Suppose output is produced according to the production function Y=K^ [(1-u)L]^(1-) where K is capital, L is the labour force, and u is the natural rate of unemployment. The national savings rate is s, and the capital depreciation rate is .

a. Express output per worker (y=Y/L) as a function of capital per worker (k=K/L) and the natural rate of unemployment (u). [2]

b. Write an equation that describes the steady state of this economy. Show this steady state equilibrium in a diagram like in the standard Solow model. [4]

c. If the government implements a policy that reduces the natural rate of unemployment, using the graph you drew in part (b), describes how this change affects output both immediately and over time. Is the steady-state effect on output larger or smaller than the immediate effect? Explain. [4]