Economic growth and economic development 503

Introduction to Modern Economic Growth
We have therefore obtained a simple characterization of the equilibrium in this
economy with labor market frictions and physical and human capital investments.
It is straightforward to observe that there is underinvestment both in human capital
and physical capital (this refers to the positive activity equilibrium; clearly, there is
even a more severe underinvestment in the no-activity equilibrium). Consider a social planner wishing to maximize output (or one who could transfer resources across
individuals in a lump-sum fashion). Suppose that the social planner is restricted by
the same random matching technology, so that she cannot allocate workers to firms
as she wishes. A similar analysis to above implies that the social planner would
¯ However,
also like each firm to choose an identical level of capital per firm, say k.
this level of capital per firm will be different than in the competitive equilibrium
and she will also choose a different relationship between human capital and physical
¯ she would make human capital decisions
capital investments. In particular, given k,
to satisfy

à ¡ ¢!
¡
¡ ¢¢
¯ h
¯ i k¯
¯ i k¯
∂F k,
h
0
,
=γ
ai
∂h
ai

which is similar to (10.40), except that λ is absent from the left-hand side. This is
because each worker considered only his share of output, λ, when undertaking his
human capital investment decisions, while the social planner considers the entire
output. Consequently, as long as λ < 1,
ˆ i (k) for all k > 0.
¯ i (k) > h
h
Similarly, the social planner would also choose a higher level of capital investment
for each firm, in particular, to satisfy the equation
¡
¡ ¢¢
Z 1
¯ h
¯ i k¯
∂F k,
di = R∗ ,
∂k
0

which differs from (10.39) both because now the term 1 − λ is not present on the

left-hand side and also because the planner takes into account the differential human
¡ ¢
¯ i k¯ . This discussion establishes
capital investment behavior of workers given by h

the following result:

Proposition 10.4. In the equilibrium described in Proposition 10.3, there is

underinvestment both in physical and human capital.
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