An Assignment Model with Divorce and Remarriage

Abstract

We develop a two-sided matching model with positive sorting, divorce and remarriage. Match quality for each couple is revealed ex post and those with poor draws divorce. Competition determines lifetime expected utilities but per-period utilities depend on the laws that govern the distribution of assets upon divorce. We discuss separately cases in which remarriage is or is not feasible and cases in which commitments are or are not made. In all cases, lifetime utilities are exactly pinned down by equilibrium (stability) requirements. Moreover, ex-post Nash bargaining and ex-ante commitment yield the same non-contingent intertemporal allocations. We then analyze the impact of changes in the property division upon divorce, considering for instance a reform that favors women. The short-term impact of the reform on the allocations of already married wives is positive. However, its long-term impact on yet unmarried women is not because such a reform generates lower utility for women within marriage which exactly offsets their higher prospective divorce settlement. When remarriage is possible, more complex effects could occur: the reform typically alters divorce probabilities and it may affect the total surplus generated by marriage, thus either increasing both spouses’ welfare or decreasing both.

Keywords: matching, intra-household allocations, Becker-Coase theorem

JEL Classification: J12, J16, J24