Monotone comparative statics with separable objective functions

Christian Ewerhart

Economics Bulletin, 2010, vol. 30, issue 3, 2259-2269

Abstract: The Milgrom-Shannon single crossing property is essential for monotone comparative statics of optimization problems and noncooperative games. This paper formulates conditions for an additively separable objective function to satisfy the single crossing property. One component of the objective function is assumed to allow a monotone concave transformation with increasing differences, and to be nondecreasing in the parameter variable. The other component is assumed to exhibit increasing differences, and to be nonincreasing in the choice variable. As an application, I prove existence of an isotone pure strategy Nash equilibrium in a Cournot duopoly with logconcave demand, affiliated types, and nondecreasing costs.

Keywords: Increasing differences, separable objective function, single crossing property; quantity competition (search for similar items in EconPapers)
JEL-codes: C6 C7 (search for similar items in EconPapers)
Date: 2010-08-26
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Working Paper: Monotone comparative statics with separable objective functions (2010)
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