Suppose that the economys production function is Y = \sqrt{k} \sqrt{an} , that the saving rate, s, is equal to 16%, and that the rate of...

6. Suppose that the economy's production function is Y =   , that the saving rate, s, is equal to 16%, and that the rate of depreciation, d, is equal to 10%. Suppose further that the number of workers grows at 2% per year and that the rate of technological progress is 4% per year.

a. Find the steady-state values of the variables listed in (i) through (v).

i. The capital stock per effective worker

ii. Output per effective worker

iii. The growth rate of output per effective worker

iv. The growth rate of output per worker

v. The growth rate of output

b. Suppose that the rate of technological progress doubles to 8% per year. Recompute the answers to part (a). Explain.

c. Now suppose that the rate of technological progress is still equal to 4% per year, but the number of workers now grows at 6% per year. Recompute the answers to (a). Are people better off in (a) or in (c)? Explain