We focus on the revealed preference conditions that characterize the collection of nite data sets that are consistent with the maximization of a weakly separable utility function. From a theoretical perspective, we show that verifying these revealed preference conditions is a difficult problem, i.e. it is np-complete. From a practical perspective, we present an integer programming approach that can verify the revealed preference conditions in a straightforward way, which is particularly attractive in view of empirical analysis. We demonstrate the versatility of this integer programming approach by showing that it also allows for testing homothetic separability and weak separability of the indirect utility function. We illustrate the practical usefulness of the approach by an empirical application to Spanish household consumption data. In this application we also include two statistical tests in which we account for measurement error. JEL Classi cation: C14, C60, D01, D10.Keywords: weak separability, revealed preference, integer programming * We thank Ian Crawford for generously providing us the data of the Encuesta Continua de Presupestos Familiares (ECPF), which we use in our empirical study. We are also grateful to Adrian Fleissig, James Swofford and Gerald Whitney for helpful comments. is paper is a merger of two working papers, Cherchye, Demuynck, and De Rock (2011c) and Hjertstrand (2011

We develop a novel framework to analyze the structural implications of the marriage market for household consumption. We define a revealed preference characterization of efficient household consumption when the marriage is stable. We characterize stable marriage with intrahousehold (consumption) transfers but without assuming transferable utility. Our revealed preference characterization generates testable conditions even with a single observation per household and heterogeneous individual preferences across households. The characterization also allows for identifying the intrahousehold decision structure (including the sharing rule) under the same minimalistic assumptions. An application to Dutch household data illustrates the usefulness of our theoretical results. (JEL D60, D63, H21, H23, I38)

We introduce a new solution concept for models of coalition formation, called the myopic stable set. The myopic stable set is defined for a very general class of social environments and allows for an infinite state space. We show that the myopic stable set exists and is non-empty. Under minor continuity conditions, we also demonstrate uniqueness. Furthermore, the myopic stable set is a superset of the core and of the set of pure strategy Nash equilibria in noncooperative games.Additionally, the myopic stable set generalizes and unifies various results from more specific environments. In particular, the myopic stable set coincides with the coalition structure core in coalition function form games if the coalition structure core is nonempty; with the set of stable matchings in the standard one-to-one matching model; with the set of pairwise stable networks and closed cycles in models of network formation; and with the set of pure strategy Nash equilibria in finite supermodular games, finite potential games, and aggregative games. We illustrate the versatility of our concept by characterizing the myopic stable set in a model of Bertrand competition with asymmetric costs, for which the literature so far has not been able to fully characterize the set of all (mixed) Nash equilibria.

A well known result in the theory of binary relations states that a binary relation has a complete and transitive extension if and only if it is consistent (Suzumura (1976), theorem 3). A relation is consistent if the elements in the transitive closure are not in the inverse of the asymmetric part. We generalize this result by replacing the transitive closure with a more general function. Using this result, we set up a procedure which leads to existence results for complete extensions satisfying various additional properties. We demonstrate the usefullness of this procedure by applying it to the properties of convexity, homotheticity and monotonicity. * Thanks to Dirk Van de gaer and two anonymous referees for helpfull comments. Aspirant Fonds voor Wetenschappelijk Onderzoek Vlaanderen (FWO). I acknowledge financial support from the Interuniversity Attraction Poles Programme-Belgian Science Policy (contract P6/07).

We develop a revealed preference approach to analyze non-unitary household consumption behavior that is not cooperative (or Pareto e¢ cient). We derive global and necessary and su¢ cient conditions for data consistency with the model. Interestingly, contrary to existing results for the di¤erential approach, these revealed preference conditions for the noncooperative model are independent from (or non-nested with) the conditions for the cooperative model. We show that the conditions can be veri…ed by means of relatively straightforward mixed integer programming (MIP) methods, which is particularly attractive in view of empirical analysis. Our framework extends to tests for separate spheres and joint contribution to public goods. An application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demonstrates the empirical relevance of the noncooperative consumption model. To the best of our knowledge, this is the …rst empirical application of the noncooperative consumption model. JEL Classi…cation: D11, D12, D13, C14.We are grateful to the editor David Myatt and two anonymous referees for helpful suggestions. This is a shortened version of the working paper that circulated under the title "Degrees of cooperation in household consumption models: a revealed preference analysis". We thank Claude d'Aspremont, Rodolphe Dos Santos Ferreira, Frederic Vermeulen and seminar participants in Leuven, Bari and Montreal for helpful discussion of this earlier paper. The usual disclaimer applies.