Competitive Search with Ex-post Opportunism

We consider a frictional market where an element of the terms of trade (price or quantity) is posted ex-ante (before the matching process) while the other is determined ex-post. By doing so, sellers can then exploit their local monopoly power by adjusting prices or quantities once the local demand is realized. We find that when sellers can adjust quantities ex-post, there exists a unique symmetric equilibrium where an increase in the buyer-seller ratio leads to higher quantities and prices. When buyers instead can choose quantity ex-post, higher buyer-seller ratio leads to higher price but lower quantity. These equilibrium allocations are generically not constrained efficient, in terms of both intensive and extensive margins. When sellers post ex-ante quantities and adjust prices ex-post, a symmetric equilibrium exists where buyers obtain no surplus. The equilibrium allocation is also constrained inefficient. If buyers choose prices ex-post, there is no equilibrium when entry is costly. This paper highlights how sellers ability to commit ex-ante to certain elements of the terms of trade is crucial in generating constrained efficient allocations.