Consider how unemployment would affect the Solow growth model. Suppose that output is produced according to the production function Y = Ka[(1 − u)L]1- a, where K is capital, L is the labour force, and u is the natural rate of unemployment. The national saving rate is the labour force grows at rate n, and capital depreciates at rate d.
a. Express output per worker (y = Y/L) as a function of capital per worker (k = K/L) and the natural rate of unemployment. Describe the steady state of this economy.
b. Suppose that some change in government policy reduces the natural rate of unemployment. Describe how this change affects out-put both immediately and over time. Is the steady-state effect on output larger or smaller than the immediate effect? Explain.