Measuring Efficiency in Imperfectly Competitive Markets: An Example of Rational Inefficiency

The standard assumption in the efficiency literature, that firms attempt to produce on the production frontier, may not hold in markets that are not perfectly competitive, 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 equilibrium and improvement targets which may not be on the production frontier when some inputs or outputs are fixed. This behavior is referred to as rational inefficiency because the firm reduces its productivity levels in order to increase profits. For a general short-run 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 equilibrium is proven. The estimation of a production frontier extends standard market analysis by allowing benchmark performance to be identified. On-line supplementary materials include all proofs and two additional results; when changes in quantity have a significant influence on price and all input and outputs are adjustable, we observe more benchmark production plans on the increasing returns to scale portion of the frontier. Additionally, a direction for improvement toward the economic efficient production plan is estimated, thus providing a solution to the direction selection issue in a directional distance analysis.