Country A and Country B both have the production function:
Y = F(K,L) = K^(1/3)L^(2/3).
a) Does this production function have constant returns to scale? Explain.
b) What is the per-worker production function, y = f(k)
c) Assume that neither country experiences population growth or technological progress and that 20-percent of capital depreciates each year. Assume further that country A saves 10% of output each year and country B saves 30% of output each year. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per worker for each country. Then find the stead-state levels of income per worker and consumption per worker.
d) Suppose that both countries start off with a capital stock per worker of 1. What are the levels of income per worker and consumption per worker?