1- Consider and economy with the following production technology: Y = 9K1/3 L2/3 , where the aggregate capital stock is K=100, and aggregate labor is L=100. The price of output is 1. a) Compute the equilibrium wage and capital return. b) Compute total payments to labor and capital. c) Show Euler's Theorem holds, i.e. show that total payments to capital and labor equal the value of output. d) What share of output goes to labor and capital? e) Suppose there is an increase in L, what would be impact on wages and capital returns?
2- Consider an economy with the following production function Y = K1/3 L2/3 a) Write down the function of production per unit of labor. b) Determine the steady state level of capital, income and consumption (all per unit of labor) as a function of the savings rate and the depreciation rate. c) Suppose that the depreciation rates is 10% per year. Compute consumption per unit of labor for a savings rate of 0%, 10%, 20%, 30%, 40%, 50%, etc. What is the savings rate that maximizes consumption per unit of labor? d) Compute the net rate of return on capital in the steady state for all the savings rates of part (c). What is the relationship between the real rate of return on capital and consumption per unit of labor?