Economic growth and economic development 687

Introduction to Modern Economic Growth
in the relative supplies of skilled workers may be at the root of the skill-biased technological change. These implications are further discussed in the next subsection.
The results of this proposition reflect the strength of the market size effect discussed above. Recall that the price effect creates a force favoring factors that become
relatively scarce. In contrast, the market size effect, which is related to the nonrivalry of ideas discussed in Chapter 12, suggests that technologies should change in
a way that favors factors that are becoming relatively abundant. Proposition 15.3
shows that the market size effect always dominates the price effect.
Proposition 15.3 is only informative about the direction of the induced technological change, but does not specify whether this induced effect will be strong enough to
make the endogenous-technology relative demand curve for factors upward-sloping.
Recall that in basic producer theory, all demand curves, and thus relative demand
curves, are downward-sloping as well. However, as hinted in Section 15.1, directed
technological change can lead to the seemingly paradoxical result that relative demand curves can be upward-sloping once the endogeneity of technology is taken into
account. To obtain this result, let us substitute for (NH /NL )∗ from (15.27) into the
expression for the relative wage given technologies, (15.19), and obtain the following
BGP relative factor price ratio (see Exercise 15.4):
ả
à
à
ả à ả2
1
H
wH

1
=
.
(15.30)

wL

L
Inspection of this equation immediately establishes conditions for strong equilibrium

(relative) bias.
Proposition 15.4. Consider the directed technological change model described
above. Then if σ > 2, there is strong equilibrium (relative) bias in the sense that an
increase in H/L raises the relative marginal product and the relative wage of the H
factor compared to the L factor.
Figure 15.3 illustrates the results of Propositions 15.3 and 15.4, referring to H as
skilled labor and L as unskilled labor as in the first application discussed in Section
15.1.
The curve marked with CT corresponds to the constant-technology relative demand from equation (15.19). It is always downward-sloping because it holds the
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