Contributions to Cournot oligopoly theory

This work contributes to a number of questions concerning oligopoly models. In particular, uniqueness of the Cournot equilibrium point is demonstrated under the assumption that either the unit price function is differentiable and the derivative is strictly negative or the cost functions are strictly convex. Also, under the assumption of either strictly decreasing unit price function or strictly convex cost functions, it is shown that (a) the total production level at equilibrium increases with entry of additional players, (b) that cooperation between some of the players necessarily entails profit for the others, and (c) cooperative grouping causes decrease in production levels.     

Cournot competition in a differentiated oligopoly

This paper studies product-quantity equilibria in an oligopoly. Products are interpreted as “qualities” and each firm chooses a quality-quantity pair, simultaneously. It is well known that a pure-strategy equilibrium in product-price pairs does not exist in this model, but a pure-strategy equilibrium in product-quantity pairs exists. Furthermore, in an example widely studied in the literature, the equilibrium has nice asymptotic properties.     

Labor-managed Cournot oligopoly with product differentiation

Two dynamic systems of labor adjustments are formulated for labor-managed firms in Cournot oligopoly with product differentiation. The global stability conditions are derived for two types of Cournot equilibria corresponding to the stationary points of the two dynamic systems.The author is grateful to two referees of this Journal for helpful comments, which have led to a radical revision of an earlier version.     

Profit sharing and strike activity in Cournot oligopoly

Within an incomplete-information framework, we develop a model of wage determination in a unionized Cournot oligopoly. The assumption of incomplete information allows the possibility of strikes or lockouts, which waste industry potential resources, at equilibrium. Facing such deadweight loss, the government or the social planner may decide to adopt a policy, such as a profit-sharing scheme. Under two different bargaining structures (firm level vs. industry level), we investigate the effects of adopting profit sharing on the wage outcome and the strike activity. If the base-wage bargaining takes place at the industry level, then the introduction of a profit-sharing scheme increases the strike activity. But if the base-wage bargaining takes place at the firm level and the number of firms in the industry is greater than two, then the introduction of a profit-sharing scheme reduces the strike activity.     

New technology adoption in a Cournot oligopoly with spillovers

In a two-stage Cournot oligopoly where a subset of firms first make a choice between two alternative production technologies independently and then all firms compete in quantity, the effect of information spillovers is analyzed when the outcome of R&D is uncertain. It is shown that the range of parameter values that support heterogeneous firms in equilibrium will diminish as information spillovers become larger. Particularly, when the spillover effect is so strong that the investment by one firm is beneficial to its R&D active rivals, all active firms will choose the same technology. A similar result can be derived from a socially desirable point of view except that the cut-off magnitude of spillovers is different. By introducing a positive success probability to characterize the uncertainty of the R&D outcome, it is found that when information spillovers are not too small, there will be underinvestment in equilibrium relative to the social optimum.     

Symmetric Cournot oligopoly and economic welfare: a synthesis

Summary Recently, Mankiw-Whinston (1986) and Suzumura-Kiyono (1987) have shown that socially excessive firm entry occurs in unregulated oligopoly. This paper extends this excess entry results by looking into strategic aspects of costreducing R&D investment that creates incentives towards socially excessive investments. In the first stage, firms decide whether or not to enter the market. In the second stage, firms make a commitment to cost-reducing R&D investment. In the third stage, firms compete in output quantities. It is shown that the excess entry holds even in the presence of strategic commitments.This is the synthesized version of the two earlier papers, Okuno-Fujiwara and Suzumura (1988) and Suzumura (1991). We are grateful to Professors J. Brander, D. Cass, M. Majumdar, A. Postlewaite, J. Richmond, A. Sandmo, B. Spencer and J. Vickers for their helpful comments and discussions on earlier drafts. Needless to say, they should not be held responsible for any remaining defects. Financial supports from the Japan Center for Economic Research, Tokyo Center for Economic Research, the Japanese Ministry of Education, and the Institute for Monetary and Economic Research, the Bank of Japan are gratefully acknowledged.     

Comparison between specific taxation and volume quotas in a free entry Cournot oligopoly

We revisit the classic discussion of the comparison between tax and quota, but in a free-entry Cournot oligopoly. We investigate a quantity ceiling regulation as a quota policy. We find that tariff-quota equivalence holds if the firms are symmetric and the number of firms is given exogenously. However the equivalence does not hold and taxes dominate quotas in the free entry market because quota can increases the number of entering firms and increases the loss caused by excessive entries.     

On hierarchical competition in oligopoly

In this paper, we consider a hierarchical oligopoly model, in which firms compete on quantities of an homogeneous product. We provide a proof and an interpretation that under the three necessary and sufficient conditions of linear aggregate demand, constant and identical marginal costs, the strategy of leaders at any stage depends neither on the number of leaders who play after nor on the number of remaining stages. So, all firms behave as Cournotian oligopolists on the residual demand. We show that these three assumptions are not only sufficient but also necessary. Any departure from any of these assumptions rules out this property.     

Agglomeration in a vertically-related oligopoly

This paper examines the location of three vertically-linked firms. In a spatial economy composed of two regions, a monopolist firm supplies an input to two consumer goods firms that compete in quantities. It is concluded that agglomeration is more likely to occur when the ratio between the transport cost of the intermediate good and the transport cost of the final good is higher. If this proportion is low, the likelihood of an agglomeration decreases with transport costs. If the ratio has an intermediate value, a non-monotonic pattern is obtained that is different from Krugman and Venables (1995).Received: October 2004, Accepted: March 2005, JEL Classification: C68, F12, F15, R12, R13This paper had the support of the Research Unit on Complexity in Economics (UECE). The author wishes to thank Masahisa Fujita, Armando Pires and an anonymous referee for helpful comments. The usual disclaimer applies.     

Merger profitability in mixed oligopoly

We analyse merger profitability in a mixed-oligopoy Cournot model. The “merger paradox” is qualified by showing that there are profitable gains for the firms participating in a horizontal merger that is not a merger to a monopoly. In particular, it is shown that merger sustainability depends on both, the privatization degree of the mixed firm and the number of non-merging firms.      

Leibniz und Cournot

Ohne Zusammenfassung     

Coalition-proof supply function equilibria in oligopoly

In an industry where firms compete via supply functions, the set of equilibrium outcomes is large. If decreasing supply functions are ruled out, this set is reduced significantly, but remains large. Specifically, the set of prices that can be sustained by supply function equilibria is the interval between the competitive price and the Cournot price. In sharp contrast, when the number of firms is above a threshold we identify (e.g., three if demand is linear), only the Cournot outcome can be sustained by a coalition-proof supply function equilibrium.     

Information Advantage in Cournot Oligopoly

Consider an oligopolistic industry where firms have access to the same technology but are asymmetrically informed about the environment. Even though it is commonplace to think that in this context superior information leads to higher profits, we find that under Cournot competition this is not generally the case: It holds when firms' technology exhibits constant returns to scale, but it does not necessarily hold otherwise. Journal of Economic Literature Classification Numbers: C72, D43, L13.     

Risk externalities in a payments oligopoly

I discuss the role to be played by central banks in payment systems by way of an oligopoly model of a payments market where firms exert negative risk externalities upon each other. A central bank participating actively in this market is modelled as benign in two ways: exerting less externalities than other banks and maximizing welfare rather than profit. Because other banks react strategically to the central bank’s presence due to its low externalities, there is a risk that it backfires, with these other banks’ taking more risky positions than if the central bank were not there. The proper role of the central bank may actually be to stay out.     

Secret information acquisition in Cournot markets

Summary. Two-stage game models of information acquisition in stochastic oligopolies require the assumption that firms observe the precision of information chosen by their competitors before determining quantities. This paper analyzes secret information acquisition as a one-stage game. Relative to the two-stage game firms are shown to acquire less information. Policy implications based on the two-stage game yield, therefore, too high taxes or too low subsidies for research activities. For the case of heterogeneous duopoly we briefly discuss comparative statics results. Received: August 9, 1999; revised version: May 31, 2000     

Higher order lags in price-adjusting oligopoly

Summary We consider price-adjusting oligopoly models involving Bertrand or adaptive expectations concerning the rivals' prices. Traditionally, one specifies these models with first order exponential adjustment lags. We introduce specific higher order exponential lags in both models, which provides a more flexible and richer dynamic specification. We show that in both cases the model with higher order lags is stable if and only if the model with first order lags is stable.An anonymous referee is gratefully acknowledged for useful comments.     

The quadratic oil extraction oligopoly

Each extractor has a distinct initial endowment of oil and a distinct quadratic extraction cost and faces a linear industry demand schedule. We observe in a discrete-time model with a finite number of periods that the open loop and closed loop solutions are the same if initial stocks are such that each competitor is extracting in every period in which her competitors are extracting.     

Mixed oligopoly and spatial agglomeration

Abstract We investigate a mixed market where a state‐owned welfare‐maximizing public firm competes against profit‐maximizing private firms. We use a circular city model with quantity‐setting competition. In contrast to a pure market case discussed by Pal (1998a) , spatial agglomeration of private firms always appears in equilibrium. All private firms locate at the same point, and the public firm locates at the opposite side. We also find that this equilibrium pattern of the location is second best provided that output of each private firm cannot be controlled by the social planner. JEL Classification: H42, L13
Oligopole mixte et agglomération spatiale Les auteurs examinent un marché mixte où une entreprise publique possédée par l'État et cherchant à maximiser le niveau de bien‐être est en concurrence avec des entreprises privées qui cherchent à maximiser leurs profits. On utilise un modèle de cité circulaire où la concurrence se fait en choisissant la quantité produite. En contraste avec le cas du marché parfait discuté par Pal (1998a), l'agglomération spatiale des entreprises privées paraît être en équilibre. Toutes les entreprises privées se localisent au même point, et l'entreprise publique se localise du côté opposé. Il appert que ce pattern d'équilibre de localisation est un équilibre de second ordre compte tenu du fait que la production de chaque entreprise privée ne peut être contrôlée par le planificateur social.