In his theory of marriage, Becker (1973) showed that assortative matching arises with either (i) supermodular productive interaction and transferable utility, or (ii) monotonic production with nontransferable utility (NTU). In an exploration of the latter NTU matching model, this paper shows how productive interaction again matters if finding partners requires timing-consuming search. I show that the reason is that one must consider the value of everyone's time.
I present a simple search-theoretic model that explores this insight. Assume that type x earns f(x,y) when matched with y, with higher types preferred (fy>0). When f(x2,y2)f(x1,y1)= f(x2,y1)f(x1,y2), all von Neumann-Morgenstern preferences over matches coincide, and perfect segregation, or equivalence classes, arises. This observation then motivates my main proposition that in any search equilibrium and for all atomless type distributions, matching is positively assortative --- i.e. the set of types with whom x matches is increasing in x --- when f is log-supermodular: f(x2,y2)f(x1,y1)>f(x2,y1)f(x1,y2) for x2>x1,y2>y1.