Suppose an economy is characterized by the standard Cobb Douglas production function in per capita terms: y=Ak^ ?? h^ (1-??). Further suppose that the rate of growth in the number of workers is L'=.02, the rate of growth in the capital stock is K'=.04and the rate of growth in labor efficiency is h'=.02. Finally, suppose that ? = ½ and the rate of growth in output per worker is (Y/L)'=y'=.04. Always show your work in answering the questions below.
a) Write the Cobb Douglass production above in terms of growth rates.
b) What is the rate of growth in capital per worker?
c) What is the productivity growth in this economy?
d) If you had lacked information on growth in the quality of the labor force, and you had therefore assumed that labor quality was not changing (i.e., that h'= 0.0), how would your answer to part (c) have differed?