Assume that a country's production function is Y = K/2*L/2 and there is no population growth or technological change. 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 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 saving rate equals the steady-state level, what is consumption per worker?
Assume that a country's production function is Y = K/2*L/2 and there is no population growth or technological change. 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 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 saving rate equals the steady-state level, what is consumption per worker?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Assume that a country's production function is Y = K/2*L/2 and there is no population growth
or technological change.
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 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 saving rate equals the steady-state level, what is consumption per worker?
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