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 the appendix to Chapter 3.)
a. What must the saving rate be in the initial steady state? [Use the steady-state relationship, sy = (d + 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?
e. What must the saving rate be to reach the Golden Rule steady state?