The objective of a privately owned firm under imperfect competition

This paper proposes a model of imperfect competition among privately owned firms that act in the best interest of their shareholders. The existence of a solution for the model is proved under weaker conditions than the ones generally used in the literature. In particular, the results did not require the existence of a continuous equilibrium price selection or concavity assumptions on the profit function.      

The price normalization problem in imperfect competition and the objective of the firm

Summary. General equilibrium models of oligopolistic competition give rise to relative prices only without determining the price level. It is well known that the choice of a numéraire or, more generally, of a normalization rule converting relative prices into absolute prices entails drastic consequences for the resulting set of Nash equilibria when firms are assumed to maximize profits. This is due to the fact that changing the price normalization amounts to altering the objective functions of the firms. Clearly, the objective of a firm must not be based on price normalization rules void of any economic content. In this paper we propose a definition of the objective of a firm, called maximization of shareholders' real wealth, which takes shareholders' demand explicitly into account. This objective depends on relative prices only. Real wealth maxima are shown to exist under certain conditions. Moreover, we consider an oligopolistic market and prove the existence of a Nash equilibrium in which each firm maximizes the real wealth of its shareholders. Received: July 10, 1997; revised version: July 27, 1998     

Indeterminacy of intertemporal equilibria under imperfect competition

Summary. It is known that overlapping generations models with imperfectly competitive firms may exhibit a continuum of stationary equilibria. The reason of this indeterminacy is that different price expectation functions of consumers lead to different objective demand functions against which firms maximize. All these expectation functions fulfill perfect foresight in the equilibrium, but they can be arbitrary off the equilibrium. In this paper it is shown that it is not this arbitrariness which is responsible for the indeterminacy, but that the continuum of stationary equilibria emerges even if expectation functions are rational. Received: March 25, 1999; revised version: February 16, 2000     

Increasing returns,entrepreneurship and imperfect competition

We study a simple bilateral oligopoly model in which individual agents, who are initially endowed with capital, decide sequentially (1) whether they want to act as producers (entrepreneurs) or as capital lenders (rentiers) and, then (2) which quantity of capital they would like to borrow or lend, though exchange of capital units against units of the produced good. Production takes place under increasing returns to scale. We show the existence of “natural equilibria”, at which wealthier capital owners become entrepreneurs while the remaining ones decide to be rentiers. We also study the efficiency of equilibria which is shown to increase by replication of the economy, but sometimes to decrease as a consequence of wealth redistribution.We thank an anonymous referee for his insightful comments     

Imperfect competition and capital accumulation: the role of price normalization

We consider a capital-accumulation model with infinitely lived households and two production sectors. The intermediate-good sector is characterized by perfect competition, a constant-returns-to-scale technology, and production externalities. The final-good sector is a monopoly operating under constant returns to scale. We analyze the general equilibrium in the sense of Gabszewicz and Vial [Journal of Economic Theory (1972) 4: 381–400] for this economy and different price-normalization rules. It is shown that the qualitative behavior of the equilibrium paths depends crucially on the chosen normalization rule. In particular, whether equilibria are monotonic or oscillating and whether indeterminacy occurs or not may depend on the choice of the numeraire.     

Specification choice and robustness in CGE trade policy analysis with imperfect competition

In order to contribute to a more comprehensive understanding of the robustness of the quantitative results of applied trade policy simulations to variations in the assumptions about firm conduct, this article provides a systematic synopsis of alternative formulations of imperfectly competitive supply behaviour in applied general equilibrium trade models and examines the sensitivity of simulated trade policy effects to the specification choice and calibration strategy within a prototype multi-country model. The analysis suggests in particular, that simulation results are generally far more sensitive to numerical specification choices at the calibration stage, than to the prior choice of firm conduct specification.     

The welfare cost of imperfect competition and distortionary taxation

The welfare cost of imperfect competition in the product and labor markets in the United States is quantified in a dynamic general equilibrium model. We find that the welfare cost of imperfect competition in the product market is 3.62 percent while it is 0.58 percent in the labor market, taking the transition path from the distorted to the optimal steady state into account. If we also take into account that the US economy is characterized by distortionary taxation, the welfare cost of the product market distortion increases to 13.51 percent and the labor market distortion to 4.35 percent.     

Price floors and competition

A potential source of instability of many economic models is that agents have little incentive to stick with the equilibrium. We show experimentally that this can matter with price competition. The control variable is a price floor, which increases the cost of deviating from equilibrium. According to traditional theory, a higher floor allows competitors to obtain higher profits. Behaviorally, the opposite result obtains with two (but not with four) competitors. An error model, which builds on Luce (Individual Choice Behavior, 1959), can adequately describe supra-Nash pricing with a low-floor, but then fails to capture the overall pro-competitive effect of a high-floor seen for duopolies.     

Electoral competition under imperfect information

Summary. This paper considers electoral competition between two office-motivated parties and one voter, in the presence of two alternative policies and under imperfect information. The theory of refinements of Nash equilibrium predicts the outcome of this three-player game: both parties faithfully use their information and try to find the best policy for the voter. We discuss the meaning of this model for Politics and prove that the same result holds for any number of voters, provided that parties are expected plurality maximizers and that voters satisfy a version of the sincere voting assumption adapted to this strategic setting.Received: 12 December 2001, Revised: 16 June 2003JEL Classification Numbers: C72, D72, D82.Correspondence to: Jean-François LaslierThanks to Gabrielle Demange, Françoise Forges, Roger Guesnerie, Jean-Fran çois Mertens, Thomas Palfrey, Sylvain Sorin and other participants in workshops and conferences in Caen, Paris, Caltech and Yale. Thanks also to two anonymous referees and to Paul Heidues and Johan Lagerlöf for their comments. This work was originated when K. Van der Straeten was at THEMA (Université de Cergy-Pontoise) and DELTA.     

Price competition in a differentiated products duopoly under network effects

We examine price competition under product-specific network effects, in a duopoly where the products are differentiated both horizontally and vertically. We emphasize the role of consumers’ expectations formation. When expectations are not influenced by prices, the market may be shared but shares must be equal unless product qualities differ or one firm, possibly even the low-quality one, may capture the entire market. When expectations are influenced by prices, which would be the case when there is commitment, competition becomes more intense and the high-quality firm tends to capture a larger market share. Under strong network effects there is a continuum of equilibria and the higher the prices, the smaller the difference between those prices can be. Requiring continuity of expectations, however, delivers a unique equilibrium where one firm captures the entire market.     

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.     

(Non)optimality of the Friedman rule and optimal taxation in a growing economy with imperfect competition

This paper shows that if capital generates production externality, there exists a wedge between returns to money and to capital, driving the Friedman rule is not optimal. However, in the absence of capital externality, the Friedman rule may be valid even under imperfect competition.     

Price competition when consumer behavior is characterized by conformity or vanity

It has long been recognized that the pleasure of consuming a good may be affected by the consumption choice of other consumers. In some cases, social pressures may lead to conformity; in some others, individuals may feel the need of exclusiveness under the form of vanity. Such externalities have proven to be important in several markets. However, the market implication of these externalities are still unclear. To investigate them, we propose to combine the consumption externality model and the spatial duopoly model. When conformity is present but not too strong, both firms remain in business but price competition is fiercer and results in lower prices. The market share of the large firm increases with the population size; as the population keeps rising, the large firm may serve the entire market and set a price that has the nature of a limit price. When conformity is strong enough, different equilibria may exist. In most of these equilibria, a single firm captures the whole market. At the other extreme, when vanity is at work, price competition is relaxed.     

Imperfect competition in two-sided matching markets

This paper considers a simple equilibrium model of an imperfectly competitive two-sided matching market. Firms and workers may have heterogeneous preferences over matches on the other side, and the model allows for both uniform and personalized wages or contracts. To make the model tractable, I use the Azevedo and Leshno (2013) framework, in which a finite number of firms is matched to a continuum of workers.In equilibrium, even if wages are exogenous and fixed, firms have incentives to strategically reduce their capacity, to increase the quality of their worker pool. The intensity of incentives to reduce capacity is given by a simple formula, analogous to the classic Cournot model, but depends on different moments of the distribution of preferences. I compare markets with uniform and personalized wages. For fixed quantities, markets with personalized wages always yield higher efficiency than markets with uniform wages, but may be less efficient if firms reduce capacity to avoid bidding too much for star workers.     

Cartel sustainability with vertical product differentiation: Price versus quantity competition

In the context of a vertically differentiated duopoly, we analyse the influence of the degree of differentiation on cartel sustainability, under both price and quantity competition. We find that, under both Bertrand and Cournot competition, the effect of vertical product differentiation on sustainability of the collusive equilibrium is unclear. It is shown that, given a degree of differentiation, price collusion is more sustainable than quantity collusion.     

非完全竞争市场假设在CGE模型中的引入及应用

通过对部门生产函数及相关参数、系数的改造,将非完全竞争市场条件引入CGE模型,并模拟在完全竞争与不完全竞争两个不同市场结构下国际油价上升对我国经济的影响.结果表明,当油品市场设定为不完全竞争时,面对国际油价上升的冲击,GDP下降的程度大于完全竞争的情况.因此随着油品市场逐渐开放,油品市场的产出增加,可以增强我国石油产业和总体经济应对国际油价上升冲击的能力,应继续推动我国石油产业市场自由化的进程.     

Price equilibrium in address models of product differentiation: unit-elastic demand

Summary. I present a class of address models of product differentiation with unit-elastic individual demand and show the existence of Nash equilibrium in prices under assumptions on utility functions and the taste and income heterogeneity across consumers. This paper complements the work by Caplin and Nalebuff (1991, Econometrica), who analyze unit demand models of product differentiation. Received: December 28, 1998; revised version: September 5, 2001     

Non-existence of Duopoly Equilibria: A Simple Numerical Example

We give a simple example to the non-existence of duopoly equilibrium in pure strategies in an economy with two goods and two types of consumers. This extends also the discussion on the incentive for trade in an oligopolistic framework initiated in Cordella and Gabszewicz (1998).     

Existence of Nash equilibria in finite extensive form games with imperfect recall: A counterexample

This paper provides an example showing that for finite extensive form games without perfect recall existence of Nash equilibria in behaviour strategies is not guaranteed in general.