# hw6 - Homework 6(Due October 16 Questions 1-4 pertain to...

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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 . As in the Solow model, let y t denote the output per worker at t , so y t = A t k β t . (By de fi nition, k t is the capital per old person at the start of t , and it is also the capital per worker at 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 from 0 to 5. Then compute the growth rate of 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) t . (1) Let k 0 = 1 . Compute k t , for t from 0 to 5. Then compute the growth rate of
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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 − β . ) 4. Let α = 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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