Efficiency loss in a Cournot oligopoly with convex market demand
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1203.6675.pdf
Description
Accepted version
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616.82 KB
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Adobe PDF
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51f717bd06e0d3385a40d19af1b24627
Author(s)
Tsitsiklis, John N.
Xu, Yunjian
Date Issued
August 2014
Journal
Journal of Mathematical Economics
Publisher
Elsevier BV
Citation
Tsitsiklis, John N. and Yunjian Xu. "Efficiency loss in a Cournot oligopoly with convex market demand." Journal of Mathematical Economics 53 (August 2014): 46-58 © 2014 Elsevier B.V.
Version
Original manuscript
Abstract
We consider a Cournot oligopoly model where multiple suppliers (oligopolists) compete by choosing quantities. We compare the social welfare achieved at a Cournot equilibrium to the maximum possible, for the case where the inverse market demand function is convex. We establish a lower bound on the efficiency of Cournot equilibria in terms of a scalar parameter derived from the inverse demand function, namely, the ratio of the slope of the inverse demand function at the Cournot equilibrium to the average slope of the inverse demand function between the Cournot equilibrium and a social optimum. Also, for the case of a single, monopolistic, profit maximizing supplier, or of multiple suppliers who collude to maximize their total profit, we establish a similar but tighter lower bound on the efficiency of the resulting output. Our results provide nontrivial quantitative bounds on the loss of social welfare for several convex inverse demand functions that appear in the economics literature. © 2014 Elsevier B.V.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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Creative Commons Attribution-NonCommercial-NoDerivs License
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DOI of Published Version
https://doi.org/10.1016/j.jmateco.2014.06.001
