Cross-Sectional Dynamics in a Two-Sided Matching Model*

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. *The model of this paper was inspired by a conversation with Doug Galbi. Computer simulations done by Parag Gupta under the DROP have also been very helpful. ~