Problem
Introduce government activity in the endogenous growth model as follows. In addition to working u units of time in producing goods, the representative consumer works v units of time for the government and produces gvH goods for government use in the current period, where g 7 0. The consumer now spends 1 - u - v units of time each period accumulating human capital.
(a) Suppose that v increases with u decreasing by an equal amount. Determine the effects on the level and the rate of growth of consumption. Draw a diagram showing the initial path followed by the natural logarithm of consumption and the corresponding path after v increases.
(b) Suppose that v increases with u held constant. Determine the effects on the level and the rate of growth of consumption. Draw a diagram showing the initial path followed by the natural logarithm of consumption and the corresponding path after v increases.
(c) Explain your results and any differences between parts (a) and (b).
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.