Economic growth and economic development 686

Introduction to Modern Economic Growth
Proof. See Exercise 15.3.

Ô

More interesting than the aggregate growth rate and the transitional dynamics
behavior of the economy are the results concerning the direction of technological
change and its effects on relative factor prices. These are studied in the next subsection.
15.3.2. Directed Technological Change and Factor Prices. Let us start
by studying (15.27). This equation implies that, in BGP, there is a positive relationship between the relative supply of the H factor, H/L, and the relative factoraugmenting technologies, NH∗ /NL∗ only when σ > 1. In contrast, if the derived
elasticity of substitution, σ, is less than 1, the relationship is reversed. This might
suggest that, depending on the elasticity of substitution between factors (or between the intermediate goods), changes in factor supplies may induce technological
changes that are biased in favor or against the factor that is becoming more abundant. However, this conclusion is not correct. Recall from Section 15.2 that NH∗ /NL∗
refers to the ratio of factor-augmenting technologies, or to the ratio of physical productivities. What matters for the bias of technology is the value of marginal product
of factors, which is affected by changes in relative prices. We have already seen that
the relationship between factor-augmenting technologies and factor-biased technologies is reversed precisely when σ is less than 1. Thus, when σ > 1, an increase in
NH∗ /NL∗ is relatively biased towards H, while when σ < 1, it is a decrease in NH∗ /NL∗
that is relatively biased towards H.
This immediately establishes the following weak equilibrium bias result:
Proposition 15.3. Consider the directed technological change model described
above. There is always weak equilibrium (relative) bias in the sense that an increase
in H/L always induces relatively H-biased technological change.
Recall that weak bias was defined in Section 15.2 with a weak inequality, so
that the proposition is correct even when σ = 1, even though in this case it can be
verified easily from (15.27) that NH∗ /NL∗ does not depend on H/L.
Proposition 15.3 is the basis of the discussion about induced biased technological
change in Section 15.1, and already gives us a range of insights about how changes
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