Macroeconomics 12th Edition by Rudiger Dornbusch ,Stanley Fischer,Richard Startz

Exercise 5

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)