Macroeconomics

Assumptions:    y

= 兹k苶;

d

= 0.1

s

k*

y*

d

k*

c*

MPK

MPK

−

d

0.0

0.0

0.0

0.0

0.0





0.1

1.0

1.0

0.1

0.9

0.500

0.400

0.2

4.0

2.0

0.4

1.6

0.250

0.150

0.3

9.0

3.0

0.9

2.1

0.167

0.067

0.4

16.0

4.0

1.6

2.4

0.125

0.025

0.5

25.0

5.0

2.5

2.5

0.100

0.000

0.6

36.0

6.0

3.6

2.4

0.083

−0.017

0.7

49.0

7.0

4.9

2.1

0.071

−0.029

0.8

64.0

8.0

6.4

1.6

0.062

−0.038

0.9

81.0

9.0

8.1

0.9

0.056

−0.044

1.0

100.0

10.0

10.0

0.0

0.050

−0.050

Finding the Golden Rule Steady State: A Numerical Example

TA B L E

7 - 3

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happens to consumption, investment, and capital when the economy makes the

transition between steady states? Might the impact of the transition deter the

policymaker from trying to achieve the Golden Rule?

We must consider two cases: the economy might begin with more capital than

in the Golden Rule steady state, or with less. It turns out that the two cases offer

very different problems for policymakers. (As we will see in the next chapter, the

second case—too little capital—describes most actual economies, including that

of the United States.)

Starting With Too Much Capital 

We first consider the case in which the

economy begins at a steady state with more capital than it would have in the

Golden Rule steady state. In this case, the policymaker should pursue policies

aimed at reducing the rate of saving in order to reduce the capital stock. Suppose

that these policies succeed and that at some point—call it time t

0

—the saving

rate falls to the level that will eventually lead to the Golden Rule steady state.

Figure 7-9 shows what happens to output, consumption, and investment

when the saving rate falls. The reduction in the saving rate causes an imme-

diate increase in consumption and a decrease in investment. Because invest-

ment and depreciation were equal in the initial steady state, investment will

now be less than depreciation, which means the economy is no longer in a

steady state. Gradually, the capital stock falls, leading to reductions in output,

consumption, and investment. These variables continue to fall until the econ-

omy reaches the new steady state. Because we are assuming that the new

steady state is the Golden Rule steady state, consumption must be higher than

it was before the change in the saving rate, even though output and invest-

ment are lower.

C H A P T E R   7

Economic Growth I: Capital Accumulation and Population Growth

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