Consider the following production function: Y K.5 ( AN ) .5 , where both the population and the pool of labor are growing at a rate n .07, the capital stock is depreciating at a rate d .03, and A is normalized to 1.
a. What are capital's and labor'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 the steady state? At what rate is total output growing? What if total factor productivity is increasing at a rate of 2 percent per year ( g .02)?