Large-Market Cournot Equilibria in Labour-Managed Economies

Abstract

A basic point in the theory of labour-managed market economies is the fundamental role of free entry in order to achieve efficiency (see Dreze, 1974; Greenberg, 1979; Ichiishi, 1977; Meade, 1972, 1979; Vanek, 1970). But modelling a framework of firm selection process can be undertaken with different approaches. Dreze, Meade and Vanek, for example, consider a perfectly competitive process; Greenberg and Ichiishi build models of coalition formation in the spirit of core theory. In the present study we take the other classical way, the Cournot oligopoly theory. In order to capture the effect of increasing competition in the Cournot oligopoly, two kinds of models have long been traditionally elaborated. In the first, the effects of an exogenously increasing number of active firms facing a given demand function are examined (see Okugushi, 1976; Ruffin, 197 1; Seade, 1980). In the second, initiated by Shubik (1959), the number of active firms and the size of the market are simultaneously increased at the same rate. In this case, what is sought is to isolate some sort of pure effect of an increasing number of competitors, and not the combined result of a greater number of firms facing a constant market. But in the two kinds of approaches the number of active firms are not explained by the theory. What is missing is consideration of the role of potential competitors. Recently Novshek (1980) proposed to give the same status to potential competitors and active firms, i.e. to consider that the potential competitors have a Cournot-type behaviour. Hence the very fact that they are not active comes from optimizing behaviour, in the same way as, for active firms, a positive production level comes from maximizing behaviour. A potential competitor taking the production of the active firms as given and maximizing his objective function remains potential only because he does not find it attractive to produce. Hence we get a unified theory which explains the number of active firms. For the case of U-shaped average cost firms, Novshek (1980) has shown that, in sufficiently large markets, first, such a free-entry Cournot equilibrium exists and, second, it is approximately a perfectly competitive equilibrium state. In this paper we study the welfare properties of free entry Cournot equilibria in labour-managed economies.' We adopt Novshek's notion of free entry which is more appealing than the classical zero profit constraint.2 A recent paper by Hill and Waterson (1983) shows that, with the zero profit definition of free entry, and strong assumptions of decreasing marginal labour productivity, uniqueness and stability of equilibria, Cournot equilibria are asymptotically efficient and furthermore have the same number of active firms in both the labour-managed and entrepreneurial frameworks. Under much weaker assumptions the graphical analysis of this paper shows that asymptotic