Assume That a Country's Production Function Is Y = K^1/2L^1/2 $y = f ( k )$

question 55

Essay

Assume that a country's production function is Y = K^1/2L^1/2. a. What is the per-worker production function $y = f ( k )$ ?
b. Assume that the country possesses 40,000 units of capital and 10,000 units of abor. 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 necessaty 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 perworker output must equal the depreciation rate multiplied by the capital-labor ratio.)
d. If the saving rate equals the steady-state level, what is consumpti on per worker?

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