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2 • An economy has a CobbDouglas production function Y=Kα(LE)1−α (For

Question

2. • 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 1/3, a saving rate of 24 percent, a depreciation rate

of 3 percent, a rate of population growth of 2 percent, and a rate of laboraugmenting

technological change of 1 percent. It is in steady state.

a. At what rates do total output, output per worker, and output per effective

worker grow?

b. Solve for capital per effective worker, output per effective worker, and the

marginal product of capital.

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?

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)? Explain your

answers.

Macroeconomics

2 • An economy has a CobbDouglas production function Y=Kα(LE)1−α (For