hw6 - k at t , for t from 1 to 5. (2) Suppose the economy...

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Homework 6 (Due October 16) Questions 1-4 pertain to the version of life-cycle model with u ( c yt ,c ot +1 )= α ln c yt +(1 α )ln c ot +1 and F ( A t ,K t ,L t )= A t K β t L 1 β t .A si nt h eS o l ow model, let y t denote the output per worker at t ,so y t = A t k β t .(Byde f nition, k t is the capital per old person at the start of t , and it is also the capital pe rwo rk e ra t t .) Here we set β =0 . 5 . It is convenient to use Excel for computation. 1. Let α =0 . 7 , A t =10 all t ,and k 0 =1 . (1) Compute k t ,for t from 0 to 5. Then compute the growth rate of k , for t from 1 to 5. (2) Compute the steady k and y . (As in the Solow model, in case A t is constant, if the economy is in the steady state at t ,then k t = k t +1 . ) 2. Let α =0 . 5 , A t =10 all t ,and k 0 =1 . (1) Compute k t ,for t from0to5 .Thencomputethegrowthrateof k at t ,for t from 1 to 5. (2) Compute the steady k and y . 3. Let α =0 . 7 and A t =10 × (1 . 01)
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Unformatted text preview: k at t , for t from 1 to 5. (2) Suppose the economy is already in the steady state at t = 0 . Compute y t , for t from 0 to 5. Then compute the growth rate of y at t , for t from 1 to 5. (As in the Solow model, in case A t = (1 + g ) t A , if the economy is in the steady state at t , then y t +1 k t +1 = y t k t and so k t +1 k t = (1 + g ) 1 1 . ) 4. Let = 0 . 5 and A t = 10 (1 . 01) t . (1) Let k = 1 . Compute k t , for t from 0 to 5. Then compute the growth rate of k at t , for t from 1 to 5. (2) Suppose the economy is already in the steady state at t = 0 . Compute y t , for t from 0 to 5. Then compute the growth rate of y at t , for t from 1 to 5. 5. [pages 13-14, 3] A2, A3, A5. 1...
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