1.Consider the following production function: Y = 9K1/3 L2/3, where the level of capital in the economy is 100 and the level of labor in the economy is 100.
a) Compute the equilibrium real wage and real rental rate on capital.
b) Compute the total payments to labor and that to owners of capital.
c) Show that Euler’s theorem holds here, that the sum of total payments to labor and capital equals total production.
d) What fraction of total production goes to paying labor; what fraction toward paying capital? Do you see a shortcut to get these shares by looking at the production function?
e) Suppose that an increase in immigration into the U.S. increases the U.S. labor force. Discuss the effect on the real wage and the real rental price of capital. Would workers currently in the U.S. be happy about the immigration? How about owners of U.S. factories?