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     

Strategic tariffs, tariff jumping, and heterogeneous firms

The majority of research to date investigating strategic tariffs in the presence of multinationals finds a knife-edge result where, in equilibrium, all foreign firms are either multinationals or exporters. Utilizing a model of heterogeneous firms, we find equilibria in which both pure exporters and multinationals coexist. We utilize this model to study the case of endogenously chosen tariffs. As is standard, Nash equilibrium tariffs are higher than the socially optimal tariffs. Unlike existing models with homogeneous firms, we find that non-cooperative tariffs promote the existence of low-productivity firms relative to the socially optimal tariffs. This highlights a new source of inefficiency from tariff competition not found in models of homogeneous firms. In addition, we find that in many cases the Nash equilibrium tariff when FDI is a potential firm structure is lower than when it is not. As a result, FDI improves welfare by mitigating tariff competition.     

Price vs quantity in a duopoly supergame with Nash punishments

We examine the endogenous choice between price and quantity behaviour in a duopoly supergame with product differentiation. We find that (i) if cartel profits are evenly split between firms, then only symmetric equilibria s obtained; (i) if instead the additional profits available through collusion are split according to the Nash bargaining solution, there are parameter regions where all subgame perfect equilibria are asymmetric, with firms colluding in price–quantity supergames.     

Leadership and Privatisation in a Mixed Multi‐product Oligopoly: An Endogenous Timing Model

This paper examines both leadership choice and welfare consequences of privatisation in an endogenous timing mixed multi‐product oligopoly. It shows that a multi‐product firm undermines the welfare‐maximising efforts of a public firm by cross‐subsidising. The paper demonstrates that a unique subgame perfect Nash equilibrium emerges in a multi‐product market, in contrast to the multiple equilibria of a single‐product market. This unique equilibrium indicates that profit‐maximising private firms retain leadership while a welfare‐maximising public firm acts as a follower. Even on the off‐equilibrium path where the public firm acts as a leader, it rarely generates maximum social welfare. However, privatising the public firm usually harms social welfare and results in a different timing structure in equilibrium.     

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.     

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.     

On-the-job search and strategic bargaining

This paper studies wage bargaining in a simple economy in which both employed and unemployed workers search for better jobs. The axiomatic Nash bargaining solution and standard strategic bargaining solutions are inapplicable because the set of feasible payoffs is nonconvex. I instead develop a strategic model of wage bargaining between a single worker and firm that is applicable to such an environment. I show that if workers and firms are homogeneous, there are market equilibria with a continuous wage distribution in which identical firms bargain to different wages, each of which is a subgame perfect equilibrium of the bargaining game. If firms are heterogeneous, I characterize market equilibria in which more productive firms pay higher wages. I compare the quantitative predictions of this model with Burdett and Mortensen's [1998. Wage differentials, employer size and unemployment. International Economic Review 39, 257-273.] wage posting model and argue that the bargaining model is theoretically more appealing along important dimensions.     

A new model of equilibrium involuntary unemployment

Summary. We show that equilibrium involuntary unemployment emerges in a multi-stage game model where all market power resides with firms, on both the labour and the output market. Firms decide wages, employment, output and prices, and under constant returns there exists a continuum of subgame perfect Nash equilibria involving unemployment and positive profits. A firm does not undercut the equilibrium wage since then high wage firms would attract its workers, thus forcing the undercutting firm out of both markets. Full employment equilibria are payoff dominated by unemployment equilibria, and the arguments are robust to decreasing returns.Received: 21 May 2001, Revised: 15 April 2003, JEL Classification Numbers: D43, E24.Correspondence to: Leo KaasWe thank an anonymous referee, Woojin Lee, Klaus Ritzberger and seminar participants in Konstanz, Manchester, Milan, Prague, Vienna, and Warwick for helpful comments. Financial support from the Economic and Social Research Council (UK) under grant L138251030 and from the Manchester School Visiting Fellowship Scheme is gratefully acknowledged.     

DOUBLE‐SIDED ADVERSE SELECTION IN THE PRODUCT MARKET AND THE ROLE OF THE INSURANCE MARKET*

I investigate the interrelation between a product market and an insurance market when adverse‐selection problems exist both in consumers and in firms. Firms offer warranties for product failures. Consumers may further purchase first‐party insurance for the residual risks of product failures. Given that the insurance market exists, two types of equilibria are possible: (a) Different firm types offer different pooling warranties attracting both good and bad consumer types or (b) good firms attract only bad consumers and bad firms attract both types of consumers. I discuss the existence and the efficiency implication of the insurance market.     

ENDOGENOUS TIMING IN QUALITY CHOICES AND PRICE COMPETITION

We modify the price‐setting version of the vertically differentiated duopoly model by Aoki (2003) by introducing an extended game in which firms noncooperatively choose the timing of moves at the quality stage. Our results show that there are multiple equilibria in pure strategies, whereby firms always select sequential play at the quality stage. We also investigate the mixed‐strategy equilibrium, revealing that the probability of generating outcomes out of equilibrium is higher than the probability of playing one Nash equilibria in pure strategies. In the alternative case with full market coverage, we show that the quality stage is solved in dominant strategies and therefore the choice of roles becomes irrelevant as the Nash and Stackelberg solutions coincide. With full market coverage and corner solution, the results show that the game has a unique subgame perfect equilibrium in pure strategies, where the high‐quality firm takes the lead in the quality stage.     

Low information nash equilibria for oligopolistic markets

This paper deals with an infinite horizon n firm oligopoly in which firms are assumed to have incomplete information about one another's actions and profit functions. An equilibrium concept is defined that is similar to the Nash non-cooperative equilibrium, but is suitable for the information assumptions of the model. The equilibrium uses a type of bounded rationality which makes firms' computations relatively easy. This is due to an implicit assumption that computation is costly and a Bayesian approach is prohibitively costly. This low information Nash equilibrium is proved to exist, and, in addition, an adaptive expectations decision process is described which, if followed by all firms, leads to the low information Nash equilibrium.     

On the existence of pure strategy Bertrand equilibrium

Summary The paper analyses the existence of pure strategy Nash equilibrium in price competition (or Bertrand equilibrium) in a homogeneous product market when costs are strictly convex and proves that if output is demand determined such equilibrium always exists. This paper also characterises such equilibria and shows that if firms are identical such equilibria are necessarily non-unique. However for firms with asymmetric costs it can be unique or non-unique.I am greatly indebted to Anjan Mukherji and Kunal Sengupta for this paper. I also express my profound gratitude to a referee of this journal for a very helpful set of suggestions.     

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.     

When should firms choose a risky new technology? An oligopolistic analysis

How to choose technology type in a competitive environment is an important and challenging problem, which has received little attention from scholars. To fill this gap, this paper builds a game-theoretic model to examine whether a firm should choose to adopt a risky new technology or to adopt a safe new technology to reduce its marginal cost. I find that the result that each firm should always choose the risky technology in a duopoly may be invalid when more firms enter the market. In this scenario, some firms should adopt the safe technology for relatively high product substitutability because the advantage of employing the risky technology is threatened by the business stealing externality, finally forming heterogeneous equilibria in which both types of technologies are present. Furthermore, I show that the heterogeneous technology choice equilibria are more likely to arise when increasing number of firms enter the market, and that in these equilibria more firms always choose the risky technology than the safe technology. This study conveys relevant economic insights for competitive firms confronted with a dilemma between taking risks in pursuit of greater technology rewards and taking no risks for conservative technology returns.     

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     

WHY DO LARGE FIRMS TEND TO INTEGRATE VERTICALLY?

We provide a theoretical framework to discuss the relation between firm size and vertical structures. The framework is based on a Hotelling model with three downstream and three upstream firms. We show that vertical integration enhances the degree of product differentiation and show the strategic complementarity of product positioning. We also show that the downstream firm that has the largest market share is more likely to integrate vertically. Enhancing the degree of product differentiation is more beneficial for the large firm than for the rest of the downstream firms because the large firm supplies a large amount of product.     

企业差异化战略对价格和质量竞争博弈均衡解的影响研究

消费者在购买商品时不仅考虑商品价格而且还要考虑商品质量水平的需求市场,如果存在两寡头企业提供某商品,必然会导致价格和质量的竞争博弈。本文研究表明:为了达到纳什均衡状态,两企业必须采取一定的差异化策略。而且在均衡状态下,如果市场是价格敏感市场,企业的差异化程度越高,对企业和消费者都越有利;如果市场是质量敏感市场,当敏感程度相对很低时,企业的差异化程度越高,对企业和消费者也都越有利;当敏感程度一般时企业可选择适当的差异化程度使得企业和消费者同时达到最大的均衡利润;但当敏感度非常高,企业差异化程度越高对企业的均衡利润越大,可对消费者的均衡利润却越小。     

The Influence of a Neighbouring Market on Product Qualities and Prices

This paper analyses a model of vertical product differentiation in which there is a primary market with two firms and a secondary market with no firms. Consumers in the secondary market incur a cost when purchasing the product from the primary market. The firms sequentially choose product quality and then simultaneously choose prices. Firm 1 always chooses the maximum quality, while firm 2's quality and the prices depend on the cost. Also, the cost determines which firm(s), if either, serves the secondary market. It is shown that the firms and the consumers of each market prefer different levels of costs.     

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.     

Competition and confidentiality: Signaling quality in a duopoly when there is universal private information

We model non-cooperative signaling by two firms that compete over a continuum of consumers, assuming each consumer has private information about the intensity of her preferences for the firms' respective products and each firm has private information about its own product's quality. We characterize a symmetric separating equilibrium in which each firm's price reveals its respective product quality. We show that the equilibrium prices, the difference between those prices, the associated outputs, and profits are all increasing functions of the ex ante probability of high safety. If horizontal product differentiation is sufficiently great then equilibrium prices and profits are higher under incomplete information about quality than if quality were commonly known. Thus, while signaling imposes a distortionary loss on a monopolist using price to signal quality, duopolists may benefit from the distortion as it can reduce competition. Finally, average quality is lower since signaling quality redistributes demand towards low-quality firms.