Generalizations and Other Applications
The results presented so far rely on a range of specific assumptions that are inherent in endogenous technological change models (e.g., Dixit-Stiglitz preferences and linear structure to ensure sustained growth).
One may naturally wonder whether the results on weak and strong equilibrium bias generalize to situations in which these assumptions are relaxed. The answer is broadly yes. In Acemoglu (2007), I show that, as long as only factor-augmenting techological changes are possible, the main results presented here also apply in an environment in which production and cost functions take more general forms. In particular, in this general environment, there is always weak (relative) equilibrium bias in response to increases in relative supplies and there will be strong equilibrium bias when the elasticity of substitution is sufficiently high. However, once we allow for a richer menu of technological changes, these results do not necessarily hold. Nevertheless, the essence of the results appears to be much more general. In Acemoglu (2007), I define the complementary notions of weak and strong 588absolute equilibrium bias, which refer to whether the equilibrium price of a factor change as the supply of that factor changes (rather than the price of a factor relative to the price of another factor, which is what I have focused on in this chapter). Under very weak regularity assumptions, there is always weak absolute equilibrium bias, in the sense that an increase in the supply of a factor always induces technological change biased in favor of that factor. Moreover, even though standard producer theory implies that an increase in the supply of a factor should reduce price, under plausible assumptions the induced technology effect can be strong enough that the price of the factor that has become more abundant can increase. In this case, there is strong absolute equilibrium bias and the (general equilibrium) demand curves for factors are upward sloping. Since these results require additional notation and somewhat different arguments, I will not present them here.
It is also useful to briefly discuss a number of other important applications of the models of directed technological change. To save space, these are not discussed in detail in the text and are left as exercises for the reader. In particular, Exercise 15.20 shows how this model can be used to shed light on the famous Habakkuk hypothesis in economic history, which relates the rapid technological progress in 19th-century United States to relative labor scarcity. Despite the importance of this hypothesis in economic history, there have been no compelling models of this process. This exercise shows why neoclassical models may have difficulties in explaining these patterns and how a model of directed technological change can account for this phenomenon as long as the elasticity of substitution is less than 1.
Exercise 15.21 shows the effects of international trade on the direction of technological change. It highlights that international trade will often affect the direction in which new technologies are developed, and this often works through the price effect emphasized above.
Exercise 15.27 returns to the discussion of the technological change and unemployment experiences of continental European countries we started with. It shows how a “wage push shock” can first increase equilibrium unemployment, and then induce endogenous capital- biased technological change, which reduces the demand for employment, further increasing unemployment.
Finally, Exercise 15.28 shows how the relative supply of factors can be endogenized and studies the two-way causality between relative supplies and relative technology can be studied.
15.8.