A simple matching model of the marriage market M. Browning P.A. Chiappori Y. Weiss 0.0.1 Sharing rules We now return to the division of marital gains. 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. On the contrary, the re- quirement of stability of the assignment restricts intrahousehold allocations by putting bounds on individual well being. We now ask how the marriage market influences the outcome in an ”ideal” frictionless case, where partners are free to break marriages and swap partners at will. Although the division within marriage is not fully determined, some qualitative properties of the division can be derived from information on the joint distribution of male and female char- acteristics together with a specification of the household production function. These features show up more clearly if one assumes continuum of agents and continuous marital attributes. Then the marriage market can (under some ad- ditional assumptions) completely pin down the ’sharing rule’, i.e. the allocation of private consumptions for each married couple. We shall consider here a case in which the trait is income (assumed to be exogenous) and denote the male income by y and the female income by z. We assume transferable utility, so that the utility frontier for a couple is defined by the equation v + u = h(y,z)+ g, (1) where g is a common gain from marriage that is unrelated to incomes. If a man with income y remains single his utility is given by h(y, 0) and if a woman of income z remains single her utility is h(0,z). We assume that h(y,z) is increasing in y and z, and set h(0, 0) to zero. We refer to h(y,z)+ g as the marital output of the couple and to the difference h(y,z)+ g − h(y, 0) − h(0,z) as the surplus generated by their marriage. A crucial feature of the problem is the interaction in the traits that the two partners bring into marriage. When income is the only marital trait then, if the partners share a public good, their incomes are complements in the marital production function. 1 We shall, therefore, focus here on the case of comple- 1 Transferable utility in the presence of public good assumes the form u i = c i g(q)+ f i (q), where c and q denote private and public consumption, respectively. The Pareto frontier is 1