Economic growth and economic development 505

Introduction to Modern Economic Growth
through prices (not through direct technological spillovers). By investing more,
workers (and symmetrically firms) increase the return to capital (symmetrically
wages), and there is underinvestment because they do not take these external effects
into consideration. Pecuniary external effects are also present in competitive markets
(since, for example, supply affects price), but these are typically “second order,”
because prices are such that they are equal to both the marginal benefit of buyers
(marginal product of firms in the case of factors of production) and to the marginal
cost of suppliers. The presence of labor market frictions causes a departure from
this type of marginal pricing and is the reason why pecuniary externalities are not
second order.
Perhaps even more interesting is the fact that pecuniary externalities in this
model take the form of human capital externalities, meaning that greater human
capital investments by a group of workers increase other workers’ wages. Notice that
in competitive markets (without externalities) this does not happen. For example,
in the economy analyzed in the last section, if a group of workers increase their
human capital investments, this would depress the physical to human capital ratio
in the economy, reducing wages per unit of human capital and thus the earnings
of the rest of the workers. We will now see that the opposite may happen in the
presence of labor market imperfections. To illustrate this point, let us suppose that
there are two types of workers, a fraction of workers χ with ability a1 and 1 − χ

with ability a2 < a1 . Using this specific structure, the first-order condition of firms,
(10.39), can be written as
³
³ ´´
³ ´´ ⎤
³
⎡
ˆ
ˆ

ˆ
ˆ
ˆ
∂F k, h2 kˆ
∂F k, h1 k
⎦ = R∗ ,
⎣
+ (1 − χ)
(10.41)
(1 − λ) χ
∂k
∂k

while the first-order conditions for human capital investments for the two types of

workers take the form
(10.42)

λaj

³ ´´
³
ˆ h
ˆ j kˆ
∂F k,
∂h

³ ´⎞
ˆ j kˆ
h

⎠ for j = 1, 2.
= γ0 ⎝
aj
⎛

ˆ 2 (k) since a1 > a2 . Now imagine an increase in χ, which corˆ 1 (k) > h
Clearly, h
responds to an increase in the fraction of high-ability workers in the population.
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