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(1) Proofs of Propositions 1, 3, and 4 are provided. Proofs of Propositions 2, 5, and 6 are straightforward but tedious, and are omitted (example calculations are provided for Proposition 6).

(2) Bagwell (1992) conducts a related analysis of a monopolist producing a product "line."

(3) Hertzendorf (1993) argues that, if advertising is stochastically observed, price and advertising expenditure will never be used in combination. Linnemer (1998) considers a firm which uses price and advertising to signal to two different audiences: it signals its product quality to consumers and its marginal cost to a potential entrant.

(4) See also Hertzendorf and Overgaard (2001a); Harrington (1987), Bagwell and Ramey (1991), and Orzach and Tauman (1996) consider limit pricing models in which two or more incumbent firms with common private information about production costs attempt to deter entry using price as a signal of cost.

(5) If the consumer's loss were verifiable, then a firm could offer a warranty specifying the consumer's extent of recovery in the event of this loss. Because the warranty contract is endogenous, warranties could serve as another route via which quality could be signalled (see Lutz, 1989, for such a model).

(6) Gal-Or (1988) also considers a two-period model in which firms learn about their costs, and those of their rivals, over time; her paper specifically omits consideration of the signalling problem. Mailath (1988) establishes conditions guaranteeing the existence of separating equilibria in abstract two-period games with simultaneous signalling.

(7) Martin (1995) considers two incumbent firms who signal privately known marginal costs to each other and a potential entrant; countervailing incentives can result in pooling. Das Varma (2003) models market competition preceded by an auction of a cost-reducing innovation. When firms compete in price strategies, they bid less aggressively.

(8) Given constant returns to scale, the same results apply for multiple identical consumers.

(9) One could allow [[theta].sub.i] to be between zero and one; then [[theta].sub.H] is the probability that a product i of high quality does not create a loss of [delta], and [[theta].sub.L] (< [[theta].sub.H]) is the probability that a product of low quality does not create a loss of [delta].

(10) For certain results we will consider limits where [lambda] goes to zero or one.

(11) Note that if [gamma] = 0, then each product is independent of each other product, and each firm has a monopoly in its product market.

(12) We generalize this cost structure to allow positive costs for the low-quality product later in the article in discussing one of our applications.

(13) In fact, we show that the separating equilibrium we discuss is the only symmetric separating equilibrium to survive refinement under the intuitive criterion. Moreover, this same refinement eliminates all (pure) pooling equilibria.

(14) Signalling causes this effect. Alternatively, if firms choose prices under uncertainty about rival quality but consumers can observe all firms' quality levels, in the resulting Bayesian-Nash equilibrium a high-quality firm will sell more output than a low-quality firm. We thank a referee for this observation.

(15) Some exceptions in the literature considering signalling by one firm do exist; see Matthews and Mirman (1983) and Daughety and Reinganum (1995, 2005); see also Daughety and Reinganum (2007) for a duopoly example with a simpler demand structure which yields results similar to Propositions 2 and 3 below.

(16) Note that [[alpha].sub.2] is a function of the parameters. This will be similarly true for other results below, which require a restriction that [alpha] be sufficiently large. We use [alpha] as the critical variable here because it can be increased without threatening to violate Assumptions 1 and 2.

(17) Of course, only parameter combinations that also satisfied Assumptions 1 and 2 were considered.

(18) In particular, for a monopoly ([gamma] = 0), [P.sub.L], [Q.sub.L], and [[PI].sub.L] are all declining in [delta].

(19) This can be done by simply raising [alpha], if necessary, because a can be raised without risk of violating Assumptions 1 and 2.

(20) The most recent bill at the federal level was HR 2657, "Comprehensive Medical Malpractice Reform Act of 2005" (introduced May 26, 2005). The first section of the bill, Section 101, provided for limits on recovery of noneconomic damages in medical malpractice suits.

(21) We assume strict liability, so a firm compensates a victim for "compensable" harms without reference to due-care standards. Although medical malpractice is technically under a regime of negligence, in what follows, a low-quality producer is negligent by assumption, whereas a high-quality producer is never negligent.

(22) Alternatively, professional licensing converts some, but not all, L-type firms into H-type firms, thereby raising the proportion [lambda] of high-quality firms in the market. From Proposition 2, this results in higher prices and profits (in high-value markets) for both types of firm. We thank a referee for suggesting this interpretation.

(23) Ronnen (1991) provides a full-information model with endogenous quality wherein minimum quality standards lower both firms' prices. Crampes and Hollander (1995) find that, under convex costs, a minimum quality standard benefits the low-quality firm and hurts the high-quality firm, which is consistent with the implications of our full-information model.

Andrew F. Daughety *

Jennifer F. Reinganum *