This paper features a simple static Cournot–Nash model of an exchange economy with two productive sectors at flexible prices and wages. The traders in the atomless sector are price-takers, while the atoms behave strategically. We focus on the consequences of strategic interactions on the market outcome. Firstly, strategic interactions create underemployment on the labor market. Secondly, when the number of atoms increases without limit, the CWE coincides with the competitive equilibrium. Thirdly, we compare the welfare reached by traders at both equilibria. Fourthly, we consider the implementation of a tax levied on strategic supplies. Finally, we compare the approach retained with the monopolistic competition framework.
A vast literature has been devoted to un(der)employment equilibrium without rigidities in a partial equilibrium framework (Cahuc and Zylberberg, 2004).1 The motivations in this paper are twofold. Firstly, it aims at providing a conceptual framework into which the determination of market general equilibrium outcome is based on strategic interactions at flexible prices and wages. Secondly, it analyzes the working and the consequences of the strategic interactions within a sector on a perfectly competitive sector with a labor market. This paper therefore considers a simple static Cournot–Nash model of an exchange economy with two productive sectors.
Two main approaches model strategic interactions in general equilibrium. First, the strategic market games consider decentralized trading posts (Shapley and Shubik, 1977, Dubey and Shubik, 1978 and Sahi and Yao, 1989). This approach was elaborated in order to circumvent the auctioneer. Second, the Cournot–Walras equilibrium (CWE) approach initially developed by Gabszewicz and Vial (1972) in an economy with production, and pursued by Codognato and Gabszewicz, 1991, Codognato and Gabszewicz, 1993 and Gabszewicz and Michel, 1997 and by d'Aspremont et al. (1997) for pure exchange economies, considers a market clearing price mechanism together with a non cooperative game on quantities. This literature focuses on the consequences of market power in general equilibrium. More specifically, the CWE models make the equilibrium prices and the allocations the results of a market price mechanism in strategic multilateral exchange. As a consequence, the market demand which addresses to each producer is made endogenous. We here propose to investigate the question of underemployment equilibrium in strategic multilateral exchange with competition à la Cournot–Walras.
Many models deal with un(der)employment in general equilibrium under imperfect competition without rigidities. Models of cooperation failures put forward un(der)employment equilibrium. Inefficiencies may be caused by local market power of firms and consumers, which stems from the fact that all goods (and all labors) are imperfect substitutes (Blanchard and Kiyotaki, 1987 and Layard et al., 1991), or that some deficiency of aggregate demand occurs (Hart, 1982, d'Aspremont et al., 1989 and d'Aspremont et al., 1990). Monopolistic competition models do not provide microfoundations which explain why monopolistic agents could not interact strategically when determining their price. In addition, no market price mechanism by which equilibrium prices would be detemined is provided. In other (oligopolistic) models, each seller either objectively knows or must conjecture subjectively the demand which addresses to her (Bénassy, 1991 and Negishi, 1961). Otherwise, models of coordination failures feature some indeterminacy (Heller, 1986, Manning, 1990 and Roberts, 1987), so multiple equilibria make economic policy difficult (Cooper, 1999 and Cooper, 2005).
In this paper, we consider a model in which the equilibrium prices are determined by a market mechanism and in which the demand functions are micro-founded. We extend the basic model of an exchange economy with a productive sector of Gabszewicz and Michel (1997). The economy includes two productive sectors and a competitive labor market.2 In one sector (the atomless sector), all the agents are price takers, while the agents in the other sector (the atomic sector) behave strategically. We therefore refer to the concept of "mixed markets" rationalized by Shitovitz (1973) in a pure exchange economy. The following results are obtained. First, the economy has a CWE with underemployment at flexible prices and wages.3 Second, when the number of atoms increases unboundedly, the underemployment CWE coincides with the full employment competitive equilibrium. Third, we compare the individual welfare reached at both equilibria. Fourth, we consider economic policy by introducing a tax levied on strategic supplies in order to reduce market distortions caused by strategic behaviors. In addition, it is shown that the tax enhances the welfare of agents belonging to the atomless sector. We compute the Chamberlin–Walras equilibrium for the same basic economy. Thus, the CWE is not Pareto dominated by the Chamberlin–Walras equilibrium. In addition, the tax policy has more impact on the market outcome in the CWE.
The paper is organized as follows. In Section 2, we describe the basic economy. Section 3 is devoted to the CWE with underemployment. Section 4 considers the implementation of a tax policy. Section 5 computes the Chamberlin–Walras equilibrium and compares it with the results previously obtained. In Section 6, we conclude.
The previous model considered a mixed markets exchange economy with production which generates underemployment in the labor market. Inefficiencies on the competitive labor market are caused by market failures. Such failures stem from strategic interactions between many atoms. In addition, the tax policy is not sufficient to eliminate market imperfections caused by strategic interactions. Finally, inefficiencies are more significant under monopolistic competition: the market imperfections are more favorable to the atoms that do not interact strategically with other competitors.
The market structure associated with the CWE concept presents two advantages. First, the market demand addressed to the atoms is here made endogenous; second, the model displays several kinds of heterogeneity and throws light on their consequences in terms of welfare.