Assortative matching and search

In Becker's (1973) neoclassical marriage market model, matching is positively assortative if types are complements: i.e., match output f(x, y) is supermodular 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(x) and log f(xy). Symmetric submodularity conditions imply negatively assortative matching. Examples show these conditions are necessary.