Irreducible economies and strongly connected graphs

Baldry, R. and Ghosal, S. (2005) Irreducible economies and strongly connected graphs. Journal of Mathematical Economics, 41(8), pp. 937-956. (doi: 10.1016/j.jmateco.2004.10.002)

Abstract

In this paper we apply graph theoretic techniques to provide results for weakening the interior endowment assumption of Arrow and Debreu [Arrow, K.J., Debreu, G., 1954. Existence of an equilibrium for a competitive economy, Econometrica 22, 265–290]. We develop two conditions – C-irreducibility and C′-irreducibility – which are sufficient for the existence of competitive equilibria in economies with weakly monotone preferences and boundary endowments. We show that C-irreducibility is different from, and C′-irreducibility weaker than, McKenzie’s irreducibility [McKenzie, L.W., 1959. On the existence of general equilibrium for a competitive market, Econometrica 27, 54–71; McKenzie, L.W., 1961. On the existence of general equilibrium: some corrections, Econometrica 29, 247–248]. We also provide conditions under which McKenzie’s irreducibility and Arrow and Hahn’s [Arrow, K.J., Hahn, F., 1971. General Competitive Analysis. Holden-Day, San Francisco] resource relatedness are equivalent. This answers an open question in the literature.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ghosal, Professor Sayantan
• Authors: Baldry, R., and Ghosal, S.
• College/School: College of Social Sciences > Adam Smith Business School > Economics
• Journal Name: Journal of Mathematical Economics
• ISSN: 0304-4068
• ISSN (Online): 1873-1538
• Published Online: 01 June 2005