3. This problem adds the government to the Solow model. Suppose that a government purchases goods in the amount of g per worker every year; with Nt workers in year t, total government purchases are gNt. The government has a balanced budget so that its tax revenue in year t, Tt, equals total government purchases. Total national saving, St, is St = s(Yt - Tt), where Yt is total output and s is the saving rate.

a. Graphically show the steady state for the initial level of government purchases per worker.

b. Suppose that the government permanently increases its purchases per worker. What are the effects on the steady-state levels of capital per worker, output per worker, and consumption per worker? Does your result imply that the optimal level of government purchases is zero?