Chapter 1. Chapter 9 – Problem 2

Step 1

Work It Out

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You must read each slide, and complete any questions on the slide, in sequence.

Question

An economy has a Cobb–Douglas production function:

Y = K^α(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 h4XZagboIgc=%.

Output per worker grows at 607M7xmPORU=%.

Question

4xfsy1uaxgvOdpWRVfroUAH3cizh9FZUgY8xojt5s01poxPU4Wxwku4NjIkcKdBUtqkOaDjViPThqNWEBZSIbgkgq4qO2FSjwfC/DrrGvl+vyHWvcD+7YK3X9ASk0fYLN9Sxhc6ROFhBoxA+CWwZrk8a4qc/XgyQ9whu13lotO0wgRHI05ddfN8fc5YnfhxxoYjQ8kYM5BTWiyDXG5+e/rMuJoX52OhcMdDgqyje+Gs=

Review pages 58-61 in Chapter 3 for a discussion of the Cobb-Douglas production function and pages 212-213 in Chapter 8 for a discussion of the per-worker production function. Review text pages 242-245 in Chapter 9 and Table 9-1 for a discussion of growth in the steady state.

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Step 2

Question

An economy has a Cobb–Douglas production function:

Y = K^α(LE)^1-α.

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

Capital per Effective Worker (k) = zhw5AiG32jY=

Output per Effective Worker (y) = XvVM00l89Is=

Marginal Product of Capital = NJcluA6RnW2MCmxSWXAxv/Y2IRBJAjM1usu7fQ==

Review text pages 242-245 for a discussion of technological progress in the Solow growth model.

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Step 3

Question

An economy has a Cobb–Douglas production function:

Y = K^α(LE)^1-α.

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 JiJQw/bEIbifhE91N/OSig== capital than at the Golden Rule steady state.

The economy has more capital than at the Golden Rule steady state. The marginal product of capital computed in Part B equals 0.031, which is lower than the value of 0.06 for the breakeven rate. This means that a decline in the capital stock will reduce output by less than it reduces breakeven investment, allowing consumption per effective worker to increase. In other words, the marginal product of capital is too low and capital is too high.

Question

To achieve the Golden Rule steady state, the saving rate needs to ihyXI3vweKBVkqtuOIeAYqcmI9iXy7Xh.

To achieve the Golden Rule steady state, the saving rate needs to decrease so that the capital stock per effective worker declines, thereby raising the marginal product of capital to equal the breakeven rate 0.06.

Question

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 1F1hSFA/y6X4GNK6/WY8jQ== than the initial steady-state rate of 3 percent.

Question

After the economy reaches its new steady state, the growth rate of output per worker will be equal to 607M7xmPORU= percent.

Review text pages 244-245 for a discussion of the Golden Rule in the Solow growth model with technological progress.

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