Misspecified profit functions and full‐cost pricing

Abstract

AbstractWe study the behavior of a firm that consistently maximizes a misspecified profit function as the misspecification error remains undetected in equilibrium. Our framework encompasses a price‐taking firm and a cost‐taking firm, which respectively take the unit price and the unit cost as given. At the stable equilibrium for the cost‐taking firm, the price increases with the level of fixed costs, a phenomenon known as full‐cost pricing. We show that the equilibrium price may be lower than the rational price and can be reached by a tatônnement process. We also describe a stochastic version of that process in a dynamic setting with random costs and Bayesian learning. Finally, we endogenize the cost curve. When technology duplication is possible, the cost‐taking firm and the rational firm end up producing the same level of output.