Assume that a country's production function is Y = AK^(1/2)L^(1/2)

a. What is the per-worker production function y = f(k) if A = 1?

b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What is Y? What is labor productivity computed from the per-worker production function? Is this value the same as labor productivity computed from the original production function?

c. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to make the given capital-labor ratio the steady-state capital-labor ratio? (Hint: In a steady state with no population growth or technological change, the saving rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital-labor ratio.)

d. If the capital stock per person equals the steady-state level, what is consumption per worker?

e. Now, assume the productivity coefficient of the economy becomes A = 2. What is per person production function f(k) now? What is the steady state capital-labor ratio (capital stock per person), if depreciation rate is 10% and saving rate is the same as you get in part (c) above? Is it higher or lower than the capital-labor ratio in part (c)? How about the consumption per person compared to your answer in part (d)?