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# exam2 problem set &amp; answers - Sample questions for...

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Page 1 Sample questions for Exam 2 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? 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? 3. 4. 5. a. As an economy moves into a recession, income falls. Illustrate graphically the impact of a decrease in income on the equilibrium interest rate using the theory of liquidity preference and the market for real money balances. Be sure to label: i. the axes; ii. the curves; iii. the initial equilibrium values; iv. the direction the curve shifts; and v. the terminal equilibrium values. b. Explain in words what happens to the equilibrium interest rate as a result of the fall in income.

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Page 2 6. Two identical countries, Country A and Country B, can each be described by a Keynesian-cross model. The MPC is .9 in each country. Country A decides to increase spending by \$2 billion, while Country B decides to cut taxes by \$2 billion. In which country will the new equilibrium level of income be greater?
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