Collective household consumption behavior: revealed preference analysis (Q2903456)

The issue is devoted to modeling of consumers' demand of a ``small group'' (with less consumers than commodities) with account of intra group interaction. It is known that the unitary approach to the modeling of individual consumers leads to the paradoxes of aggregate (market) demand which have been revealed by \textit{W. M. Gorman} [Econometrica 21, 63--80 (1953; Zbl 0052.15905)] and \textit{H. Sonnenschein} [Econometrica 40, 549--563 (1972; Zbl 0262.90006)]. So, the scope of the investigation is actual and interesting. The model under investigation is some developing of the model of market behavior of a small group which have been investigated by \textit{P. A. Chiappori} and \textit{I. Ekeland} [Econometrica 77, No. 3, 763--799 (2009; Zbl 1182.91065)]. Here individual preferences are represented via utility functions. Each of the functions depends on privately and/or public goods, and the utility of each member may depend on private consumption of others. The investigation questions are necessary and sufficient conditions for the model identifiability and recovering methods for the underlying structure. This problem is an ill-posed one, and it can be effective solved under additional assumptions with respect to the sought characteristics. Unlike of the predecessors, which fulfilled an analytical investigation in terms of the Slutsky matrix, the authors of the issue develop a nonparametric ``revealed preference'' approach. It is assumed that in addition to the customary discrete trade data, i.e. prices and quantities relevant to the household for each period of observation, \textit{assignable quantities} consumed by single members also are given. The authors obtain a Mixed Integer Programming characterization of Generalised Axiom of Revealed Preference which is effective for checking the collective rationalizability of the data. The model's structure, which is being recovered, is the \textit{sharing rule} for distribution of the household income across the household members. The proposed testing and recovery methods are illustrated on data drawn from the Russian Longitudinal Monitoring Survey.