How can consider an economy with the following production function Y = K1/3 L2/3
1. Write down function of production per unit of labor.
2. Describe the steady state level of income, capital and the consumption (all per unit of labor) as a function of the savings rate and depreciation rate.
3. Assume that the depreciation rate is 10 percent 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 capital in steady state for all savings rates of part
5. Calculate the relationship among the real rate of return on capital and the consumption per unit of labor?