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The effect of economic policy in oligopoly. A variational inequality approach

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  • Giovanni Crespi

Abstract

Directional derivatives are the ideal tool to model simultaneous shifts of the instruments of economic policy. Provided the equilibrium solution of an oligolistic model are differentiable with respect to the parameter, such a problem can be easily solved considering shift in single instruments, i. e. partial derivatives, and then multiplying these derivatives by a vector rapresenting the direction of the simultaneous shifts. However even differentiability of the objective functions may not be enough to guarantee differentiability of the equilibrium. Byformulating an oligopolistic model with transportation costs by variational inequalities, we solve this problem even for non differentiable equilibrium solution.

Suggested Citation

  • Giovanni Crespi, 2001. "The effect of economic policy in oligopoly. A variational inequality approach," Departmental Working Papers 2001-09, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    • Handle: RePEc:mil:wpdepa:2001-09
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    References listed on IDEAS

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    1. Jerzy Kyparisis, 1992. "Parametric Variational Inequalities with Multivalued Solution Sets," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 341-364, May.
    2. Anna Nagurney & Kanwalroop Dhanda, 2000. "Noncompliant oligopolistic firms and marketable pollution permits: Statics and dynamics," Annals of Operations Research, Springer, vol. 95(1), pages 285-312, January.
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