Consider the Solow model, where aggregate output is produced according to the following production function,

Yt = zK t N 1 t (1)

where < 1 and z is productivity (TFP). The labour force grows at an exogenous rate n per period. The economy saves a constant fraction of its income It = sYt , and consumes the rest. Capital accumulation is subject to distortions 1 that reduce the efficiency of capital. In particular, aggregate capital per worker evolves according to,

Kt+1 = Kt + It Kt (2)

(a) Solve for the steady state levels of capital per worker, output per worker, investment per worker and consumption per worker. Hint: first express the production function and the capital accumulation equation in per worker terms.

(b) What is the growth rate of output per worker and capital per worker in the steady state? Would these growth rates be different if the economy started off at a level of capital per worker below the steady state one? If yes, what would they be?

(c) Consider two economies A and B, which are otherwise identical except for their investment distortions : economy A has higher distortions than economy B (A > B). (i) Will these two economies have the same level of output per worker in the long run? Explain. (ii) Will they have the same growth rates of output per worker and aggregate output in the long run? Explain.

(d)If < s, how does the steady-state level of the capital stock compare to the golden rule level of the capital stock? Hint: solve for the golden rule level of capital per worker first.

(e) Suppose that the economy is initially in steady-state and that the population drops to half (but has no effect on the total capital stock). What will be the effect on output per worker in the short run and the long run? Hint: use a graph to explain your answer.