The Price Normalization Problem in Imperfect Competition and the Objective of the Firm

General equilibrium models of oligopolistic competition give rise to relative prices only without determining the price level. It is well known that the choice of a numéraire or, more generally, of a normalization rule converting relative prices into absolute prices entails drastic consequences for the Nash equilibria. In this paper we show that, given a firm has chosen a particular profit function as its objective, profit maximization can be expressed in such a way that it depends on relative prices only. However, the choice of such an objective function need not be in the interest of the shareholders. This problem is overcome by relating the profits of a firm to the aggregate demand of its shareholders. We propose a definition of the objective of a firm, called maximization of shareholders' real wealth, which does not depend on any price normalizaion. Real wealth maxima are shown to exist under certain conditions. Moreover, we consider an oligopolistic market and prove the existence of a Nash equilibrium in which each firm maximizes the real wealth of its shareholders. As a consequence, there is no need for absolute prices in the theory of imperfect competition.