Suppose that the growth rate of gross urban product for an urban area is: y 0:25

Suppose that the growth rate of gross urban product for an urban area is:

y ¼ 0:25ð Þþ k 0:75ð Þþ e t k ¼ ð Þþ s=v j e ¼ n þ m;

where y is the growth rate of GUP, k the growth rate of capital, l the growth rate of labor, t the rate of technical change, s the saving rate, v the capital/output ratio, j the rate of in-migration of capital, n the natural rate of growth of labor in the urban area, and m the rate of in-migration of labor.

a. Assume that s¼ 0.1, v¼ 4, j¼ 0.05, n¼ 0.02, m¼ 0.03, and t ¼ 0.03. Calculate y.

b. Calculate the percentage growth in y that can be attributed to 1, Labor force growth

a. Natural growth

b. Migration 2, Capital growth

a. Natural growth through local saving

b. Migration of capital 3, Technical change 4, Suppose that the aggregate production function for the urban area is:

Y ¼ AertLaKb;

where Y is output, r the rate of technical change, t is time, L the labor input, K the capital input, and a and b are the elasticities of output with respect to labor and capital. Assume that r ¼ 0.02, a ¼ 0.75, and b ¼ 0.25.

a. Prove that a and b are the elasticities of output with respect to labor and capital.

b. Derive the basic growth equation in Section C for this model.

c. What is the rate of growth of this economy if labor grows at 1% per year and capital grows at 2% per year? What is the rate of growth of the wage rate under these conditions (assuming that labor is paid its marginal product)?