Question

Suppose output, Y t, is produced using capital, K t, and labor, N t, according to the production function: Y t = A ⋅ ( K t α N t 1 − α + K t β N t 1 − β )where the parameters satisfy 0 < α < 1, 0 < β < 1 and A > 0.

a) (5 pts) Write the production function in “per worker” terms. That is, if we define y t = Y t N t, and k t = K t N t, write y t as a function of k t.

b) (10 pts) In the Solow model, the rental rate on capital, r t, equals the marginal product of capital (MPK). Use your answer to part (a) to find the expression for r t in terms of k t.

Answer 1

Answer: a) In order to show the steady state for Pnitial level of goverment purchasesper worker grouphically, observe that with budget being balanced, I = g. Neational saving & s= SCY-T) ESN (4-5) ESN (7-9 > set savings equal to investment I = entd) K & substitute y=f(1) SN(4-8)= (htdk s(y-9) = md) R S (f(K)-g) (n+d) k. Following drawn below is the grouph that clearly shows the steady state for initial level of goverment purchases per worked k* = equilibrium point of coupital- a labor ratio. Here +dJk Sf(K). S[F )-9 K*

o suppose of government increases Its purchase per worker, then curve s[fci)-g) will shift downwards. Hence, the coupital laubor ratio is lower in the steady-state edullibslum, Hence does the output per worker, consumption per worked and coupital per worker. The optimal level of the government Purchauses is depends upon the costs and benefits of these purchases and PS not zero necessarfly.