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Increasing Returns and Efficiency$
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Martine Quinzii

Print publication date: 1993

Print ISBN-13: 9780195065534

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780195065534.001.0001

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Existence

Existence

Chapter:
(p.77) 5 Existence
Source:
Increasing Returns and Efficiency
Author(s):

Martine Quinzii

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195065534.003.0005

This chapter considers the problem of the existence of a marginal cost pricing equilibrium. A recent study shows that a marginal cost pricing equilibrium exists under relatively weak assumptions. This chapter describes the proof of Bonnisseau and Cornet (1990a), which introduces some interesting techniques to show that the set of feasible production plans, although non-convex, is sufficiently regular to permit the use of the standard Kakutani fixed-point theorem. The methods of proof which have been successful for proving the existence of equilibrium for a convex economy do not directly apply to a non-convex economy. The properties of continuity and convexity of a Clarke normal cone lead to a straightforward application of the fixed point theorem. This chapter examines the single firm existence theorem and presents an example of productive inefficiency.

Keywords:   existence, cost pricing, proof, Kakutani, convex economy, non-convex economy, convexity, normal cone, productive inefficiency

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