Steady state question
The capital share of GDP is about 40 percent, the average growth in output is about
2 percent per year, the depreciation rate is about 3 percent per year, and the capital–output ratio
is about 1.5. Suppose that the production function is Cobb–Douglas and
in a steady state.
a. What must the saving rate be in the initial steady state? [Hint: Use the steady-state
relationship, sy = (δ + n + g)k.]
b. What is the marginal product of capital in the initial steady state?
c. Suppose that public policy alters 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?
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c. Suppose that public policy alters the saving rate so
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In the nation of Wiknam, the capital share of GDP is 40 percent,
the average growth in output is 4 percent per year, the
depreciation rate is 6 percent per year, and the capital–output
ratio is 5. Suppose that the production function is Cobb–Douglas
and that Wiknam has been in a steady state. (For a discussion of
the Cobb–Douglas production function, see Chapter 3.)
c. Suppose that public policy alters the saving rate so
that the economy reaches the Golden...
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