A classification approach to Walrasian equilibrium with substitutability

Yang, Yi-You (2013): A classification approach to Walrasian equilibrium with substitutability.

Abstract

In exchange economies with indivisible objects, the substitutability of agents' preferences is essential for the guaranteed existence of Walrasian equilibrium. In this paper, we analyze the ranges of variation for agents' preferences that will guarantee the existence of equilibrium when some agents' preferences are known to satisfy the substitutability condition. Our approach is based on a classification result that partitions the set of economies into disjoint weak similarity classes such that whenever a weak similarity class contains an economy with an equilibrium, each economy in this class also has an equilibrium. The links among economies in the same weak similarity class are established with the notion of monotonization and tax systems.

• Item Type: MPRA Paper
• Language: English
• Keywords: Equilibrium; indivisibility; substitutability; free disposal; tax system.
• Subjects: D - Microeconomics > D5 - General Equilibrium and Disequilibrium; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies

References

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

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

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

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

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

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