Interfaces with Other Disciplines
Price and quality competition: The effect of differentiation and vertical integration

https://doi.org/10.1016/j.ejor.2006.04.028Get rights and content

Abstract

This paper studies an instance of price and quality competition between firms as seen in the recent Internet market. Consumers purchase a product based on not only its price but also its quality level; therefore, two firms compete in determining their prices and quality levels to maximize their profits. Characterizing this competition from a microeconomic viewpoint, we consider two possible business strategies that firms can utilize to overcome the competition—the differentiation and the vertical integration with another complementary firm. We show an interesting result not seen in the well-known Bertrand price competition: not only does the differentiation always increase the firms’ profits, but also it can increase the consumer’s welfare in a quality-sensitive market. We further derive that under some mild conditions the monopolistic vertical integration that excludes the combination-purchase with a competitor’s product is beneficial for both the integrated firm and its consumers.

Introduction

In this paper, we consider a price and quality competition between two firms. Consumers buy a product in consideration of not only its price but also its quality level, which is a measurable value exhibiting a “more is better” property. Under this demand structure, firms compete with each other in determining their prices and quality levels to maximize their profits. Using a game theoretic approach, we describe this competition theoretically and consider the two possible business strategies under the competition: the differentiation by some factors other than price and quality, and the vertical integration with another firm. The purpose of this paper is to analyze the effect of the above strategies in terms of the welfare of both firms and consumers from a microeconomic viewpoint by using a comparative static.

We note that this study is strongly motivated by a real-world case, that is, the competition among Internet service providers (ISPs) in the recently emerging broadband Internet market in Japan. Since the regional telecom carriers, NTT East and NTT West, and a new venture, Tokyo Metallic, launched their ADSL services in 1999 respectively, a number of new entrants have appeared in this market. The competition between these firms resulted in a sharp decline of the user’s fees (see Fig. 1.11). This surprising decline made the Japanese broadband Internet market progress rapidly and on average the user’s fees for Japanese ISP firms became lower than those in US, Korea and other countries, see MPHPT (2003). However, on the other hand, this competition yielded some losers, who were driven out of business. This prompted the Japanese Ministry of Public Management, Home Affairs, Posts and Telecommunications (MPHPT) to start an investigation and evaluation of the state of the competition, see MPHPT (2004a). This remarkable growth of the broadband Internet market in Japan even attracted the attention of other countries.

We recognize that in offering a broadband Internet service the competition would have a different mechanism from the price competition usually discussed. That is, the consumers would require not only an acceptable price (user’s fee), but also the quality level necessary for a comfortable downloading of broadband contents (e.g. a movie, a voice and so on). This is confirmed by the results of a consumer questionnaire conducted by MPHPT (2004b) in which they state that consumers consider some factors of quality level (e.g. the maximum circuit speed rate) in making their choice of ISP. Therefore, the firms also should consider at least two factors—the price and the quality level, and optimize them in order to earn their profits. This action by a firm would cause the price and quality competition.

How can the firms overcome the competition? We present two possible business strategies in this paper. One is the differentiation—whereby firms create their own value for a product by, for example, utilizing a brand name so that some consumers will want to buy their product regardless of its price and quality level. Therefore, we first attempt to analyze the effect of the differentiation under the price and quality competition. Subsequently, under varying levels of differentiation we consider the vertical integration with another firm offering the complementary product. Specifically, we focus on the monopolistic vertical integration, which does not allow the combination-purchase with the competitor’s product (see MPHPT, 2002). Indeed, in the above Japanese market, Yahoo BB has employed this business model where consumers can only buy its attractive online contents when also purchasing its ADSL service, see Taniwaki (2003). As shown in Fig. 1.1, the leader of the emerging progress, Yahoo BB, who suddenly entered the ADSL market in 2001, launched its service at a surprisingly low price and acquired numerous customers. However, does the monopolistic integration employed by the leader really contribute to increase the welfare of the firm and its consumers? Intuitively, to release its online contents which are attractive to other ISPs’ consumers seems rather more profitable, does not it? In this paper, we try to answer this question by theoretically analyzing the monopolistic vertical integration under the price and quality competition.

As is indicated above, the Internet market motivates our study; however, it would also be applicable to other business scenes. For example, consider a competition among PC manufacturers. The consumers would determine the purchase of a PC based on not only its price but also its quality level—CPU speed, memory capacity, and so on. If a PC were differentiated by some factors (e.g. design, brand, etc.), it would attract the consumers to buy it. Thus, the manufacturers also face the price and quality competition, and the differentiation strategy. On the other hand, when software is offered only with a specific PC/OS, it would be possible to describe this situation as our model of the monopolistic vertical integration.

We develop our analysis in a microeconomic framework. There are a number of the microeconomic literatures in existence, which focus on price and quality competition. Specifically, the spatial competition model originated by Hotelling (1929) is one that is widely used as a model of a product differentiation, where a customer’s “location” can be interpreted by an “ideal-point” of the consumer’s taste preference. While much of the marketing literature is based on the Hotelling’s model, some different approaches have recently been employed to formulate a price and quality competition. For example, Li and Lee (1994) analyze a competition between two firms, which involves a price and a delivery-speed, where a queuing model describes the delivery performance. However, our study is more closely related to Banker et al. (1998). They investigate a price and quality competition under a duopolistic setting, where the consumers’ demand is modeled as a linear function of a price and a quality level and the cost as a quadratic function of the quality level. While the Hotelling’s model assumes that consumers have heterogeneous taste preference and each of them buys only the most preferred single product, this linear demand model considers a consumer’s utility from buying a multiple of differentiated products, see Oz (1995) for the detail. Banker et al. (1998) derive the equilibrium price and quality and analyze the impact of the relative cost advantage in quality improvement on the equilibrium quality level, the effect of the horizontal integration between two firms, and so on. However, they do not investigate our topics of interest—the differentiation and the vertical integration.

Economides (1999), on the other hand, does show the important result of the vertical integration with the choice of a quality level. He examines whether the sole vertically-integrated monopolist can achieve higher profit and consumer surplus by providing a composite good, compared to the case where the dual disintegrated monopolists provide the complementary goods, respectively. Generally speaking, the vertical integration under a price competition solves the so-called “double marginalization problem” (see e.g. Tirole, 1990) and can increase the surplus of the firm and the consumer. Economides (1999) shows that this result also holds in the case where the quality choice is considered. However, it should be noted that the setting analyzed by Economides (1999) assumes the dual monopolists in pre-integration, not an existence of firms faced by a horizontal competition at all. In contrast, we assume the existence of three firms—two competitive firms providing a commodity and a monopolist providing the complementary commodity. In this case, the issue would be more complicated since the vertical integrated firm has alternatives about bundling strategy with the rest of their goods. Economides (1998) deals with the incentive for a monopolist in an upstream market to raise the costs of the rivals to his downstream subsidiary by discriminatory quality degradation. Oystein (2004) analyzes the vertical integration in the broadband Internet market; the main topics of discussion are the relation between a price regulation to the vertically-integrated firm and his strategy of investments for the quality improvement. Matsubayashi et al. (2002) examines the merger effect of two firms under a network equilibrium model. All of these studies have different viewpoints from ours.

As previously specified, our model employed in this paper refers to Banker et al. (1998). We first assume that consumers determine their purchase based on a “perceived price,” which is a weighted combination of the price and the quality level. With this measure, we use a linear demand model. The latter seems more suitable for our purpose rather than the Hotelling’s model when taking into account the following observations in the Japanese broadband Internet market: (i) an agent often enters multiple ISPs’ services at once, e.g. one chooses ISP A for his business use and ISP B for his private use, and so on, and (ii) consumers frequently switch an ISP due to the low switching cost and this would be able to be regarded as the purchase of multiple brands in a short term. It is of importance that the parameters of the differentiation are separately expressed from those of the consumer characteristic in our demand function. Thus, it is possible to observe the effect of the differentiation explicitly, which is not the case in the original Bankers’ model. With this demand structure, we formulate a non-cooperative game, where two firms compete with each other in determining their prices and quality levels simultaneously. The outcome of the game is characterized and the impacts of the differentiation on the outcome are analyzed in terms of the welfare of each firm and the consumers, i.e. the profits and the perceived price. Furthermore, we model the vertical integration under the price and quality competition and investigate the effect by using a comparative static.

We first find some interesting insights in our price and quality competition, which are not seen in the well-known Bertrand price competition. It is shown that the Nash equilibrium in our game does not exist unless both firms are relatively differentiated, while the Bertrand competition usually ensures the existence of the equilibrium even for a completely homogeneous case. Moreover, the differentiation surprisingly increases not only the welfare of firms but also that of consumers in a quality-sensitive market, while the Bertrand competition leads to a decrease of consumers’ welfare. We next show that the monopolistic vertical integration as seen in the above Yahoo BB’s business model has a positive effect. Specifically, the integration is beneficial for both the integrated firm and its consumers if all the competitor’s consumers switch to it after the integration. In contrast, we obtain an interesting result for the most highly differentiated case; if only less than half of the consumers switch, the integration is beneficial even in comparison with the situation where the integrated firm allows the combination-purchase with the competitor’s product. In addition, we show that the threshold of the switching rate for the integration to be beneficial decreases as the consumers’ valuation of quality becomes more sensitive.

The rest of the paper is organized as follows. Section 2 introduces our model and formulates a price and quality competition between two firms as a non-cooperative game. Section 3 gives the Nash equilibrium of the game and analyzes the effect of the differentiation. In Section 4, we investigate the effect of the monopolistic vertical integration in comparison with the competitive environment. In Section 5, we further consider other possible situations and reevaluate the monopolistic integration. Section 6 summarizes our findings. All proofs of results are given in Appendix.

Section snippets

The model

Let p(0  p) be the price and x(0  x) be the quality level of a commodity A, respectively. Here x implies a summary level of all more-is-better quality attributes of A. Consumers buy the commodity A based on the perceived price w  αp  βx, where α and β are positive parameters given by a market. We assume a duopoly market consisting of two firms, 1 and 2, offering A. To concentrate our attention on the effect of the differentiation between firms, we make simple assumptions that the two firms are

The Nash equilibrium and effects of the differentiation

From the symmetry of firms, the equilibrium prices and quality levels if they exist are identical for both firms. So we now denote them as p and x. As we state the following theorem, the equilibrium is clearly characterized by the sign of T  β  αϵ which means the consumers’ valuation of quality level relative to price (normalized by the variable cost of the quality level).

Theorem 3.1

The unique Nash equilibrium (p, x) exists if, and only if 4αϕ(a2  b2)  aT2 > 0. (p, x) is described as follows:

  • 1.

    when T  0: p=(a-

The effects of the vertical integration

As seen in the previous section, the differentiation between two firms is beneficial to the welfare of both consumers and firms under price and quality competition. Then in this section, we try to investigate the effect of the vertical integration with another complementary firm under a differentiated situation. Specifically, under varying levels of differentiation between two firms offering commodity A, we consider the vertical integration between one of the two firms (say firm 1) and another

The integration effect under other possible situations

In the previous section, the effect of the monopolistic vertical integration is discussed by making a comparison in a situation where the three firms simply compete with each other. However, in order to suggest that the effect always occurs, it would not suffice to analyze this case only. Specifically, it may be more profitable for the integration firm to allow consumers the combination of B and firm 2’s A. In addition, the assumption under which all consumers of firm 2 switch to firm {1, 3}

Concluding remarks

In this study, we explored some topics arising from the price and quality competition between two symmetric firms by utilizing a game theoretic approach. For the analysis, a typical linear demand model was employed which incorporated explicitly the degree of the differentiation between the firms. First we showed that the differentiation was required for the existence of the Nash equilibrium and that the characteristic of the equilibrium depended on the demand structure—consumers’ relative

Acknowledgement

The author acknowledges constructive comments by two anonymous referees on an earlier draft.

References (19)

  • N. Economides

    The incentive for non-price discrimination by an input monopolist

    International Journal of Industrial Organization

    (1998)
  • N. Economides

    Quality choice and vertical integration

    International Journal of Industrial Organization

    (1999)
  • N. Matsubayashi et al.

    Merger effect of two firms under network equilibrium

    European Journal of Operational Research

    (2002)
  • R.D. Banker et al.

    Quality and competition

    Management Science

    (1998)
  • P.S. Desai

    Quality segmentation in spatial markets: When does cannibalization affect product line design?

    Marketing Science

    (2001)
  • R. Dewan et al.

    Organizing distribution channels for information goods on the Internet

    Management Science

    (2000)
  • A. Dixit

    A model of duopoly suggesting a theory of entry barriers

    Bell Journal of Economics

    (1979)
  • H. Hotelling

    Stability in competition

    Economic Journal

    (1929)
  • K. Kim et al.

    Product design with multiple quality-type attributes

    Management Science

    (2002)
There are more references available in the full text version of this article.

Cited by (92)

View all citing articles on Scopus
View full text