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### 305hw5a

Course: ECON 305, Fall 2009
School: Sveriges...
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Set Problem #5 Answer Key Economics 305: Macroeconomic Theory Spring 2007 1 Chapter 9, Problem #1 There are two eects of an increase in the depreciation rate. First, given the marginal product of capital in period two, M PK , the net marginal product of capital, M PK d, will decrease when the depreciation rate increases. For any given real interest rate, this eect lowers the rms preferred level of K , and...

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Set Problem #5 Answer Key Economics 305: Macroeconomic Theory Spring 2007 1 Chapter 9, Problem #1 There are two eects of an increase in the depreciation rate. First, given the marginal product of capital in period two, M PK , the net marginal product of capital, M PK d, will decrease when the depreciation rate increases. For any given real interest rate, this eect lowers the rms preferred level of K , and shifts the investment demand curve out. The second eect can be seen by rearranging the equation K = (1 d)K + I to I = K K + dK. Given the initial capital stock, K, more investment will be required to achieve a given second-period capital stock if the depreciation rate is higher. Therefore, when d increases, the investment demand curve shifts in. The two eects work in opposite directions, and so, given the real rate of interest, investment may either rise or fall with an increase in the depreciation rate. 2 Chapter 9, Problem #3 For the rst policy, the output subsidy, there will be no direct eect on investment. That is, a subsidy of t for each unit of output produced in the current period aects neither the marginal cost of investment nor the marginal benet from investment for the rm. However, there will be an indirect eect: by raising the marginal benet from current production, the subsidy will increase the rms current labour demand. Given the consumers labour supply curve, this will push the output supply curve out. Interest rates will fall, and so investment will increase. If there is an investment tax credit, that is, a subsidy of s per unit invested in the current period, then the marginal cost of investment is 1 s instead of 1. The rms optimal investment rule is now to invest to the point where M PK d = r s(1 + r). Therefore, the investment tax credit will increase investment, shifting the optimal investment schedule to the right. Both policies would tend to increase investment. I would suspect the second policy would have a larger eect - direct eects are usually stronger than indirect eects - but it is not clear which way it would go. 3 Chapter 9, Problem #6 First we consider direct eects. A future increase in government spending generates a negative income eect for the consumer. Therefore, current-period consumption declines and current-period labour supply increases. The increase in current-period labour supply shifts the output supply curve out. The decrease in current-period consumption shifts the output demand curve in. The anticipated increase in spending government has no direct eect on the rm. 1 ECON 305, Spring 2007 2 The results are summarized in Figure 1. The equilibrium interest rate unambiguously declines, so investment unambiguously increases. What happens to the equilibrium level of employment and output depends on the relative strength of the dierent eects: labour supply goes up because of the negative shock to the consumers lifetime income, but down because interest rates have gone down. Figure 1 is drawn to assume the rst of these eects dominates. The equilibrium level of output probably increases from Y to Y , in which case the level of employment rises from N to N . If, overall, employment and output increase, then it must be the case that the real wage falls. The overall eect on consumption is also unclear: the income eect tends to lower consumption, while the decline in the real interest rate tends to increase consumption. Figure 1: ECON 305, Spring 2007 3 4 Chapter 9, Problem #7 Labour supply shifts to the right, so output supply also shifts out. Consumption demand also increases, so the output demand curve must also shift out. Output must increase; the real interest rate may rise or fall. In light of the increase in output, equilibrium employment must increase. A higher level of employment, in the absence of a shift in the labour demand curve, implies that the real wage rate must also fall. The eecgt on investment depends on what has happened to the real interest rate: investment rises if the re...

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