Cross-Sectional Dynamics in a Two-Sided Matching Model

This is my paper that started my interest in heterogeneous agent search models. I first presented it in 1992 at Summer in Tel Aviv and then at MIT. Later on, several other economists discovered my main block sorting result (including Hector Chade, Jan Eeckhout, and later, Burdett and Coles, who published it in the QJE in 1997). After this early draft, I later sleuthed  and found work in operations research by McNamara and Collins (1990) that has the main result, but assumes a fixed “infinite” population, i.e. ignores its endogeneity. Later on, dealing with this endogeneity in richer models became my great nemesis.  ( ͡° ͜ʖ ͡°)
Do read my brief synopsis in section 4.2.1 of Sorting Through Search and Matching Models in Economics.

Abstract: We explore a two-sided matching model with a continuum of agents indexed by efficiency parameters in (0,1), and assume that the flow output of the match (x, y) is 2xy. To incorporate nominal rigidities, we consider the nonstandard assumption of equal-output sharing, and show that the multiplicative production function engenders a natural segmentation of (0,1) into equivalence classes of agents willing to match with one another. This produces a discontinuous wage profile. We also analyze the non-steady state dynamics of the model, where the no-discounting case proves a fruitful benchmark. We find that quits endogenously arise as a non-steady state phenomenon. In the appendix, we describe the steady-state of the model under the standard Nash equal-surplus division rule.