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.
Distilled versions of this paper appear in my pedagogical papers:
Frictional Matching Models, Annals Reviews of Economics
and also as part of a larger picture of my search and matching work in:
Sorting Through Search and Matching Models in Economics, Chade, Eeckhout, and Smith, Journal of Economic Literature, 2017, 55(2), 1–52