In his 1956 seminal paper, Paul Samuelson proves the impossibility of constructing a social indifference curve. Observing the family as a meaningful consumption unit in the market, he then asks under what conditions can we observe well-behaved family demands. Assuming fixed commodity types and the existence of “consensus” (interrelated preferences among family members), he concludes that the family can behave like a “representative consumer” if income can always be redistributed to maintain the marginal value of one dollar (or “ethical worth”, as Samuelson puts it) is constant across all family members.
Samuelson’s “consensus” is what Gary Becker calls “altruism”. Becker (1991) argues that an altruist in the family will incorporate the utility of others into her own utility function and maximize this quasi-joint function according to budget constraint. The implication of his model is that altruism encourages beneficiaries to behave cooperatively but could lead to noncooperative behaviours among beneficiaries.
McElroy and Horney (1981) introduced cooperative Nash bargaining into household decisions. In their model, each spouse has a “threat point” — maximum utility outside the household — that shifts their relative bargaining positions. In addition, the objective for both spouse is to maximize their joint gain from the marriage, denoted by the product of their individual gains. The beauty of this model lies in its capacity to translate price and income changes into not only the shift of budget constraint but also the tilting of the Iso-Gain Product Curve (counterpart of utility curves in individual maximization problem). For example, if the wife receives a promotion, she contributes more income to the household but a greater proportion will be spent on goods to her favor. Extrahousehold Environmental Parameters (EEPs) such as marriage laws, gender ratio, and tax rates, are also incorporated into the model.
It might be helpful for readers to visualize their theory in the graph below. The hyperplane is the pooled income budget constraint, and the three axes denotes the amount of consumption for each person’s leisure and their family good, X. Note that the objective is to maximize household joint gains (a set of nested balls) under their budget constraint. A change in price or income, or the EEPs, will change the objective function and cause the orientation of the utility ball to tilt. This tilting reflects the change in relative bargaining power and will lead to the new equilibrium.
For a neat comparison of Nash bargaining and neoclassical model and a scratch of empirical testing methods, refer to McElroy (1990).
Becker, G. 1991. A Treatise on the Family. Cambridge, Mass. : Harvard University Press.
McElroy, M. B., and Horney, M. J. 1981. “Nash-Bargained Household Decisions: Toward a Generalization of the Theory of Demand,” International Economic Review 22(2): 333-349.
McElroy, M. B. 1990. “The Empirical Content of Nash-Bargained Household Behavior,” Journal of Human REsources 25(4): 559-583.
Samuelson, P. 1956. “Social Indifference Curves,” Quarterly Journal of Economics 70(1): 1-22.