# CH7 - Import Settings Base Settings Brownstone Default...

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Import Settings: Base Settings: Brownstone Default Information Field: Level Information Field: Sub Topic Information Field: Topic Highest Answer Letter: D Multiple Keywords in Same Paragraph: No Chapter: CH7 Instruction: Name: __________________________ Date: _____________ Short Answer 1. Assume that a country's production function is Y = K 1/2 L 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 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? Ans: a. y = k 1/2 . b. Y = 20,000; Y / L = 2; y = 2; yes

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c. s = 0.2. d. Consumption per worker will be 1.6. Sub Topic: Alternative Perspectives on Population Growth Topic: Numerical Problems 2. Assume that a country's per-worker production is y = k 1/2 , where y is output per worker and k is capital per worker. Assume also that 10 percent of capital depreciates per year (= 0.10). a. If the saving rate ( s ) is 0.4, what are capital per worker, production per worker, and consumption per worker in the steady state? ( Hint: Use sy = k and y = k 1/2 to get an equation in s , , k , and k 1/2 , and then solve for k .) b. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.6. c. Solve for steady-state capital per worker, production per worker, and consumption per worker with s = 0.8. d. Is it possible to save too much? Why? Ans: a. k = 16; y = 4; consumption per worker is 2.4. b. k = 36; y = 6; consumption per worker is 2.4. c. k = 64; y = 8; consumption per worker is 1.6. d. Yes. If the capital stock gets so big that the extra output produced by more capital is less than the extra saving needed to maintain it, extra capital reduces consumption per worker. The saving rate exceeds the Golden Rule rate. Sub Topic: Alternative Perspectives on Population Growth Topic: Numerical Problems 3. Suppose that two countries are exactly alike in every respect except that the citizens of country A have a higher saving rate than the citizens of country B. a. Which country will have the higher level of output per worker in the steady state? Illustrate graphically. b. Which country will have the faster rate of growth of output per worker in the steady state? Ans: a. Country A will have the higher level of output per worker.
b. In the steady state, the growth rate of output per worker will be zero in both country A and country B.

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