This paper was begun during a visit at the Cowles Foundation in Fall 2000 and revised during a visit in Fall 2002: Michael Magill and Martine Quinzii are grateful for the stimulating environment and the research support provided by the Cowles Foundation. We are also grateful to Bob Shiller for helpful discussions, and to participants at the Cowles Conference on Incomplete Markets at Yale University, the SITE Workshop at Stanford University, the Incomplete Markets Workshop at SUNY Stony Brook during the summer 2001, the Southwest Economic Conference at UCLA, and the Conference for the Advancement of Economic Theory at Rhodes in 2003 for helpful comments. Many thanks to Bill Brainard whose numerous insightful questions and comments greatly improved the final version of the paper. Unfortunately the authors are solely responsible for the remaining weaknesses.

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Abstract:The paper presents a model of an exchange economy with indivisible goods and money.There are a finite number of agents, each one initially endowed with a certain amount of money and at most one indivisible good. Each agent is assumed to have no use for more than one indivisible good. It is proved that the core of the economy is nonempty. If utility functions are increasing in money, and if the initial resources in money are in some sense "sufficient" the core allocations coincide with the competitive equ~brium allocations.With restrictions on the set of feasible allocations, the same model is used to prove the existence of stable solutions in the generalized "marriage problem". However it is shown that, even ff money enters the model, these solutions cannot generally be obtained as competitive equilibria.