# HW5 - 5 In the life-cycle model let u c yt c ot 1 ln c yt 1...

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Homework 5 (Due October 22) 1. Refer to case 1, Handout 2. Answer the three questions there. 2. Refer to case 2, Handout 2. Use the formula provided there to solve the optimal c 0 , c 1 . 3. Refer to case 3, Handout 2. Use the formula provided there to solve the optimal c 0 , c 1 . 4. Refer to page 17, L4 (example 5). There is a claim saying that corner solutions can be ruled out. The following is a simple way to confirm this clam. (i) First, find the (positive) solution for the last equation in that page. Denote that solution by c 0 and denote the corresponding date-1 consumption by c 1 . Then compute the value of U c 0 , c 1 . (ii) Compute the values of U 0,1.1 1 1/1.1  and U 1 1/1.1,0 . (iii) Compare U c 0 , c 1 with U 0,1.1 1 1/1.1  and U 1 1/1.1,0 . (iv) What can you conclude from the comparison in step (iii)?
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Unformatted text preview: 5. In the life-cycle model, let u c yt , c ot 1 ln c yt 1 − ln c ot 1 and F A t , K t , L t A t K t L t 1 − . As in the Solow model, let y t denote the output per worker at t , so y t A t k t . (By definition, k t is the capital per old person at the start of t , and it is also the capital per worker at t .) Let 0.5, 0.7, A t 10 all t , and k 1. (1) Compute k t , for t from 0 to 3. Then compute the growth rate of k , for t from 1 to 3. (2) Compute the steady k and y . (As in the Solow model, in case A t is constant, the economy is in the steady state at t if k t k t 1 .)...
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