Platform pricing in matching markets

Existing models of two-sided markets explain why platforms charge different prices between buyers and sellers. Generally, the platform will subsidize participation on a side of the market the higher is that side's positive crossside externality to users on the other side of the market. However, in matching markets there also exists a negative own-side congestion externality that the platform internalizes by taxing users for its presence. Assuming a monopoly platform pricing model, the first contribution of this paper is to show that these positive cross-side and negative own-side externalities can be summarized by the matching elasticity derived from a general matching function that captures the efficiency of the platform's matching technology. The platform charges a lower price to a side of the market the higher is that side's matching elasticity. The second contribution of this paper is to show that the platform's pricing strategy only partially internalizes the efficiency of its matching technology, compared to the social optimum. In particular, we discuss the possibility that a monopoly matchmaker sets too high a price on the low-price side of the market and too low a price on the high-price side of the market, resulting in insufficient inequality in prices between sides of the platform.