Consider the standard Solow Model without technological progress but with population growth. The production function is:

Yt = F(Kt, Lt) = AKtLt1-

where Kt is the capital stock at time t and A and represent exogenous parameters. The capital stock evolves according to the following equation:

Kt+1 = (1 )Kt + It

where is the rate of depreciation. Letting s denote the saving rate of the economy, assume that total national savings, St, is:

St = sYt - hKt

where the extra term, hKt, reflects the idea that when wealth (as measured by the capital stock) is higher, saving is lower. (Wealthier people have less need to save for the future). All other aspects of the economy are unchanged and population grows at rate n.

a. [14 pts] Derive the law of motion of the capital-labor ratio. Then, find the steady-state values of the (i) capital-labor ratio k, (ii) per-worker output y, and (iii) per-worker consumption c. On a graph with k on the horizontal axis, depict the steady state for this economy b. [12 pts] Consider the effect of a one-time, permanent increase in h within the economy. What happens to the steady-state levels of the (i) capital-labor ratio k, (ii) output per worker y, and (iii) consumption per worker c? Use the same graph as in part a. to illustrate the effect of the increase in h on the steady-state capital-labor ratio.

c.[7 pts] Finally, suppose that the economy is in steady state, and suddenly h decreases temporarily and then goes back to its initial level. Graph the time path of output per capita and use it to describe the short-run and long-run effects of the temporary change in h.