A Cournot-Nash Model of Family Decision Making

This paper develops a model of two person family. Each family member attempts to maximize his or her own utility. Yet they are interdependent in two respects. Family members are interdependent, first of all, because they care about each other. Second, there are local public goods or household expenditures within the family, such as housing. The presence of household expenditures means that one family member's consumption choices affect the other family member's level of well-being. The two family members' interdependent utility maximization problems are first solved using a non-cooperative, or Cournot-Nash, game theoretic framework then the model is extended to take the Cournot-Nash equilibrium as a threat point in a bargaining game. The model's predictions differ substantially from the "unitary" framework usually used in economic analysis, in which households maximize a single household utility function. When the spouses are relatively equal in income, or when one spouse is much wealthier than the other and the wealthier spouse has all the bargaining power in the family, the equilibrium depends, as in the unitary model, on household income but not on the division of income between spouses. In the intermediate case between equality and substantial inequality or in the case where one spouse is much wealthier than the other but the wealthier spouse does not have all the bargaining power, the distribution of income does shape expenditure patterns, contrary to the predictions of the unitary model. The contribution of the paper is to provide a rigorous derivation of the properties of household demands in the Cournot-Nash setting, a full analysis of the determinants of intra-household resource allocation, including the effect of varying household bargaining power, and an explication of the model’s implications for policy analysis.