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Article Excerpt
We examine the interplay of imperfect competition and incomplete information in the context of price competition among firms producing horizontally and vertically differentiated substitute products. Incomplete information about vertical quality (consumer satisfaction) signalled via price softens price competition. Low-quality firms always prefer the incomplete information game to the full-information analog. Moreover, for "high-value" markets with a sufficiently high proportion of high-quality firms, these firms also prefer incomplete information to full information. We find that an increase in the loss to consumers associated with the low-quality product may perversely benefit low-quality firms; we consider applications to tort reform and professional licensing.
1. Introduction
In this article, we examine the interplay of imperfect competition and incomplete information in the context of a multifirm industry producing horizontally differentiated substitute products with an associated vertical quality measure, such as consumer satisfaction with a firm's product. We find that incomplete information about quality that is signalled via price softens price competition by firms. Further, we show that low-quality firms always prefer playing the incomplete information game to the full-information analog: their prices are higher and so are their profits. Moreover, for "high-value" markets (suitably defined), if the proportion of high-quality firms is high enough, high-quality firms also prefer incomplete information to full information. This is in contrast to the results for a monopolist, who would prefer full information so as to avoid the price distortion associated with signalling.
Other unexpected results of the interplay between imperfect competition and incomplete information also emerge; these results reflect both a firm's best-response behavior vis-a-vis its rivals and its incentive compatibility conditions vis-a-vis its own alter ego. For high-value markets, equilibrium prices, quantities, and profits for both types of firms are increasing in the proportion of high-quality firms; this parameter does not affect equilibrium play in the monopoly signalling model or in the full-information model. In equilibrium, low-quality firms produce greater output than do high-quality firms, a reversal of the result that obtains under full-information imperfect competition. Finally, an increase in the loss borne by consumers due to the low-quality product can (for portions of the parameter space) perversely increase the low-quality firm's price, quantity, and profits; this effect also does not arise in the monopoly signalling model or in the full-information model. This last result suggests that recent proposals for tort reform may actually increase the likelihood of harm and lawsuits and that licensing of professional services can result in increased competitiveness and lower prices.
Plan of the paper. In Section 2, we provide a brief review of the literature. Section 3 provides the model and results. Section 4 discusses some implications and applications of the model. Section 5 provides a brief summary and conclusions. Supplementary material, including complex formulas and selected proofs, is contained in the Appendix. (1)
2. Related literature
There are several strands of literature that are related to this work. One body of related work involves a monopolist using price to signal product quality. Bagwell and Riordan (1991) examine a two-type model in which a high-quality product is more costly to produce than is a low-quality product (we adopt this formulation below, but with multiple firms). In equilibrium, the low-quality firm chooses its full-information price, whereas the high-quality firm distorts its price upward relative to the full-information price for high quality. (2) Daughety and Reinganum (1995) provide a model with a continuum of types in which quality is viewed as product safety. When a product fails and harms a consumer, the liability system determines how the associated losses are allocated across the parties. In equilibrium, higher prices signal safer products when the consumer bears a sufficiently high share of the loss, whereas lower prices signal safer products when the firm bears a sufficiently high share of the loss. Daughety and Reinganum (2005) consider a model in which quality is a safety attribute and the firm may engage in confidential settlement of lawsuits. Following first-period production, the monopolist learns its product's safety through harmed consumers who seek compensation. The firm settles lawsuits confidentially, which (potentially) reduces the viability of suits and prevents future consumers from observing directly the product's safety. Although confidentiality lowers the firm's expected liability costs, it also depresses demand for its product. Daughety and Reinganum (2005) characterize when this tradeoff induces the firm to prefer confidentiality versus a regime of openness (in which suits cannot be settled confidentially, and thus future consumers observe directly the product's safety).
There is a strand of the literature which considers price and advertising as joint signals of product quality. For example, Milgrom and Roberts (1986) provide a two-type monopoly model in which the cost of high quality may be higher or lower than that of low quality, and repeat sales are an important attribute of the model. They identify various conditions under which high quality may be signalled with a high price alone, a low price alone, or a combination of price and advertising expenditure. (3) Hertzendorf and Overgaard (2001b) and Fluet and Garella (2002) examine very similar duopoly models in which firms use price and advertising expenditure to signal their qualities. Whereas consumers do not know either firm's quality, both firms know both firms' qualities. (4) Moreover, consumers do not have a preference between the two goods, provided they are of the same quality and charge the same price (i.e., there is no horizontal differentiation). In equilibrium, price alone can signal quality when vertical differentiation is substantial, but otherwise advertising is required as well. When advertising is not used, quality is signalled with upward-distorted prices, but when advertising is used, prices may be driven below their full-information levels.
Daughety and Reinganum (2007) provide a duopoly model in which each firm uses its price to signal its product quality; this model differs from those above in three important respects. First, only price can be used to signal quality. Second, the products on offer are differentiated, both horizontally and, possibly, vertically. Third, each firm's quality is its private information. This information structure arises naturally in the context of quality as safety under a regime that permits confidential settlement of lawsuits (as described above). By settling confidentially with consumers harmed in the current period, the firm prevents future consumers and its rival from learning its quality. In the next period, each firm has private information about its own quality, which sets up the signalling game in which a firm's price may reveal its product quality. That paper employs a post-sale subgame involving tort liability, and therefore makes other simplifying assumptions to enhance tractability; in particular, a fixed number of consumers distributed along a line is assumed, with each consumer demanding a single unit. Moreover, it is assumed that the market is always fully covered; that is, every consumer buys a unit of the good. As a consequence, the market size is fixed exogenously.
A special case of the model described above is one wherein consumers bear the full loss associated with low quality; this can be interpreted as a "consumer satisfaction" model as introduced in Milgrom and Roberts (1986). In a consumer satisfaction model, the consumer simply receives lower utility from low-quality products than from high-quality products but, because utility is unverifiable, no compensation can be promised (e.g., a warranty cannot be used to insure the consumer against a loss of utility from low quality). (5)
The current article also considers a consumer satisfaction model in which each firm has private information about its product quality, but employs a more general demand and market structure. A representative consumer has a linked system of demand functions for n differentiated products (each produced by a single firm), and each firm will noncooperatively choose its price given its private information. Thus, the size of each firm's market, as well as the size of the total market for all n differentiated products, is determined endogenously. This means that we are able to examine the effect of changes in the number of firms, in the degree of substitutability of the products, and in the consumer's willingness to pay on equilibrium behavior.
Other (more tangentially related) literatures include those involving quality-guaranteeing prices and those involving disclosure of quality. In the quality-guaranteeing price literature (dating back to the early 1980s; see, e.g., Klein and Leffler, 1981), firms choose their qualities, as well as their prices, whereas consumers observe only the prices. Equilibrium is characterized by a price premium that is sufficient to induce firms subsequently to provide high quality. Thus, unobservable quality relaxes price competition. A recent example is Bester (1998), who relates the magnitude of this effect to the degree of endogenous horizontal product differentiation. Levin, Peck, and Ye (forthcoming) provide a model in which two firms have private information about the quality of their respective products, but can engage in costly disclosure. Consumers are located along a line between the two products, reflecting horizontal product differentiation. The cost of production is independent of quality and thus no signalling is possible. In equilibrium, firms engage in socially excessive disclosure. The current article differs from the quality-guaranteeing price literature because Nature chooses firm quality in our model, and differs from the disclosure literature because firms cannot credibly disclose quality and must instead resort to signalling.
Finally, there is also a small literature on noncooperative signalling when each firm has private information about its cost of production. The most closely related paper is Mailath (1989), which provides an n-firm oligopoly model with linear demand and constant marginal costs in which firms produce horizontally differentiated products and engage in noncooperative price competition across two periods. (6) A firm's first-period price can signal its (privately observed) marginal cost of production, which influences its rivals' pricing behavior in the second period. (7) Consumers have no inference problem, because they care only about prices, not marginal costs. Mailath finds that firms' prices are upward distorted (in order to persuade rivals to price higher in the second period) relative to the "non-signalling benchmark," which retains incomplete information in the first period but assumes that the firms' types are exogenously revealed prior to the second period (so the signalling motive is removed).
Although we also use a horizontally differentiated products model with linear demand and constant marginal costs, our model differs from that of Mailath in other ways. First, we consider a one-shot (three-period) model wherein each firm signals its quality to consumers, rather than to its rivals. Second, a firm's product quality (type) affects both its constant marginal cost of production and the demand curve it faces, because product quality also reflects vertical differentiation. Finally, in our model, the nonsignalling benchmark is the full-information outcome in which both rivals and consumers observe product quality directly. Like Mailath, we find that equilibrium prices are upward distorted relative to our (full-information) benchmark prices.
3. Model setup and results
Our model employs a representative consumer, who consumes some of each product, and n firms, each of whom produces one of the products, under conditions of constant marginal costs. The products are horizontally and vertically differentiated, where the quality of the product (the vertical attribute) takes on two possible levels (high and low). In period one, Nature independently draws a type for each firm from a common distribution and each firm observes its type. In period two, firms simultaneously choose prices. Finally, in period three, the representative consumer observes all prices and buys quantities of the products accordingly. In the incomplete-information model, firms do not observe the types of other firms, and consumers do not observe directly the type of any firm. In the full-information model, firms and consumers observe all the types in period two before firms choose prices. In all settings, we restrict the analysis to interior equilibria.
Consumer model. To keep things as simple as possible, we consider a single consumer (8) who consumes a variety of goods; products 1, 2, ..., n are differentiated substitute goods and good n + 1 is a numeraire good. Each product is made by a different firm, and we assume there are n [greater than or equal to] 2 products. Products 1, 2, ..., n may be of either high or low quality (signified by H or L, respectively). Let [[theta].sub.i] be an indicator function which takes on the value 1 when product i is of high quality and the value when product i is of low quality. We assume that the consumer derives utility from the product, less a loss per unit consumed, which is zero for the high-quality good and [delta] > for the low-quality good. (9) The occurrence of this loss is unverifiable (e.g., an uncomfortable mattress, a lazy real estate agent, or a mediocre meal) and therefore cannot be covered by a warranty. Nature determines product quality independently for each firm, and Pr{H} is given by [lambda] [member of] (0, 1). (10) The consumer receives higher utility from a high-quality product i than a low-quality product i, but both versions of product i are worthwhile. In particular, we assume the consumer's utility function is quadratic in the n differentiated products, with the parameters [alpha] >...
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