1. Consider an economy described by the production function:

Y = F(K,L) = K³L⁷

a. What is the per worker production function?

b. Assuming no population growth or technological progress, find the steady state capital stock per worker , output per worker, and consumption per worker as a function of the savings rate and the depreciation rate.

c. Assume that the depreciation rate is 10% per year. Make a table showing steady state capital per worker, output per worker, and consumption per worker for savings rates of 0%, 10%, 20%, 30%, and so on. What saving rate maximizes output per worker? What saving rate maximizes consumption per worker?