# hw4 - Homework 4(Due October 4 1(The Solow model with...

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Homework 4 (Due October 4) 1. (The Solow model with exogenous technological progress.) The tech- nology level at t is given by A t = (1 + g ) t A 0 , where g 0 . To keep the case simple, let us assume n = 0 . Now the transitional equation is simply k t +1 = s · A t · ( k t ) β + (1 δ ) k t . (1) That is, we simply replace the constant A in the previous transitional equa- tion with A t . Regarding the steady state, by de fi nition (see PPT4), if the economy is in the steady state at t , then y t +1 k t +1 = y t k t . (2) Substituting y t = A t k β t and y t +1 = A t +1 k β t +1 into Equation (2) and doing some algebra, we have k t +1 k t = (1 + g ) 1 1 β . (3) (If we apply g = 0 to Equation (3), then we get k t +1 = k t , as in the previous study.) To see how to use the new transitional equation (Equation (1)) and the new steady-state relationship between k t +1 and k t (Equation (3)), let us do some exercises. Let A 0 = 1 , g = 0 . 01 , β = 0 . 5 , and δ = 0 . 9 . (1) Suppose k 0 = 1 and s = 0 . 5 . Use Equation (1) to compute k t and the growth rate of k at t , for t = 1 , 2 , and 3 . (2) Suppose k 0 = 1 and s = 0 . 6 . Use Equation (1) to compute k t and the growth rate of k at t , for t = 1 , 2 , and 3 . (3) Suppose s = 0 . 5 and the economy is in the steady state at

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