ECON 2202-001 Intermediate Macroeconomics Chapter 8 Homework Assignment 8-1. In the United States, the capital share of GDP is about 30 percent, the average growth in output is about 3 percent per year, the depreciation rate is about 4 percent per year, and the capital–output ratio is about 2.5. Suppose that the production function is Cobb–Douglas, so that the capital share in output is constant, and that the United States has been in a steady state. (For a discussion of the Cobb–Douglas production function, see Chapter 3.) a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state relationship sγ = (δ + n + g)k.] b. What is the marginal product of capital in the initial steady state? c. Suppose that public policy raises the saving rate so that the economy reaches the Golden Rule level of capital. What will the marginal product of capital be at the Golden Rule steady state? Compare the marginal product at the Golden Rule steady state to the marginal product in the initial steady state. Explain. d. What will the capital–output ratio be at the Golden Rule steady state? (Hint: For the Cobb–Douglas production function, the capital–output ratio is related to the marginal product of capital.) e. What must the saving rate be to reach the Golden Rule steady state? 8-2. In the economy of Wolosovia, the owners of capital get two-thirds of national income, and the workers receive one-third. a. The women of Wolosovia stay at home performing household chores, while the men work in factories. If some of the women started working outside the home so that the labor force increased by 5 percent, what would happen to the measured output of the economy? Would labor productivity— defined as output per worker—increase, decrease, or stay the same? Would total factor productivity increase, decrease, or stay the same? b. In year 1, the capital stock was 60, the labor input was 36, and output was 120. In year 2, the capital stock was 65, the labor input was...

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