Consider the following production function. Y=K^5 (AN)^.5 , where both the population and the pool of labor are growing by rate n=.07, the capital stock is deprecciating at a rate of d= .03, and A is normalized to 1.
A. What are the capitals and labour’s shares of income?
B. What is the form of this production function?
C. Find the steady state values of k and y when s=.20
D. At what rate is per capita output growing at a steady state? At what rate is total output growing? What if the total factor of productivity is increasing at a rate of 2 percent year (g=.02)?