Suppose Country X\'s production function is given by where Kt is the capital and

Question

Suppose Country X's production function is given by where Kt is the capital and N is the labour which is constant. The evolution of the capital stock is given by KH-(1-5)K. + It where is the depreciation rate. Derive the output per worker f a. b. Derive and show that in the Solow growth model, the steady state capital per worker needs to satisfy: = 20s where s is the saving rate. Country X has a 36% saving rate, and 26% depreciation rate. c. Calculate the steady-state output per worker (Y/N) d. Calculate the steady-state consumption per worker (C/N)* e. Calculate the rate that Capital per worker (K/N) grows in the steady state. . Capital (K) grows in the steady state.

Explanation / Answer

Answering the first question as per Chegg policy

a. Outper worker f(Kt/N) when F(Kt,N) = 20Kt1/2N2/3

Dividing the production function by N

f(Kt/N) = (20Kt1/2N2/3)/N

f(Kt/N) = 20Kt1/2N2/3-1

f(Kt/N) = 20Kt1/2N-1/3

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