Rational Inefficiency: A Nash-Cournot Oligopolistic Market Equilibrium
Lee, C-Y. and A.L. Johnson, 2015. “Measuring Efficiency in Imperfectly Competitive Markets: An Example of Rational Inefficiency,” Journal of Optimization Theory and Applications 164(2): 702–722.
45 Pages Posted: 20 Apr 2012 Last revised: 23 Feb 2018
Date Written: April 19, 2012
The standard assumption in the efficiency literature that firms desire to produce on the production frontier may not hold in an oligopolistic market where the production decisions of all firms will determine the market price, i.e. an increase in a firm’s output level leads to a lower market clearing price and potentially-lower profits. This paper models both the production possibility set and the inverse demand function and identifies a Nash-Cournot equilibrium and improvement targets which may not be on the production frontier. This behavior is referred to as rational inefficiency because the firm reduces its productivity levels in order to increase profits. For a general multiple input/output production process which allows a firm to adjust its output levels and variable input levels, the existence and the uniqueness of the Nash-Cournot equilibrium is proven. The relationship between the benchmark frontier, scale properties and allocative efficiency is discussed. When changes in quantity have a significant influence on price, we observe more benchmark production plans on the increasing returns to scale portion of the frontier. Additionally, a direction for improvement towards the allocatively efficient production plan is estimated, thus providing a solution to the direction selection issue in a directional distance analysis.
Keywords: Cournot-Nash Equilibrium, Oligopolistic Market, Allocative Efficiency, Nonparametric Frontiers
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