Consider the production function Y = F (K, L) = Ka * L1-a, where 0 < α < 1. The national saving rate is s, the labor force grows at a rate n, and capital depreciates at rate δ.
(a) Show that F has constant returns to scale.
(b) What is the per-worker production function, y = f(k)?
(c) Solve for the steady-state level of capital per worker (in terms of the parameters of the model).
(d) Solve for the golden-rule steady-state level of capital per worker. (in terms of the parameters of the model).
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