Ordinal Versus Cardinal Complementarity: The Case of Cournot Oligopoly

CORE Discussion Paper No. 2004/36

17 Pages Posted: 4 Mar 2007

See all articles by Rabah Amir

Rabah Amir

University of Arizona - Department of Economics; University of Arizona

Date Written: June 2004

Abstract

While ordinal complementarity is more general than cardinal complementarity, the corresponding global sufficient conditions placed on the primitives of a constrained optimization problem are generally not comparable. We explore this issue in detail for the special case of a Cournot firm. We derive necessary and sufficient conditions for downward-sloping best-responses by imposing the ordinal test only for output levels that are actually reached. Both global tests, cardinal and ordinal, are shown not to be critical sufficient conditions. Finally, we confirm that checking supermodularity of suitably transformed profits can work when the global tests for ordinal and cardinal complementarity both fail.

Keywords: Cournot oligopoly, complementarity, supermodularity, single-crossing property

JEL Classification: C72, D43, L13

Suggested Citation

Amir, Rabah, Ordinal Versus Cardinal Complementarity: The Case of Cournot Oligopoly (June 2004). Available at SSRN: https://ssrn.com/abstract=967645 or http://dx.doi.org/10.2139/ssrn.967645

Rabah Amir (Contact Author)

University of Arizona - Department of Economics ( email )

Tucson, AZ 85721
United States

University of Arizona ( email )

Department of History
Tucson, AZ 85721
United States

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