Adv. Math. Econ. 11, 45-76 (2008)

Core convergence in economies with bads

Chiaki Hara

Institute of Economic Research, Kyoto University

Received: September 11, 2007 Revised: December 4, 2007

JEL classification: C62, C71, D41, D43, D51, D61

Mathematical Subject Classification (2000): 28A20, 60B05, 60B10, 91A12, 91A13, 91B50, 91B76

Abstract. We investigate how the presence of bads, causing disutility to consumers, affects the emergence of the price-taking behavior. Specifically, we give two examples of sequences of increasingly populous finite economies in which the core convergence property holds and, yet, for which there is a sequence of coalitions, one from each economy, such that the size of the coalition relative to the economy converges to zero but the share of the coalition in the aggregate consumption of bads converges to one. The limit atomless economy has a Walrasian equilibrium in one of the two examples but not in the other.

Key words: Bads, core convergence, equilibrium existence, perfect competition, atomless economy, uniform integrability