Macroeconomics

F I G U R E

8 - 1

Technological Progress and

the Solow Growth Model

Labor-augmenting technologi-

cal progress at rate g enters our

analysis of the Solow growth

model in much the same way

as did population growth at

rate n. Now that k is defined as

the amount of capital per

effective worker, increases in

the effective number of workers

because of technological

progress tend to decrease k. In

the steady state, investment

sf (k) exactly offsets the reduc-

tions in k attributable to depre-

ciation, population growth,

and technological progress.

Investment,

break-even

investment

k* Capital per effective worker, k

Break-even investment, (

d  n  g)k

Investment, sf(k)

The steady

state

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C H A P T E R   8

Economic Growth II: Technology, Empirics, and Policy

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The introduction of technological progress also modifies the criterion for the

Golden Rule. The Golden Rule level of capital is now defined as the steady state

that maximizes consumption per effective worker. Following the same arguments

that we have used before, we can show that steady-state consumption per effec-

tive worker is

c*

= f(k*) − (

d

+ n + g)k*.

Steady-state consumption is maximized if

MPK

=

d

+ n + g,

or

MPK

−

d

= n + g.

That is, at the Golden Rule level of capital, the net marginal product of capital,

MPK

−

d

, equals the rate of growth of total output, n

+ g. Because actual

economies experience both population growth and technological progress, we

must use this criterion to evaluate whether they have more or less capital than

they would at the Golden Rule steady state.