2. (30 points) For the UK economy suppose that output is produced
according to the production function $Y_t = K_t^\alpha[(1 - u)A_tL_t]^{1-\alpha}$,
where K is capital, L is the labour force, u is the natural rate of
unemployment and A is the efficiency of labour. The national saving
rate is s, the labour force grows at rate n, the efficiency of labour
grows at rate of g and capital depreciates at rate $\delta$.
(a) Express output per effective worker as a function of capital per
effective worker and the natural rate of unemployment.
(b) Compute the Law of Motion of Capital per effective worker and
find the equation that describes the steady state of this economy.
(c) Find the steady state level of capital and output per effective
worker of this economy and illustrate the steady state graphically.
(d) Suppose that originally the UK is at steady state and some
change in government policy increases the natural rate of unemployment. Using the graph you drew in the previous question,
describe how this change affects output per effective worker both
immediately and over time. Is the steady state effect on output
larger or smaller than the immediate effect? Explain.
