Production in the country of CapitalBerg can be characterized by the following function: Y = 2K0.2L0.8 and that CapitalBerg initially has 200 units of labor and 1000 units of capital.
a) Calculate the marginal product of labor and marginal product of capital for CapitalBerg.
b) Show with calculus that the production function exhibits diminishing returns to capital.
c) Calculate the total payments to labor and capital in CapitalBerg.
d) Suppose that in CapitalBerg there is a large increase in investment that adds a lot more capital to the economy. What happens to the rental rate of capital and real wage rate in CapitalBerg? Briefly explain.
e) Again suppose that in CapitalBerg there is a large increase in investment that adds a lot more capital to the economy. What happens to the income shares of capital and labor in this economy? No math is necessary but it may help to see the answer if you pretend that capital increased from 1000 to 1500 while the amount of labor stayed the same.
f) In the production function for CapitalBerg briefly explain what the "2" represents.