An economy has a Cobb–Douglas production function:
Y = Kα(LE)1-α.
(For a review of the Cobb–Douglas production function, see Chapter 3.) The economy has a capital share of a quarter, a saving rate of 48 percent, a depreciation rate of 2 percent, a rate of population growth of 1 percent, and a rate of labor-augmenting technological change of 3 percent. It is in steady state.
a. At what rates do total output, output per worker, and output per effective worker grow?
Total output grows at %.
Output per worker grows at %.
Output per Effective Worker is:
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An economy has a Cobb–Douglas production function:
Y = Kα(LE)1-α.
(For a review of the Cobb–Douglas production function, see Chapter 3.) The economy has a capital share of a quarter, a saving rate of 48 percent, a depreciation rate of 2 percent, a rate of population growth of 1 percent, and a rate of labor-augmenting technological change of 3 percent. It is in steady state.
b. Solve for capital per effective worker, output per effective worker, and the marginal product of capital.
Capital per Effective Worker (k) =
Output per Effective Worker (y) =
Marginal Product of Capital =
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An economy has a Cobb–Douglas production function:
Y = Kα(LE)1-α.
(For a review of the Cobb–Douglas production function, see Chapter 3.) The economy has a capital share of a quarter, a saving rate of 48 percent, a depreciation rate of 2 percent, a rate of population growth of 1 percent, and a rate of labor-augmenting technological change of 3 percent. It is in steady state.
c. Does the economy have more or less capital than at the Golden Rule steady state? How do you know? To achieve the Golden Rule steady state, does the saving rate need to increase or decrease?
The economy has capital than at the Golden Rule steady state.
To achieve the Golden Rule steady state, the saving rate needs to .
d. Suppose the change in the saving rate you described in part (c) occurs. During the transition to the Golden Rule steady state, will the growth rate of output per worker be higher or lower than the rate you derived in part (a)? After the economy reaches its new steady state, will the growth rate of output per worker be higher or lower than the rate you derived in part (a)?
During the transition to the Golden Rule steady state, the growth rate of output per worker will be than the initial steady-state rate of 3 percent.
After the economy reaches its new steady state, the growth rate of output per worker will be equal to percent.
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