TACTICS AND STIGLER FLEXIBILITY. PART I: linear differential model for a single-product firm

A firm which sells its product in a free competition market where the exchange price remains stationary, determines the quantity of goods to be produced equaling marginal cost to marginal revenues. In this paper we consider the more general case of markets with price instabilities. To this aim we: i) propose a simple mathematical model for describing the structure of industrial organizations, ii) determine the mathematical concept which expresses the Stiglerian flexibility for an industrial organization. In this way we give a precise meaning to the classical definition of flexible industrial organizations which reads as follow: " a flexible industrial organization permit to approximate the best technology for any output, at the cost of not being able to use the best technology for any output " ( see [2] on pg. 315 ). In the framework of the aforementioned model it is possible to introduce the concept of tactics ( time dependent production regime ) chosen by a firm as a response to price instability and to prove that the presence of exchange price instability enriches the manifold of industrial organizations which are competitive. Indeed we characterize the manifolds of equally competitive industrial organizations as the level curves of the previously introduced profit function.