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HW4 - then the consumption at t 1 is c 1 1 − c(ii...

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Homework 4 (Due February 27) 1. Refer to page 5, L4. (1) Explain why it is impossible to have r 1 5% and i 1 4%. (2) Explain why it is impossible to have r 1 5% and i 1 6%. (3) One can identify r in the model to the return for stocks and identify i in the model to the return for treasury bonds. In reality those returns are different. Find a factor missing in the model which can cause the difference in returns. 2. Refer to pages 8, L4. Suppose that K 0 L 0 100, A 0 1 and 0.5. (1) Can K , L 0.9,1.1 maximize the firm’s profit? (2) Can K , L 1,1 maximize the firm’s profit? (3) Can K , L 2,2 maximize the firm’s profit? (Hint: (i) Compute r 0 and w 0 under given K 0 , L 0 , A 0 and . (ii) Then compute the profit for each K , L .) 3. [page 12, 3] NQ 1 (a, b, c). 4. The individual maximizes U c 0 , c 1 3 c 0 2 c 1 subject to c 0 c 1 1. What is the optimal c 0 , c 1 ? (Hint: (i) If the consumption at t 0 is c
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Unformatted text preview: then the consumption at t 1 is c 1 1 − c . (ii) Consuming c at t 0 and c 1 1 − c at t 1 gives utility in the amount of 3 c 2 1 − c . (iii) The choice of c is between 0 and 1.) 5. This question pertains to the AK model in [Ch 5, 1]. The AK model differs from the standard Solow model in that the production function in the AK model is simply Y AK with A 0. (1) Explain why the labor input is omitted in the AK model. (2) What is the marginal product of capital? (3) Verify that when the labor input is constant, the transitional equation is k t 1 sAk t 1 − k t . (4) Verify that as is implied by the equation in part (3), the growth rate of k at t 1 does not depend on the value of k at t ....
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