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Unformatted text preview: Problem 1 CompMaker has an (expected) future marginal product of capital function given by MPK f =20 0.02*K f , where K f is the capital stock. Here MPK f is measured in real terms, i.e. units of output. The depreciation rate is 20% per period and the real rate of interest is 5%. Also, assume that the price of one unit of capital relative to one unit of output is 4. The current amount of capital owned by the firm is 500 units. a) What is the marginal product of capital at the current level of the capital stock? MPK = 20 0.02*500 = 10 b) What is the real user cost of capital? UC =( P k /P)(r + d) = 4*(0.05 + 0.2) = 1 c) What is the firms desired level of capital? MPK = UC, 20 0.02K f = 1 delivers K f = 950 d.)What will be the level of investment this period, assuming that the firm wants to reach its desired level of K in one period? I = K f (1-d)K = 950 0.8*500 = 550 Problem 2 A consumer lives three periods, called the learning period, the working period, and the retirement period. Her income is 200 during the learning period, 800 during the working period, and 200 again during the retirement period. The consumers initial assets are 300. The real interest rate is zero. The consumer desires perfectly smooth consumption over her lifetime. a. What are consumption and saving in each period, assuming no borrowing constraints? What happens if the consumer faces a borrowing constraint that prevents her from borrowing? happens if the consumer faces a borrowing constraint that prevents her from borrowing?...
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- Winter '08