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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 > 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 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 672