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?