Competitive equilibrium for indivisible objects

Yang, Yi-You (2013): Competitive equilibrium for indivisible objects.

Abstract

We study an exchange economy with indivisible objects that may not be substitutes for each other, and we introduce the p-substitutability condition, a relaxation of the gross substitutes condition of Kelso and Crawford (1982), in which a parameter vector p is adopted to permit complicated types of complementarity. We prove that for any economy E, there exists a corresponding vector p^{E} such that the p^{E}-substitutability condition is sufficient to guarantee the existence of a competitive equilibrium, and that the largest competitive price of each object is equal to its contribution to the social welfare. Our approach relies on a classification result that partitions economies into disjoint similarity classes such that whenever a similarity class contains an economy with an equilibrium, each economy in this class also has an equilibrium.

• Item Type: MPRA Paper
• Language: English
• Keywords: Indivisibility, equilibrium, gross substitutability, p-substitutability
• Subjects: D - Microeconomics > D5 - General Equilibrium and Disequilibrium; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies

References

1. BIKHCHANDANI, S., AND J. W. MAMER (1997): "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, 74, 385-413.

2. FUJISHIGE, S., AND Z. YANG (2003): "A Note on Kelso and Crawford's Gross Substitutes Condition," Mathematics of Operations Research, 28, 463-469.

3. GUL, F., AND E. STACCHETTI (1999): "Competitive Equilibrium with Gross Substitutes," Journal of Economic Theory, 87, 95-124.

4. HATFIELD, J.W., AND F. KOJIMA (2010): "Substitutes and Stability for Matching with Contracts," Journal of Economic Theory, 145, 1704-1723.

5. HATFIELD, J.W., AND P. MILGROM (2005): "Matching with Contracts," American Economic Review, 95, 913-935.

6. KELSO, A., AND V.P. CRAWFORD (1982): "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, 50, 1483-1504.

7. MA, J. (1998): "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, 82, 458-468.

8. REIJNIERSE, H., A. VAN GELLEKOM, AND J. A.M. POTTERS (2002): "Verifying Gross Substitutability," Economic Theory, 20, 767-776.

9. SUN, N., AND Z. YANG (2006): "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, 74, 1385-1402.