Misspecified profit functions and full-cost pricing

We 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.