The Golden Rule:
Consider an economy with the following production function Y = K^1/3 L^2/3
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?