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     

A NOTE ON MARKET COVERAGE IN VERTICAL DIFFERENTIATION MODELS WITH FIXED COSTS

With fixed costs of quality improvement, we find that a covered market outcome with an interior solution in the price stage is not a Nash equilibrium. When the degree of consumer heterogeneity is high (low) enough, an uncovered market outcome (a covered market outcome with a corner solution in the price stage) is the only Nash equilibrium. When the degree of consumer heterogeneity is moderate, both of the two market outcomes are Nash equilibria, but an uncovered market outcome yields higher social welfare than a covered market outcome with a corner solution in the price stage.     

EFFECTS OF ASYMMETRIC INFORMATION WITHIN A FIRM ON OLIGOPOLISTIC MARKET OUTCOMES

I analyze the implications of the Laffont–Tirole type agency problems on oligopolistic market outcomes. In the model, a firm's marginal cost is decreasing in managerial effort and is subject to an additive shock. Both managerial effort and the realization of the shock are a manager's private information. A firm first offers a menu of contract to its manager, and then competes in the product market. As in the model of single principal and single agent, the incentive contracts implement efforts that are distorted downward relative to full information. In this model, with multiple agency relationships, an additional source for upward distortion of effort emerges as a result of the interaction in the product market. The results are robust to whether firms compete in price or quantity.     

MARKET PRICE MECHANISMS AND STACKELBERG GENERAL EQUILIBRIA: AN EXAMPLE

This paper considers Stackelberg competition in a general equilibrium framework with a productive sector. The working of market power and the configurations of strategic interactions are complexified by the presence of a leader. Two market price mechanisms are studied: one is associated with the Stackelberg–Walras equilibrium and the other is linked to the Stackelberg–Cournot equilibrium. Throughout the example of a two commodity economy, several results are obtained about equilibria mergings and about welfare comparisons.     

The Dixit–Stiglitz economy with a ‘small group’ of firms: A simple and robust equilibrium markup formula

In a general version of Dixit–Stiglitz two-sector economy, we present three variants of the concept of oligopolistic equilibrium in price-quantity pairs (d’Aspremont and Dos Santos Ferreira, 2016) integrating income feedback effects in three different ways. For the first two variants (Ford effects ignored or restricted to profits), a single and simple equilibrium markup formula is derived involving, for each firm, a conduct parameter indicating its degree of competitive toughness. Different specifications of these conduct parameters lead to different oligopolistic equilibria in prices and/or in quantities. In particular in the standard Dixit–Stiglitz economy, we show, that the first order conditions of a symmetric oligopolistic price equilibrium correspond to a unique degree of competitive toughness in the general markup formula, This degree is decreasing (and the markup increasing) as more feedback effects are taken into account by firms. On the contrary, for the third variant, introducing full Ford effects leads to lower markups and higher competitive toughness in the standard Dixit–Stiglitz economy and under conditions ensuring the equilibrium markup to remain in tne right interval,     

PRODUCT QUALITY,REPUTATION, AND MARKET STRUCTURE*

In a repeated game in which firms simultaneously choose price and product quality, but quality is observed only after consumption takes place, equilibria exhibiting high quality may exist in oligopoly markets even when the low‐quality one is a unique equilibrium outcome in monopoly and competitive markets. Oligopolists can sustain high quality through the threat of both a loss of reputation and a breakdown in tacit collusion. While we abstract from other reasons that market structure might affect product quality, we show that the inverted‐U shaped relationship between feasible quality and market structure is robust to several generalizations of the model.     

Choosing price or quantity? The role of delegation and network externalities

We consider a differentiated duopoly and endogenise the firm choice of the strategy variable (price or quantity) to play on the product market in the presence of network externalities. We model this choice by assuming both competition between entrepreneurial (owner-managed) firms and competition between managerial firms in which market decisions are delegated from owners to revenue-concerned managers. While network externalities are shown not to alter the symmetric equilibrium quantity choice arising in the no-delegation case, sufficiently strong network effects allow us to eliminate the multiplicity of equilibria under delegation and lead to a unique equilibrium in which both firms choose price.     

Conjectural variations, symmetric equilibria and economic policy

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.     

Imperfect competition in financial markets and capital structure

We consider a model of corporate finance with imperfectly competitive financial intermediaries. Firms can finance projects either via debt or via equity. Because of asymmetric information about firms’ growth opportunities, equity financing involves a dilution cost. Nevertheless, equity emerges in equilibrium whenever financial intermediaries have sufficient market power. In the latter case, best firms issue debt while the less profitable firms are equity-financed. We also show that strategic interaction between oligopolistic intermediaries results in multiple equilibria. If one intermediary chooses to buy more debt, the price of debt decreases, so the best equity-issuing firms switch from equity to debt financing. This in turn decreases average quality of equity-financed pool, so other intermediaries also shift towards more debt.     

A Two-stage Price-setting Duopoly: Bertrand or Stackelberg

This paper investigates a two-stage price-setting duopoly with differentiated goods. First, each firm announces its price; second, it chooses its actual price; and finally the market opens. Once a firm announces a price, it is able to discount it but not raise it. The model includes Stackelberg-type and Bertrand-type equilibria as possible outcomes. Whether Bertrand or Stackelberg appears in equilibrium depends on the properties of demand functions crucially. We find three patterns of equilibrium outcomes; one case has Bertrand equilibrium only, another has Stackelberg only, and the other has both equilibria     

Cooperative oligopolistic pricing

The main purpose of the present paper is to show that the equilibrium price in an oligopolistic market with cooperative pricing but noncooperative production as a rule approaches neither the monopoly price (when there are few firms) nor the competitive price (when there are many firms). Instead it is equal to that price which maximizes collective sales revenues if the industry's demand curve is inelastic, while it is “almost” competitive if demand is elastic.     

Exhaustible Resources,Non-Convexity and Competitive Equilibrium

Theoretical underpinnings of competitive equilibrium in an exhaustible-resource market with non-convex (u-shaped) costs are proposed. The analysis extends to intertemporal production Novshek and Sonnenschein’s approximation of static competitive equilibrium by limits of Cournot equilibria. A problem with using Novshek and Sonnenschein’s method is that oligopolistic equilibrium, even an open-loop equilibrium, to which limits might be applied, does not exist when there is a non-convex technology. Using epsilon equilibrium as the equilibrium concept finesses this problem. There are two types of limiting competitive equilibrium. A third type of competitive equilibrium that has been prominent in the literature is found to be inconsistent with limiting approximations.     

Tariffs vs Quotas in a Model of Trade with Capital Accumulation*

This paper examines the equivalence among price‐modifying and quantity‐fixing international trade policies in a differential game. We employ two well‐known capital accumulation dynamics for firms, due to Nerlove and Arrow and to Ramsey, respectively. We show that, in both cases, open‐loop and closed‐loop Nash equilibria coincide. Under the former accumulation the tariff‐quota equivalence holds, while, in general, it does not under the latter. Moreover, in the Ramsey model, the country setting the trade policy (weakly) prefers a quantity‐equivalent import quota to the adoption of the tariff. These results are not a consequence of the equilibrium concept we adopt (with and without market power), but directly follow from the interplay between market power and the properties of accumulation dynamics.     

Modelling Policy Issues in a World of Imperfect Competition

General equilibrium theory constitutes a sound basis for the discussion of policy issues if firms do not have market power. However, if firms influence prices strategically, the concept of profits loses its meaning due to the price normalization problem. Hence, it is unclear how to model the behavior of oligopolistic firms. In order to provide a conceptual foundation for the analysis of policy issues in the case of imperfect competition, we discuss ways to formulate the objective of a strategic firm. In particular, we investigate the concept of real wealth maximization that is based on profits as well as on shareholders' aggregate demand.     

Profit maximization mitigates competition?

Summary. We consider oligopolistic markets in which the notion of shareholders’utility is well-defined and compare the Bertrand-Nash equilibria in case of utility maximization with those under the usual profit maximization hypothesis. Our main result states that profit maximization leads to less price competition than utility maximization. Since profit maximization tends to raise prices, it may be regarded as beneficial for the owners as a whole. Moreover, if profit maximization is a good proxy for utility maximization, then there is no need for a general equilibrium analysis that takes the distribution of profits among consumers fully into account and partial equilibrium analysis suffices.     

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.     

Supply Disruptions and Regional Price Effects in a Spatial Oligopoly—An Application to the Global Gas Market

Supply shocks in the global gas market may affect countries differently, as the market is regionally interlinked but not perfectly integrated. Additionally, high supply‐side concentration may expose countries to market power in different ways. To evaluate the strategic position of importing countries with regard to gas supplies, we disentangle the import price into different components and characterize each component as price increasing or price decreasing. Because of the complexity of the interrelations in the global gas market, we use an equilibrium model programmed as a mixed complementarity problem (MCP) and simulate the blockage of liquefied natural gas (LNG) flows through the Strait of Hormuz. This enables us to account for the oligopolistic nature and the asymmetry of the gas supply. We find that Japan faces the most severe price increases, as the Japanese gas demand completely relies on LNG supply. In contrast, European countries such as the UK benefit from good interconnection to the continental pipeline system and domestic price taking production, both of which help to mitigate an increase in physical costs of supply as well as in the exercise of market power.     

OLIGOPOLISTIC PRODUCT WITHHOLDING IN RICARDIAN MARKETS

We consider strategic behaviour in the rental market for quality-differentiated goods. In his classic analysis Ricardo showed that at the competitive equilibrium the price of the marginal unit is driven to zero. An oligopolistic market structure usually leads to a radically different equilibrium. Deliberate withholding of units often becomes part of a firm's best response, and whenever this occurs, a pure strategy equilibrium fails to exist. A necessary but not sufficient condition for a pure strategy equilibrium to exist is for one firm to own all the best quality units. A mixed strategy equilibrium always exists and the associated payoff is aiways greater than the competitive payoff.     

QUANTITY VERSUS PRICE IN A HOMOGENEOUS PRODUCT DUOPOLY*

In a simple homogeneous product setting, the paper looks at the debate on whether firms should choose quantity or price as their strategic variable. It examines a two-stage game between firms with symmetric costs in which the firms choose the strategic mode of operation in the first period and then, in the second period, price or output are chosen simultaneously according to the mode chosen in the first stage. In this game it is possible to have two Nash equilibria where either both play in quantities or both play in prices. One firm choosing price and the other quantity can never be a Nash equilibrium in the two-stage game. Both choosing quantity is always a Nash equilibrium. Both choosing prices may be a Nash equilibrium only in some situations: the structure of the cost functions decides this issue.     

Too Much Monitoring, Not Enough Performance Pay

This paper endogenises the internal organisation of competitive firms in a simple general equilibrium framework. The options are monitored teams, unmonitored teams motivated by collective performance pay, and self-employment. The choice of incentive scheme depends on market price and also affects price through its influence on output. As more people opt for self employment, pecuniary externalities increase the pressure on the rest to follow suit and Pareto rankable multiple equilibria arise. The conditions for a competitive equilibrium to be constrained efficient are restrictive and everyone may gain from policies limiting monitoring and self employment and from the imposition of entry taxes.