In this paper, I analyze a decentralized search and matching economy with transferable utility composed of heterogeneous agents. I explore whether Becker's assortative matching result generalizes to an economy where agents engage in costly search. In an economy with explicit additive search costs, complementarities in joint production (supermodularity of the joint production function) lead to assortative matching. This is in contrast to previous literature, which had shown that in a search economy with discounting, assortative matching may fail even when the joint production function is supermodular.