1 to I 2 in Figure 4.6. Saving and investment increase, as does the real interest rate. Figure 4.6 (d) The increase in expected future income decreases current desired saving, as people increase desired consumption immediately. The rise of the future marginal productivity of capital shifts the investment curve to the right. The result, as shown in Figure 4.7, is that the real interest rate rises, with ambiguous effects on saving and investment.

5 Figure A temporary increase in government spending reduces national saving. Whether the spending is financed by current taxes or by borrowing (and raising future taxes), consumption falls, but not by the full amount of the spending. Since S = Y C d G, national saving declines. This is shown in Figure 4.13 as a shift to the left in the saving curve. The real interest rate must increase to get S = I, so I declines as well. It makes no difference whether the temporary increase in spending is funded by taxes or by borrowing. Figure 4.13 In the case of infrastructure spending, MPK f rises, so investment increases. Saving shifts from S 1 to S 2 and investment shifts from I 1 to I 2 in Figure With upward shifts in both saving and investment, the new equilibrium is one with a higher real interest rate. However, saving and investment at the new equilibrium may be higher or lower. The effect on consumption is unclear as well. The higher real interest rate reduces consumption, but future income is higher, which increases consumption. If investment actually rises, then the increase in government spending causes private investment to be crowded in rather than crowded out. In this case consumption is crowded out.

6 Figure When there is a temporary increase in government spending, consumers foresee future taxes. As a result, consumption declines, both currently and in the future. Thus current consumption does not fall by as much as the increase in G, so national saving (S d = Y C d G) declines at the initial real interest rate, and the saving curve shifts to the left from S 1 to S 2, as shown in Figure Thus the real interest rate increases and consumption and investment both fall. Figure 4.15 When there is a permanent increase in government spending, consumers foresee future taxes as well, with both current and future consumption declining. But if there is an equal increase in current and future government spending, and consumers try to smooth consumption, they will reduce their current and future consumption by about the same amount, and that amount will be about the same amount as the increase in government spending. So the saving curve in the saving-investment diagram does not shift, and there is no change in the real interest rate. Since the saving curve shifts upward more in the case of a temporary increase in government spending, the real interest rate is higher, so investment declines by more. However, consumption falls by more in the case of a permanent increase in government spending.