In Becker's (1973) neoclassical marriage market model, matching is positively assortative if types are complements: i.e., match output f(x, y) is suipermoddlar in x and y. We reprise this famous result assuming time-intensive partner search and transferable output. We prove existence of a search equilibrium with a continuum of types, and then characterize matching. After showing that Becker's conditions on match output no longer suffice for assortative matching, we find sufficient conditions valid for any search frictions and type distribution: supermodularity not only of output f, but also of log f, and log f Symmetric submodularity conditions imply negatively assortative matching. Examples show these conditions are necessary.

We extend the concept of competitive search equilibrium to environments with private information, and in particular adverse selection.Principals (e.g.employers or agents who want to buy assets) post contracts, which we model as revelation mechanisms.Agents (e.g.workers, or asset holders) have private information about the potential gains from trade.Agents observe the posted contracts and decide where to apply, trading off the contracts' terms of trade against the probability of matching, which depends in general on the principals' capacity constraints and market search frictions.We characterize equilibrium as the solution to a constrained optimization problem, and prove that principals offer separating contracts to attract different types of agents.We then present a series of applications, including models of signaling, insurance, and lemons.These illustrate the usefulness and generality of the approach, and serve to contrast our findings with standard results in both the contract and search literatures.