Economic growth and economic development 506

Introduction to Modern Economic Growth
³ ´
³ ´
ˆ 2 kˆ constant, (10.41) implies that kˆ should increase, since
ˆ 1 kˆ and h
Holding h
³ ´
³ ´
ˆ 2 kˆ and
ˆ 1 kˆ > h
the left-hand side has increased (in view of the fact that h

∂ 2 F (k, h) /∂k∂h > 0). Therefore, capital-skill complementarity combined with the

pecuniary externalities implies that an improvement in the pool of workers that
firms face leads to greater investments by firms. Intuitively, each firm expects the
average worker that it will be matched with to have higher human capital and since
physical and human capital are complements, this makes it more profitable for each
firm to increase
investments by firms, in
³ ´
³ their
´ physical capital investment. Greater
ˆ h for each h, in particular for h
ˆ 2 kˆ . Since the earnings of type
turn, raise F k,
³ ´´
³
ˆ h
ˆ 2 kˆ , their earnings will also increase as a result
2 workers is equal to λF k,

of the response of firms to the change in the composition of the workforce. This

is therefore an example of human capital externalities, since greater human capital
investments by one group of workers have increased the earnings of the remaining
workers. In fact, human capital externalities,
³ in
´´this economy, are even stronger,
³
ˆ h
ˆ 2 kˆ /∂h and thus encourages further
because the increase in kˆ also raises ∂F k,
investments by type 2 workers. These feedback effects nonetheless do not lead to

divergence or multiple equilibria, since we know from Proposition 10.3 that there
exists a unique equilibrium with positive activity. We summarize this discussion
with the following result:
Proposition 10.6. The positive activity equilibrium described in Proposition
10.3 exhibits human capital externalities in the sense that an increase in the human capital investments of a group of workers raises the earnings of the remaining
workers.
10.7. Human Capital Externalities
The previous section illustrated how a natural form of human capital externalities
can emerge in the presence of capital-skill complementarities combined with labor
market imperfections. This is not the only channel through which human capital
externalities may arise. Many economists believe that the human capital stock of the
workforce creates a direct non-pecuniary (technological) spillover on the productivity
of each worker. In The Economy of Cities, Jane Jacobs, for example, argued for
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