Industry Dynamics: Foundations for Models with an Infinite Number of Firms

30 Pages Posted: 9 Nov 2011

See all articles by Gabriel Y. Weintraub

Gabriel Y. Weintraub

Stanford Graduate School of Business, Stanford University; Columbia University - Columbia Business School - Decision Risk and Operations

C. Lanier Benkard

Stanford Graduate School of Business; National Bureau of Economic Research (NBER)

Benjamin Van Roy

Stanford University - Management Science & Engineering

Multiple version iconThere are 2 versions of this paper

Date Written: August 9, 2010

Abstract

This paper explores the connection between three important threads of economic research offering different approaches to studying the dynamics of an industry with heterogeneous firms. Finite models of the form pioneered by Ericson and Pakes (1995) capture the dynamics of a finite number of heterogeneous firms as they compete in an industry, and are typically analyzed using the concept of Markov perfect equilibrium (MPE). Infinite models of the form pioneered by Hopenhayn (1992), on the other hand, consider an infinite number of infinitesimal firms, and are typically analyzed using the concept of stationary equilibrium (SE). A third approach uses oblivious equilibrium (OE), which maintains the simplifying benefits of an infinite model but within the more realistic setting of a finite model. The paper relates these three approaches. The main result of the paper provides conditions under which SE of infinite models approximate MPE of finite models arbitrarily well in asymptotically large markets. Our conditions require that the distribution of firm states in SE obeys a certain “light-tail” condition. In a second set of results, we show that the set of OE of a finite model approaches the set of SE of the infinite model in large markets under a similar light-tail condition.

JEL Classification: E22, L11, L13

Suggested Citation

Weintraub, Gabriel Y. and Benkard, C. Lanier and Van Roy, Benjamin, Industry Dynamics: Foundations for Models with an Infinite Number of Firms (August 9, 2010). Journal of Economic Theory, Vol. 146, p. 1965, 2011; Columbia Business School Research Paper. Available at SSRN: https://ssrn.com/abstract=1957367

Gabriel Y. Weintraub (Contact Author)

Stanford Graduate School of Business, Stanford University ( email )

Stanford, CA 94305
United States

Columbia University - Columbia Business School - Decision Risk and Operations ( email )

New York, NY
United States

C. Lanier Benkard

Stanford Graduate School of Business ( email )

Stanford, CA 94305-5015
United States
650-723-4124 (Phone)
650-725-0468 (Fax)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Benjamin Van Roy

Stanford University - Management Science & Engineering ( email )

473 Via Ortega
Stanford, CA 94305-9025
United States

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