In this chapter we discuss in more detail the determination of the division of the marital surplus and how it responds to market conditions. If each couple is considered in isolation, then, in principle, any efficient outcome is possible, and one has to use bargaining arguments to determine the allocation. From a global perspective, however, the stability of the assignments restricts the possible divisions because of the ability to replace one spouse by another one. The options for such substitution depend on the distributions of the marital-relevant attributes in the populations of men and women to be matched. In this chapter we precisely ask how the marriage market influences the outcome in the ideal, frictionless case discussed previously. Although the division within marriage is not always fully determined, some qualitative properties of the division can be derived from information on the joint distribution of male and female characteristics together with a specification of the household output function.

As before, we discuss separately the cases of discrete and continuous distributions. The general intuition goes as follows: in the discrete case, competition puts bounds on individual shares but does not completely determine them; this is so because on the marriage market, each potential spouse has only a finite number of “competitors,” none of whom is a perfect substitute – so some elements of “bilateral monopoly” persist.