# 2. Ã¢â‚¬Â¢ An economy has a Cobb-Douglas production function_Y=KÃŽÂ±(LE)1Ã¢Ë†â€™ÃŽÂ±.(For

2. Ã¢â‚¬Â¢ An economy has a Cobb-Douglas production function:
Y=KÃŽÂ±(LE)1Ã¢Ë†â€™ÃŽÂ±.
(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

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