Country a and country b both have the production function y 5 f(k, l) 5 k1/3l2/3.
a. does this production function have constant returns to scale? explain.
b. what is the per-worker production function, y 5 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 percent of output each year and country b saves 30 percent 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 steady-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?
e. remembering that the change in the capital stock is investment less depreciation, use a calculator (or, better yet, a computer spreadsheet) to show how the capital stock per worker will evolve over time in both countries. for each year, calculate income per worker and consumption per worker. how many years will it be before the consumption in country b is higher than the consumption in country a?