In this paper, we consider conjectural variations in a simple static general equilibrium model under oligopolistic competition. The modeling of conjectures captures the role played by beliefs in a micro-founded model. So, the economy may have three kinds of symmetric general equilibria. Furthermore, these equilibria can be Pareto-ranked by the conjectural variation parameter. Finally, we consider the implementation of a tax on the strategic behaviors in case of balanced-budget rule. The comparative statics illustrates the idea according to which the effectiveness of the multiplier mechanism to mitigate the market distortions depends on the symmetric equilibrium considered. Therefore, the effect of the tax on the prices and economic activity depends on the degree of market power which is conjectured by the agents.
Some economists put forward the role of conjectures in strategic interactions (Dutt and Sen, 1995 and Friedman and Mezzetti, 2002). The conjectural approach takes into account the perceptions by individuals of their market environment, and intends to study price formation without an auctioneer by attempting a general equilibrium analysis of imperfect competition (Gale, 1978 and Hahn, 1977). These conjectures illustrate the way a firm belonging to a given industry anticipates the reactions of its direct rivals when it decides to increase its supply of a unit on the market (Bowley, 1924). The role played by (consistent) conjectures has mainly been developed in the context of production economies under partial equilibrium analysis (Bresnahan, 1981, Dixit, 1986, Figuières et al., 2004 and Perry, 1982).
In this paper, we consider conjectural variations in a general equilibrium model with imperfect competition in the spirit of Hart (1982), Heller (1986), Jones and Manuelli (1992) or Roberts (1987). In order to simplify, we only focus on strategic interactions on the output markets and do not develop the labor market analysis.1 More precisely, we propose to generalize the oligopoly-Nash model proposed by Cooper (1999).2 We henceforth consider a large but finite number of goods, and put forward the role played by conjectural variations. Conjectural variations have already been introduced in a one sector imperfect competition model with wage-bargaining in the labor market in order to capture their influence on the markup (Dutt and Sen, 1995). Nevertheless, the preceding approach includes three shortcomings. First, it does not feature the role played by conjectural variations in the allocation of resources, while we model their influence on the equilibrium outcome. Second, the market demand addressed to each producer is exogenous; it is here derived from explicit optimizing behaviors. Third, it neglects the interactions between markets, whereas the present model generalizes the one good framework and emphasizes the strategic interactions among many agents in multiple interrelated markets.
This paper thus captures the role played by conjectural variations on market power and equilibrium allocation. The model can be represented as a two-step game: first, the market-clearing prices are determined for given strategies; second, the equilibrium strategies are determined at these equilibrium prices.3 Several kinds of equilibria can arise. We restrict the analysis to symmetric equilibria.4 Furthermore, we study the relationships between welfare, economic policy and conjectural variations. Four kinds of results are obtained. Firstly, the equilibrium prices and level of activity decrease with the conjectural variations parameter. Secondly, the economy may have three symmetric general equilibria. Thirdly, these symmetric equilibria can be Pareto-ranked by the conjectural variations parameter. Hence, the level of welfare associated with the competitive equilibrium allocation is highest. Fourthly, it is shown, on the one hand, that a per unit tax levied on the strategic supplies has a positive effect on the market outcome and, on the other hand, that the competitive equilibrium tax rate is the lowest equilibrium tax rate.
The paper is organized as follows. In Section 1, we describe the basic model. Section 2 is devoted to the analysis of the symmetric equilibria. Section 3 deals with welfare and economic policy. In Section 4, we conclude.
When the degree of competition is parameterized by conjectural variations, three symmetric general equilibria can occur. Furthermore, market distortions caused by strategic behaviors can be dampened by a tax policy through the multiplier mechanism. One salient feature of the model is that a tax policy strengthens the effects of changes in real autonomous expenditure, whatever the degree of competition. Correlatively, the effectiveness of the multiplier mechanism to mitigate the consequences of market inefficiencies depends on the symmetric equilibrium considered. Hence, the effect of the tax critically depends on the extent of market power expected by the agents.
In the previous model, the multiplicity of equilibria does not akin to an indeterminacy of the kind prevalent in coordination games (Cooper, 1999). The reason is that the strategic complementarities are not sufficiently strong to generate multiple equilibria for given conjectures; all the best-responses are here linear functions of strategies. Furthermore, the economic policy does not create some indeterminacy as in Schmitt-Grohé and Uribe (1997). One possible extension could consider non constant returns to scale technologies, which could lead to the existence of coordination failures (Cooper and John, 1988).
