Consider an economy with the following production function Y = K^1/3 L^2/3
1. Write the function of production per unit of labor.
2. Calculate the steady state level of income, capital, and the consumption as a function of the savings rate and depreciation rate.
3. Assume that the depreciation rates are 10% per year. Calculate the consumption per unit of labor for a savings rate of 0%, 10%, 20%, 30%, 40%, 50%, etc. Determine the savings rate that maximizes the consumption per unit of labor?
4. Calculate the net rate of return on the capital in steady state for all the savings rates of part (c). Determine the relationship among the real rate of return on capital and the consumption per unit of labor?