Consider a group consisting of S members facing a common budget constraint p'xi=1: any demand vector belonging to the budget set can be (privately or publicly) consumed by the members. Although the intragroup decision process is not known, it is assumed to generate Pareto-efficient outcomes; neither individual consumptions nor intragroup transfers are observable. The paper analyzes when, to what extent, and under which conditions it is possible to recover the underlying structure-individual preferences and the decision process-from the group's aggregate behavior. We show that the general version of the model is not identified. However, a simple exclusion assumption (whereby each member does not consume at least one good) is sufficient to guarantee generic identifiability of the welfare-relevant structural concepts.

We analyze under which conditions a given vector field can be disaggregated as a linear combination of gradients. This problem is typical of aggregation theory, as illustrated by the literature on the characterization of aggregate market demand and excess demand. We argue that exterior differential calculus provides very useful tools to address these problems. In particular, we show, using these techniques, that any analytic mapping in Rn satisfying Walras Law can be locally decomposed as the sum of n individual, utility-maximizing market demand functions. In addition, we show that the result holds for arbitrary (price-dependent) income distributions, and that the decomposition can be chosen such that it varies continuously with the mapping. Finally, when income distribution can be freely chosen, then decomposition requires only n/2 agents.

The neoclassical theory of demand applies to individuals, yet in empirical work it is usually taken as valid for households with many members. This paper explores what the theory of individuals implies for households that have more than one member. We make minimal assumptions about how the individual members of the household resolve conflicts. All we assume is that however decisions are made, outcomes are efficient. We refer to this as the collective setting. We show that in the collective setting household demands must satisfy a symmetry and rank condition on the Slutsky matrix. We also present some further results on the effects on demands of variables that do not modify preferences but that do affect how decisions are made. We apply our theory to a series of surveys of household expenditures from Canada. The tests of the usual symmetry conditions are rejected for two-person households but not for one-person households. We also show that income pooling is rejected for two-person households. We then test for our collective setting conditions on the couples data. None of the collective setting restrictions are rejected. We conclude that the collective setting is a plausible and tractable next step to take in the analysis of household behavior.