8.x. A change in the capital stock This question is an extended version of problem 7.x. Assume a one-time decrease in the capital stock, possibly caused by a natural disaster or an act of war. Assume that population does not change. a. Use a variant of Figure 8.8 to determine the effects on the market for capital services. What happens to capital input, KK, and the real rental price, R/P? What happens to the interest rate, i? b. Use a variant of Figure 8.3 to determine the effects on the labor market. What happens to labor input, L, and the real wage rate, w/P? c. What happens to output, Y, and consumption, C? What happens to investment, I? What happens over time to the stock of capital, K? w/P supply curve for labor L demand curves for labor (w/P)2 (w/P), L' (A2) L" (A1) L", L L L2 Figure 8.3 Clearing of the Labor Market At the technology level A1, the demand for labor, labeled L (A1) along the blue curve, slopes downward versus the real wage rate, w/P. At the higher technology level, A2, the demand for labor, labeled L (A2) along the red curve, is larger at any given w/P. These two curves are the same as those shown in Figure 7.5. The supply of labor, L', shown in green, slopes upward versus w/P because we assume that the substitution effect dominates over the income effect. Thus, the increase in the technology level from A to Az raises the real wage rate from (w/P), to (w/P), and raises labor input from L, to L2. R/P supply curve for capital services (KK) demand curves for capital services (R/P)2 (R/P), (KK)^(A2) (KK)^(A1) (KK)". (KK) (KK)(KK)2 Figure 8.8 Clearing of the Market for Capital Services At the technology level A1, the demand for capital services, labeled (KK)^(A1) along the blue curve, slopes downward versus the real rental price, R/P. At the higher technology level A2, the demand for capital services, labeled (KK)'(A2) along the red curve, is larger at any given R/P. These curves are the same as those in Figure 8.5. The supply of capital services, (KK)", slopes upward versus R/P along the green curve because an increase in R/P raises the capital utilization rate, k (see Figure 8.7). Thus, an increase in the technology level from A to A2 raises the market-clearing real rental price from (R/P), to (R/P), and the quantity of capital services from (KK), to (KK)2. Since the stock of capital, K, is fixed, the increase in capital services reflects the rise in the utilization rate from ki to K2, as in Figure 8.7