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.     

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.     

COMPETITION FOR MARKET SHARE OR FOR MARKET SIZE: OLIGOPOLISTIC EQUILIBRIA WITH VARYING COMPETITIVE TOUGHNESS*

For an industry producing a composite commodity, we propose a comprehensive concept of oligopolistic equilibrium, allowing for a parameterized continuum of regimes varying in competitive toughness. Each firm sets simultaneously its price and its quantity under two constraints, relative to its market share and to market size. The price and the quantity equilibrium outcomes always belong to the set of oligopolistic equilibria. When firms are identical and we let their number increase, any sequence of symmetric oligopolistic equilibria converges to the monopolistic competition outcome. Further results are derived in the symmetric CES case, concerning in particular the collusive solution enforceability.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

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,     

Codetermination,Price Competition and the Network Industry

This research develops a tractable two‐stage non‐cooperative game with complete information describing the behaviour of price‐setting firms that must choose to be profit maximisers or bargainers under codetermination in a network industry with horizontal product differentiation. The existing theoretical literature has already shown that codetermination might arise as the endogenous market outcome in a strategic competitive quantity‐setting duopoly. In sharp contrast with this result, the present article shows that codetermination does never emerge as a Nash equilibrium in a price‐setting non‐network duopoly. Then, it aims at highlighting the role of network externalities in determining changes of paradigm of the game and letting codetermination become a sub‐game perfect Nash equilibrium when prices are strategic substitutes or strategic complements. This equilibrium may be Pareto efficient. Results allow distinguishing between mandatory codetermination and voluntary codetermination. The article also proposes a model of endogenous codetermination according to which every firm may choose to bargain with its own corresponding union bargaining unit only whether the firm's bargaining strength is exactly the profit‐maximising one. The equilibrium outcomes emerging in this case range from a uniform Nash equilibrium, in which both firms are codetermined, to mixed Nash equilibria, in which only one of them chooses to be codetermined. These results are ‘network depending’ and do not hold in a non‐network duopoly.     

Some Implications of Imperfect Competition For Recent Trade Theory*

This paper argues that in a general-equilibrium context, it is not sensible for oligopolistic (and mono-polistically competitive) firms to maximize profit, because the outcome would be sensitive to the choice of the numeraire. the natural objective of these firms would be to maximize the utility of the shareholders if the shareholders are identical. I show that even if each firm takes the representative individual's marginal utility of income as given, the outcome of the utility maximization objective is Pareto optimal, and in equilibrium, each firm equates price with marginal cost.     

上市公司兼并与收购的财富效应

并购引起了收购公司和目标公司股价的变化 ,因而引起了收购公司和目标公司股东财富的变化。本文采用事件研究法 ,对 1 999— 2 0 0 0年中国证券市场深、沪两市共 3 49起并购事件进行了实证研究。结果表明 ,并购能给收购公司的股东带来显著的财富增加 ,而对目标公司股东财富的影响不显著 ;不同类型的并购有不同的财富效应 ;国家股比重最大和法人股比重最大的收购公司其股东能获得显著的财富增加 ,而股权种类结构对目标公司股东财富的影响不显著。     

AN OLIGOPOLISTIC HECKSCHER–OHLIN MODEL OF FOREIGN DIRECT INVESTMENT*

We develop a 2 × 2 × 2 trade model in which one of the two sectors is perfectly competitive and the other is oligopolistic. The oligopoly sector consists of a given number of identical firms for each country, but they are free to locate in either country. The allocation of the firms between the two countries is endogenously determined, and changes in factor prices play a crucial role in establishing this equilibrium. Under this framework we examine the validity of factor price equalization, patterns of trade and gains from trade. Effects of technological progress and preference changes on firm locations are also analysed.     

Supermarket Choice and Supermarket Competition in Market Equilibrium

Multi-store firms are common in the retailing industry. Theory suggests that cross-elasticities between stores of the same firm enhance market power. To evaluate the importance of this effect in the U.K. supermarket industry, we estimate a model of consumer choice and expenditure using three data sources: profit margins for each chain, a survey of consumer choices and a data-set of store characteristics. To permit plausible substitution patterns, the utility model interacts consumer and store characteristics. We measure market power by calculating the effect of merger and demerger on Nash equilibrium prices. Demerger reduces the prices of the largest firms by between 2 and  3.8%  depending on local concentration; mergers between the largest firms lead to price increases up to  7.4%  .     

On intrabrand and interbrand competition: The strategic role of fees and royalties

We examine oligopolistic markets with both intrabrand and interbrand competition. We characterize equilibrium contracts involving a royalty (or wholesale price) and a fee when each upstream firm contracts with multiple downstream firms. Royalties control competition between own downstream firms at the expense of making them passive against rivals. When the number of downstream firms is endogenous, each upstream firm chooses to have only one downstream firm. This result is in sharp contrast to previous literature where competitors benefit by having a larger number of independent downstream firms under only fixed fee payments. We discuss why allowing upstream firms to charge per-unit payments in addition to fixed fees dramatically alters their strategic incentives.     

Price dispersion in oligopoly

In the world of perfect markets consumers are assumed to respond instantly to every small price change. However, in the real world it is not clear that any small price change will have a great impact on consumers' decisions and that, regardless of their habit, they will shift from one brand to the other. The purpose of this paper is to examine oligopolistic price competition under the assumption that consumers are non-responsive to small price differences. The paper proves the existence of equilibrium in which firms do not necessarily charge the same price; however some of the firms charge their monopolistic price and others charge prices close to that price.     

Uncertainty and the comparative dynamics of stock price

This article derives an envelope theorem for dynamic economic problems under conditions of uncertainty. The theorem is motivated through analysis of a firm with an objective of maximizing shareholders' wealth. Envelope results are used to determine how the value of the optimizing firm is expected to change in response to shifts in several variables including the risk-free interest rate, the market risk premium, the tax rate, and the prices of output and inputs. Uncertainty is introduced into the model using a general measure-theoretic approach which does not require restrictive assumptions regarding the behavior of the problem's stochastic variables.     

Price Competition and Product Differentiation When Consumers Care for the Environment

Increasing environmental awareness may affect the pleasure of consuming a good for which an environment friendly substitute is available. In this paper, we investigate the market implication of product differentiation when customers are concerned about environmental aspects of the good. We use the spatial duopoly model to determine how environmental concern affects prices, product characteristics and market shares of the competing firms. Our analysis is based on a two-stage game, where at the first stage each firm chooses the characteristic of its product. At the second stage, each firm chooses its price. Equilibrium prices and market shares are affected by consumer awareness of the environment and by the higher costs for producing those goods. As for the Nash equilibria in the characteristics, we find three equilibria depending on the parameter constellation. In order to find out whether the market functions in an optimal way, we determine the choice of environmental characteristics by a welfare maximizing authority. The objective of the paper is to understand the environmental quality choices facing firms and to provide policies that would align private choices with the social optimum.JEL classifications: L11, Q38, H23     

Multi-Sector Model of Tradable Emission Permits

This paper presents a multi-sector model of tradable emission permits, which includes oligopolistic and perfectly competitive industries. The firms in oligopolistic industries are assumed to exercise market power in the tradable permit market as well as in the product market. Specifically, we examine the effects of the initial permit allocation on the equilibrium outcomes, focusing on the interaction among these product and permit markets. It is shown that raising the number of initial permits allocated to one firm in an oligopolistic industry increases the output produced by that firm. Under certain conditions, raising a “clean” (less-polluting) firm’s share of the initial permits can lead to reductions in both the product and permit prices. We discuss criteria for the socially optimal allocation of initial permits, considering the trade-off between production inefficiency and consumer benefit.     

Commitment and price competition in a dynamic differentiated-product duopoly

This paper characterizes linear Markov-perfect equilibrium in a duopolistic environment where firms engage in dynamic price competition. Firms have constant (but potentially different) marginal costs and produce differentiated products. We show that, for the case of linear demand, dynamically stable Markov-perfect equilibrium prices are strictly higher than one-shot Nash equilibrium prices, but lower than fully collusive (monopoly) prices. We provide closed-form solutions for the Markov-perfect equilibrium prices which, in principle, can be estimated given data on firm demand and costs. Our results suggest that static two-stage models of price commitment are on reasonably solid ground in that they might be viewed as a reduced form for more complicated dynamic models.     

Costly Search, Capacity Constraints, and Bertrand Equilibrium Price Dispersion

This article analyzes the impact of transaction (search) costs and capacity constraints in an almost competitive market with homogeneous firms that compete on price. We characterize conditions under which Nash equilibria with price dispersion exist; in equilibrium, firms play pure strategies in prices and consumers adopt a symmetric mixed search strategy. Price dispersion is possible even though consumers all have the same search cost and valuation for the item and prices charged by all firms are common knowledge.     

Vertical Product Differentiation When Quality is Scarce: The Case of n > 2 Firms

This paper describes a model of vertical product differentiation in which more than two firms compete in quality and price. Quality is of fixed supply, so firms participate in an auction to attain it. Firms then simultaneously choose prices. The paper determines equilibrium bids in the quality auction and the Bertrand equilibrium prices. In equilibrium one firm attains all the units of quality, but pays a price such that it, like the minimum-quality firms, earns zero profits. Aggregate welfare is computed, and is shown to decrease as competition increases.     

Price distributions and competition

This paper utilizes an equilibrium search model to investigate market structure and price dispersion. In a market with one large firm and a competitive fringe, the large firm offers the highest price. Fringe firms offer a distribution of lower prices.     

Rationing rule, imperfect information and equilibrium

Summary. The impact of imperfect information on the price setting behaviour of firms is analysed. Specifically, consumers support an information cost to become informed about prices. Firms are endowed with U-shaped average cost curves. If a firm does not supply more than its competitive supply as determined by its marginal cost schedule, then we show that the existence of a pure strategy equilibrium is conditional on the rationing rule employed. If uninformed consumers are served first then the monopoly price is the sole equilibrium whenever consumers' information costs are high enough. Otherwise, a pure strategy equilibrium fails to exist contrary to the results of Salop and Stiglitz (1977) or Braverman (1980) who implicitly suppose that firms supply all the demand at a given price. Received: May 17, 1999; revised version: September 15, 2000