Suppose that the production of the national economy is given by Y = K^α. N^1-α
Also assume that α = 1/3.
a. Is this production function characterized by constant economies of scale? Explain.
b. Are there diminishing marginal returns of capital?
c. Are there diminishing marginal returns of labor?
d. Write the production function as the relationship between production per employee and capital intensity.e. For the given savings rate s and depreciation rate δ, indicate what the capital intensity is in the steady state.
f. Specify the value for production per employee in the steady state.
g. Calculate the level of production per employee in the steady state for δ = 0.08 and s = 0.32.
h. Suppose that the depreciation rate remains unchanged, but the savings rate is halved to 0.16. In the new steady state, what is the level of production per employee?