Quantity competition vs. price competition under optimal subsidy in a mixed oligopoly

This paper reconsiders the literature on the irrelevance of privatization in mixed markets within which both quantity and price competition are investigated under product differentiation. By allowing for partially privatization of a state-controlled firm, we explore competition under different timings of firms' moves and derive the conditions under which an optimal subsidy allows to achieve maximum efficiency. We show that, irrespective of the mode of competition, while the ownership of the controlled firm is irrelevant when firms play simultaneously, it matters when firms compete sequentially, requiring the leader to be publicly-owned for an optimal subsidy to restore the first-best. The paper also focuses on the extent to which a subsidy is needed to attain the social optimum in the considered scenarios, providing an ordering which highlights the subsidy equivalence between Cournot (Bertrand) private leadership and simultaneous Bertrand (Cournot) under duopoly, and the dominance of the former in oligopoly.     

Bilateral oligopoly and quantity competition

Bilateral oligopoly is a market game with two commodities, allowing strategic behavior on both sides of the market. When the number of buyers is large, bilateral oligopoly approximates a game of quantity competition played by sellers. We present examples which show that this is not typically a Cournot game. Rather, we introduce an alternative game of quantity competition (the market share game) and, appealing to results in the literature on contests, show that this yields the same equilibria as the many-buyer limit of bilateral oligopoly, under standard assumptions on costs and preferences. We also show that the market share and Cournot games have the same equilibria if and only if the price elasticity of the latter is one and investigate the differences in equilibria otherwise. These results lead to necessary and sufficient conditions for the Cournot game to be a good approximation to bilateral oligopoly with many buyers and to an ordering of total output when they are not satisfied.     

Is a Unique Cournot Equilibrium Locally Stable?

We consider a homogeneous product oligopoly, where the Cournot equilibrium is regular and unique. We show that for a duopoly, a unique Cournot equilibrium is always locally stable. For a “n” firm asymmetric cost oligopoly a unique Cournot equilibrium is locally stable under very general conditions. The sufficient conditions for local stability of a unique Cournot equilibrium are much less restrictive than what the existing literature suggests. For a symmetric cost oligopoly the unique Cournot equilibrium is almost always locally stable, except for a perverse case. Journal of Economic Literature Classification number: L13.     

The empirical content of Cournot competition

We consider the testable implications of the Cournot model of market competition. Our approach is nonparametric in the sense that we abstain from imposing any functional specification on market demand and firm cost functions. We derive necessary and sufficient conditions for (reduced form) equilibrium market price and quantity functions to be consistent with the Cournot model. In addition, we present identification results for the corresponding inverse market demand function and the firm cost functions. Finally, we use our approach to derive testable restrictions for the models of perfect competition, collusion and conjectural variations. This identifies the conditions under which these different models are empirically distinguishable from the Cournot model. We also investigate empirical issues (measurement error and omitted variables) related to bringing our testable restrictions to data.     

Environmental innovation policy and international competition

We consider one polluting industry in an open economy. The national government implements a policy of industrial pollution control, by inducing appropriate technological innovation to reduce toxic emissions. The emission-reducing innovations are developed through firm-specific costly investments. Under different hypotheses on market structure (perfect competition, Bertrand and Cournot oligopoly), international competition forces the national government to subsidize innovation. The appropriate subsidy scheme varies according to the information available to the government and according to market structure. If information is asymmetric, the subsidy must include the information premium necessary to separate different types of firms.     

Permit Trading and Credit Trading: A Comparison of Cap-Based and Rate-Based Emissions Trading Under Perfect and Imperfect Competition

This paper compares emissions trading based on a cap on total emissions (permit trading) and on relative standards per unit of output (credit trading). Two types of market structure are considered: perfect competition and Cournot oligopoly. We find that output, abatement costs and the number of firms are higher under credit trading. Allowing trade between permit-trading and credit-trading sectors may increase welfare. With perfect competition, permit trading always leads to higher welfare than credit trading. With imperfect competition, credit trading may outperform permit trading. Environmental policy can lead to exit, but also to entry of firms. Entry and exit have a profound impact on the performance of the schemes, especially under imperfect competition. We find that it may be impossible to implement certain levels of total industry emissions. Under credit trading several levels of the relative standard can achieve the same total level of emissions.     

Cournot Oligopoly and the Theory of Supermodular Games

We reconsider the Cournot oligopoly problem in light of the theory of supermodular games. Invoking the recent ordinal version of this theory proposed by Milgrom and Shannon, we generalize Novshek's existence result, derive the associated uniqueness result, give an extension of a classical existence result under symmetry, and provide conditions making a Cournot oligopoly into a log-supermodular game (with the natural order on the action sets). We also provide extensive and precise insight as to why decreasing best-responses are widely regarded as being “typical” for the Cournot model with production costs. Several illustrative examples are provided.Journal of Economic LiteratureClassification Numbers: C72, L10, L13.     

Price and quantity competition under free entry

This paper complements that of Cellini et al. (Cellini, R., Lambertini, L., Ottaviano, G. I. P., 2004. Welfare in a differentiated oligopoly with free entry: A cautionary note. Research in Economics, 58:125–33.), which shows that Cournot competition may generate higher welfare compared to Bertrand competition in an economy with free entry. Unlike them, we provide a more general proof for this result and show that Cournot competition generates higher welfare compared to Bertrand competition when the products are sufficiently differentiated. If the products are close substitutes, welfare is higher under Bertrand competition. We show that these qualitative results hold whether or not number of varieties increases market size. We also show when the active firms earn higher profits under Bertrand competition compared to Cournot competition.     

Information sharing about a demand shock

This paper examines two questions in asymmetric Cournot and Bertrand oligopoly with a demand shock. Under which conditions is information sharing a subgame-perfect equilibrium? What is the welfare effect when firms are better off? Given these questions, the normal assumptions in the earlier literature can be relaxed in three ways: demand functions can be asymmetric; a demand shock can affect firms differently; distributions of the demand shock and information signals can be arbitrary. Under these general assumptions, the answer to the first question is: every firm's response to the demand shock is stronger when all firms have perfect information than when one firm does so alone; the answer to the second question is: social welfare increases in Cournot competition, and consumer surplus decreases in Bertrand competition.     

Volume and share quotas in Cournot competition

In this paper, we theoretically discuss volume and share quotas in the market where firms engage in Cournot competition. We show the equivalence among specific taxes, and volume quotas and share quotas with respect to equilibrium quantities. By using these results, we analyze comparative statics effects of volume and share quotas. Further, we apply the results to the examination of international oligopoly models with tariffs, import volume quotas, and import share quotas. Finally, we extend the model to endogenize the set of firms and derive a non-equivalence result of volume quotas and specific taxes.     

Quasi-Competitive Cournot Oligopoly with Product Differentiation and Symmetric Firms

Since Vives (1984 ), Cheng (1985 ) and Okuguchi (1987 ), the equilibria in Bertrand and Cournot oligopolies with product differentiation have been known to differ. Okuguchi (2005 ) has shown that Bertrand price‐adjusting oligopoly with product differentiation and symmetric firms is quasi‐competitive but not perfectly competitive in the limit state of infinite number of firms. This paper formulates and analyzes two types of Cournot output‐adjusting oligopoly with product differentiation and symmetric firms, in one of which symmetric firms producing the same goods are assumed to collude, and in the other, collusion is ruled out. The limit states are shown to be different in two oligopolies but they are both quasi‐competitive.     

Information quality choice and information disclosure in oligopoly

In this paper, we provide a framework to analyze the information disclosure and information quality choice in the oligopoly in which one firm has the opportunity to choose her information quality flexibly and then decide her information disclosure rule after she has observed her information.We find that in the Cournot (Bertrand)competition, when the goods are substitutes (complements) and the degree of substitution (complement) is small enough, the firm will choose the maximal information quality. However, if the degree of substitution (complement) is large enough, the information quality is some intermediate value. On the other hand, in the Cournot (Bertrand) competition, when the goods are complements (substitutes), the maximal information quality will be chosen. We also find that the Fully Revealing case in which the probability of information disclosure is one will occur in (i) the Cournot competition with sufficiently small degree of substitution; (ii) the Cournot competition when goods are complements; (iii) the Bertrand competition when goods are substitutes; (iv) the Bertrand competition with sufficiently small degree of complements. Moreover, we show that the No Revealing case in which the probability of information disclosure is zero will never show up.     

Downstream mode of competition with upstream market power

In a two-tier oligopoly, where the downstream firms are locked in pair-wise exclusive relationships with their upstream input suppliers, the equilibrium mode of competition in the downstream market is endogenously determined as a renegotiation-proof contract signed between each downstream firm and its exclusive upstream input supplier. We find that the upstream–downstream exclusive relationships credibly sustain the Cournot (Bertrand) mode of competition in the downstream market, when the goods are substitutes (complements). In contrast to previous studies, this result holds irrespectively of the degree of product differentiation and the distribution of bargaining power between the upstream and the downstream firm, over the pair-specific input price.     

A dynamic Stackelberg model with production-adjustment costs

We investigate the (dynamic) stability of a stackelberg oligopoly model of a market of a homogeneous good, with output competition, one Stackelberg leader and a number of identical followers. We assume that each firm incurs quadratic production-adjustment costs if it changes its output. We present a simple necessary and sufficient condition for stability of the model. Using the condition, we compare the stability of this model with the stability of two related Cournot models in which all firms present are followers. It turns out that the Stackelberg model is more stable than these two Cournot models.     

Contestability and the Indeterminacy of Free-Entry Equilibria

A general notion of market perfect contestability is introduced. It coincides with the definition given by Baumol et al . under Bertrand competition, but is compatible with Cournot competition as well as monopolistic competition. Using this notion, we illustrate the fact that the number of active firms in free-entry equilibrium may be largely indeterminate and different levels of positive profits may in many cases be sustained. This is shown to be true, in spite of market perfect contestability, under either Cournot competition or product differentiation. Examples are given for both cases. Appropriate conditions of increasing returns are required.
JEL Classification Numbers: D5, D43.     

Price formation in heterogeneous oligopoly

Conclusion An equilibrium price vector has been defined and its existence and function in static price formation in cases of heterogeneous oligopoly has been established. Hitherto, authors have been misled, we think, by misinterpreting the role of reaction functions, which are central to our argument. After defining and proving the existence and uniqueness of an equilibrium price vector, it is possible to construct a generalization of the wellknown equilibrium concept of the Nash-Cournot game solution. It has previously been thought that the restriction to the Cournot solution is one of the main drawbacks to using game theoretical solutions to the problem of oligopoly. We have developed a generalization of the Nash solution in order to deal with a type of reaction hypothesis which cannot be expressed in terms of the Cournot reaction function. The new set of reaction functions here introduced demonstrate conclusively that the so-called identity on a Nash and a Cournot equilibrium is only of a formal character.We would like to thank F. Delbaen, R. A. Hirschfeld and K. Okuguchi for useful comments on an earlier draft of this paper.     

On the Neutrality of Profit Taxation in a Mixed Oligopoly

This paper investigates the neutrality of profit taxation in a mixed oligopoly where one (partially) public firm competes with private firms. We find that the neutrality of a profit tax is robust under a general cost and a general demand function as long as the degree of privatization is endogenously determined. This result is also true when product heterogeneity is considered under both Cournot and Bertrand competition. By contrast, if the degree of privatization is exogenously given, the profit tax neutrality holds only in the cases where the public firm is fully privatized or fully state-owned; otherwise, the neutrality breaks down.     

CHANGES IN DEMAND FUNCTION IN COURNOT OLIGOPOLY

Abstract.  The effects of change in the market (inverse) demand function are systematically analysed for Cournot oligopoly without product differentiation. The general comparative-static results are stated using the original data on firms' cost functions and inverse demand function. Three special models are examined in light of our results. The stability condition is shown to be insufficient for determinate comparative statics.     

Free and second-best entry in oligopolies with network effects

We compare the number of firms in equilibrium in a Cournot industry with positive network effects and complete compatibility, under free and second-best entry. Under free entry, the firms decide whether to enter the market or not; in the second-best problem, the number of firms is established by the regulator to maximize social welfare (the regulator controls entry but not production). We show that when individual equilibrium output decreases with entry (business-stealing competition), free entry may lead to more or less firms than the second-best problem. This contrasts with the standard (nonnetwork) Cournot oligopoly model, wherein with business-stealing competition, free entry leads to an excessive number of firms compared with the second-best solution.