If I increase the supply of something, its price should go down. And if I decrease the supply, its price should rise. Some markets do not seem to follow this pattern, however, with skilled labor in the US since 1970 being a famous example. As the percentage of college-educated workers has risen the U.S., the premium paid to the college educated has also risen. How can this be? One hypothesis is skill-biased technical change: the innovation that has occurred over the past few decades, computers included, has been complementary with the skills of educated workers. When might we expect innovation to complement certain factors?
An old and incorrect answer, previously discussed on this site, is that innovation will replace “expensive” factors of production. If labor is dear, for instance, firms will try to invent machines to replace labor. This intuition is wrong: in competitive markets, all factors are paid their marginal products, so saying labor is “dear” is just like saying labor is productive. And you might imagine we’d want to develop innovations that are complementary to our most productive factors!
Daron Acemoglu has a nice paper from a few years back – already very highly cited – dealing with these issues. Take a good produced using two factors with a CES production function; that is, the way in which factors are substituted for one another does not depend on how much of each factor we are already using. Let each factor have its marginal productivity improve by technology multipliers A1 and A2, and let innovations (which increase A1 or A2) be developed in any structure where the amount of new innovation responds in the natural way to the social value created by improving the technology multiplier. Acemoglu uses a monopoly innovator, but broader assumptions here about how social value is captured will not change the basic point.
The social value of innovations in each factor are increasing in the price paid to the factor and the total quantity of that factor used. If one factor is, say, skilled labor, then my incentive to create innovations improving the productivity of skilled labor depends both on how much skilled labor will be used, and on how productive the marginal skilled labor already is (since my invention is a multiplier on the existing marginal product). Imagine now that I increase the relative supply of skilled labor, exogenously. Will I see more or less skilled labor-augmenting invention? On the one hand, there is more skilled labor, so I can sell my innovation to a bigger market, but on the other hand this extra labor has a lower marginal product, so there is less productivity to enhance. Which effect dominates? With CES production, there is a simple rule. If the two factors are gross substitutes, an increase in the relative supply of a factor will increase the incentive to develop innovations augmenting that factor, and vice versa for gross complements. That is, with gross substitutes, an increase in the supply of one factor will not affect the relative factor prices (read: relative marginal products) very much, so the effect of an increased amount of that factor which I can augment dominates the effect of lower marginal product on that factor.
In the short run, before innovations can be created, the now more abundant factor sees its rent (wage) decline. This is the usual substitution effect. But what about in the long run, after technology is created? Here we need to model explicitly the monopolists who create inventions. It turns out that if the elasticity of substitution between factors is sufficiently high, an exogenous increase in the relative supply of one factor will increase the rent received by that factor. That is, the long run factor demand curves will slope up! This is because when the factors are gross substitutes (the elasticity of substitution is at least 1), innovation will be directed toward the now more abundant factor. The higher the elasticity, the more innovation. At some point, there is so much productivity-enhancing innovation directed toward the more abundant factor that even though the marginal units of this factor were relatively unproductive without the innovation, and hence received a lower wage, the response by innovators will be high enough that the now-more-abundant factor is paid even more than it was before the exogenous supply increase. A quick aside: theoretically, the increased elasticity (though not the sign change) of long-run response vis-a-vis short-run response is well known. It is called the Le Chatelier Principle and comes to economics via Paul Samuelson. Milgrom and Roberts have a lovely paper on why Le Chatelier works. The three theorems in this paper are proof positive of the usefulness of monotone comparative statics. Topkis is used to prove a result in two lines that must have taken pages to prove, and in less generality, with earlier techniques.
Consider again the concrete example of skilled labor since 1970. Goods are produced with skilled and unskilled labor. The supply of skilled labor increases, due to the GI Bill and other exogenous factors. This causes the skill premium to fall initially. If the elasticity of substitution is above 2, the long run wage premium to skilled labor will increased due to the effect of incentives to develop technologies augmenting the now larger base of skilled labor. This is one explanation for why you may have seen skill-biased technological change after the 1960s, and why there may have been enough of it to raise the skill premium. (Note that the elasticity of substitution itself is fixed in this model, but you might imagine that certain types of innovations may affect this factor.)
Those interested in Acemoglu’s work may enjoy an empirical paper by a PhD student on the job market this year, Walker Hanlon, applying Acemoglu’s result to the context of the Cotton Crisis, the shift in Britain from using US to using Indian cotton during the US Civil War. He has some nice data showing that even though Indian cotton became relatively abundant, there was a great amount of invention dealing with gins and other techniques for handling idiosyncratic issues in the Indian supply, and that the elasticity of substitution between US and Indian cotton was high enough that, indeed, the relative price of Indian cotton to US cotton rose by the end of the Civil War despite the relative abundance of the Indian cotton.
A Fine Theorem 