We propose a new model of two-sided matching markets, which allows for complex heterogeneous preferences, but is more tractable than the standard model, yielding rich comparative statics and new results on large matching markets.
We simplify the standard Gale and Shapley (1962) model in two ways. First, we assume that a finite number of agents on one side (colleges or firms) are matched to a continuum mass of agents on the other side (students or workers). Second, we show that stable matchings can be characterized in terms of supply and demand equations.
We show that, very generally, the continuum model has a unique stable matching, which varies continuously with the underlying fundamentals. Moreover, stable matchings in the continuum model are the limit of the set of stable matchings in large discrete economies, so that the continuum model is an approximation of the standard Gale and Shapley model in markets where agents on one side are matched to many agents on the other side.
We apply the model to a price-theoretic analysis of how competition induced by school choice gives schools incentives to invest different aspects of quality, and of the distortions in privately optimal investments. As another application, we characterize the asymptotics of school choice mechanisms used in practice, generalizing previous results of Che and Kojima (2010).