False Advertising and Consumer Protection Policy

Transcription

1 False Advertising and Consumer Protection Policy Andrew Rhodes and Chris M. Wilson March 12, 2015 Abstract There is widespread evidence that some rms use false advertising to overstate the value of their products. In a standard setting with rational consumers and a general form of demand, we present a model in which a regulator is able to verify and punish false claims. There is a natural equilibrium in which rms over-claim probabilistically, and in which tougher regulation leads to more informative advertising. To assess a range of policy issues, we then establish a set of demand and parameter conditions to characterise the optimal level of regulatory punishment under dierent welfare objectives. Keywords: Misleading Advertising; Deceptive Advertising; Persuasion; Cost-Pass Through JEL codes: D83; L15; L51; M37 Rhodes: Toulouse School of Economics, France; andrew.rhodes@tse-fr.eu. Wilson: School of Business and Economics, Loughborough University, UK; c.m.wilson@lboro.ac.uk. We would like to thank Mark Armstrong, Daniel Garcia, Justin Johnson,Tianle Zhang, and the participants at various presentations including the 7th Workshop on Economics of Advertising and Marketing (Vienna) and the NIE workshop on Advertising (Manchester). We also thank Kamya Buch for her research assistance. 1

2 1 Introduction Many adverts make explicit claims about product quality attributes such as eectiveness, durability, origin, and so forth. Consumers often rely on these claims when deciding whether or not to buy a product. Therefore, in many countries consumer protection authorities punish rms whose claims are judged to be untrue. However, despite this, there is abundant evidence that some rms still engage in false advertising. For example, Dannon recently paid $21 million to 39 US states after being challenged by the FTC for exaggerating the health benets of its Activia yogurts and DanActive drinks. 1 Many other well-known rms have also been successfully prosecuted for making misleading claims, including Reebok, Skechers, L'Oreal, Kellogg's and Lexus. 2 Academic work has further documented false advertising in various industries, including over-the-counter weight loss products and winter sports markets (Cawley et al 2013, Zinman and Zitewitz 2013). Surprisingly, the theoretical literature has traditionally had little to say about such false advertising. However, once we account for the possibility that advertising claims could be false, many new and important questions arise. For example, under what circumstances is false advertising (most) harmful to consumers? Can government regulation against false advertising have any `perverse' or unintended consequences? Why are consumer protection authorities not tougher on false advertising in practice? Which markets should these authorities target when monitoring advertising claims? Can an industry-led self-regulation approach ever be socially optimal? To answer these and other questions, we aim to better understand the fundamental equilibrium eects of advertising policy on the level of false advertising, product pricing and market welfare. While these issues may rst appear unwieldy, we show how false advertising can be analysed with familiar tools with rational consumers and a general form of consumer demand. In particular, we consider the pricing and advertising behavior of a monopolist, who is privately informed about whether its product is of `low' or `high' quality. The rm chooses a price and makes a claim about the quality of its product. Consumers then observe the claim, update their beliefs about quality, and choose whether or not to purchase the product. Finally, a consumer protection authority may check the claim, and punish the rm if it exagerated its product quality. We think this set-up closely approximates many important product markets. Individual consumers are often unable to verify claims, or can only do so after using a product for a long time, as in the case of health products. However government agencies play an important role in uncovering and punishing false claims. In many jurisdictions, including the US and the EU, authorities either actively monitor adverts 1 See Accessed on 05/28/ See and as well as and for a range of other cases. All websites accessed on 05/28/

3 or else check them following consumer complaints, and then implement punishments, often in the form of a monetary nes or adminsitration costs. 3 The paper rst characterizes a natural equilibrium where the high type advertises truthfully, but where the low type may engage in false advertising. In particular, when the punishment is suciently high, there is no false advertising in equilibrium, and so consumers can infer product quality and each type then responds with its optimal associated price. However, for lower levels of punishment, the low type engages in false advertising with positive probability by mixing between pooling with the high type by using a false advert with a relatively high price, and advertising truthfully with a relatively low price. Given the low type's strategy, consumers rationally believe that any claim of high quality is correct with a non-zero probability. Therefore, a low type's use of false advertising can stimulate demand in equilibrium, as consistent with some empirical evidence (e.g. Cawley et al 2013). However, such false advertising never systematically deceives consumers or raises the low type's prots because consumers' beliefs must be correct on average, and because any increase in prots are oset by the expected CPA punishment. In the extreme, when the level of punishment becomes suciently small, the low type always nds it optimal to conduct false advertising as consistent with a fully pooling equilibrium. Hence, our equilibrium provides an attractive, smooth unication of some familiar ideas: when punishments are weak, advertising is cheap talk; when punishments are strong, advertising is equivalent to fully veriable quality disclosure; and when punishments are moderate, our equilibrium provides a novel case where adverts are partially veriable and where the low type engages in false advertising with an interior probability. The paper continues by exploring how changes in the level of punishment aect a variety of welfare measures. We rst consider consumer surplus. Here, an increase in the level of false advertising via a reduction in the level of punishment creates two eects. First, the increase in lying generates a `persuasion' eect which lowers consumer surplus by prompting consumers to overestimate a low type's product quality and then buy at too high or price and/or to buy too many units. In its expression, this eect is akin to a formalization of Dixit and Norman's (1978) classic analysis of persuasive advertising. However, here our eect derives from a change in consumers' beliefs, rather than a change in consumers' preferences. Second, the increase in lying also generates a `price' eect that raises consumer surplus. Here, the 3 In the US, most federal-level regulation is conducted by the FTC, who actively monitor markets and punish any guilty rms with measures including orders to conduct corrective advertising, and monetary penalties in the form of civil nes and/or consumer compensation. In Europe, most countries employ varying levels of industry self-regulation alongside statutory authorities, as coordinated by the European Advertising Standards Alliance. For instance, in the UK, most regulation is conducted by the industry-led Advertising Standards Authority (ASA) which is endorsed by various governmental bodies. The ASA often uses consumer complaints to guide its investigations, but it also conducts direct monitoring of markets. On nding an oense and a subsequent referral to the govermental authorities, rms can be ned, and employees can even face imprisonment. 3

4 increase in false advertising leads consumers to correctly lower their expectations of quality after observing a high claim, which then prompts any type with a high claim to lower its price. By then utilising some recent results on cost-pass-through (see Weyl and Fabinger 2013) we provide some demand and parameter conditions to characterise the optimal level of punishment. In many cases, the persuasion eect dominates such that consumer surplus is maximised by raising punishments to eliminate all false advertising. This is consistent with the instinctive view that false advertising should always be banned. However, we also formalise a range of other market conditions, such as the case where the high quality product is suciently desirable, where the price eect can dominate. In these cases, we oer the striking result that the regulator should implement some moderate or even zero level of punishment in a way that permits the existence of false advertising, and generates a level of consumer surplus that exceeds that under full information (where there is no false advertising). Next, we turn to the eect on prots. The low type always prefers weaker punishments, and the high type always prefers stronger punishments. However, we demonstrate that the latter's preference always (weakly) dominates, such that, ex ante, the monopolist itself always prefers (weakly) higher punishments with (weakly) lower levels of false advertising. Hence, relative to consumers, the monopolist always prefers a weakly stronger level of punishment. Moreover, if the monopolist could commit to some of punishment, as may be consistent with some forms of industry self-regulation that are popular in Europe, the monopolist would commit to a level of punishment that could be too strong for consumers. Finally we consider the eect of policy on total welfare. We show that depending on parameters, the regulator should implement a level of punishment that coincides exactly with the level preferred by either consumers or the monopolist. This provides a novel explanation for why false advertising can increase total welfare. Related Literature: Traditionally, economics has had little to say about consumer protection policy. However, some recent work has begun to analyse such policies in a variety of contexts. 4 Here, we focus on false advertising. Aside from some early works, such as Nelson (1974), Kotowitz and Mathewson (1979), and Beales et al (1981), the advertising literature has largely ignored false advertising (see the reviews by Bagwell 2007 and Renault 2014). However, false advertising has been considered in a few other recent papers. These papers dier from ours in their focus and approach. All papers in this area must face one fundamental issue regarding how false advertising can be credible. Some papers bypass this issue by assuming that consumers naively believe all claims (e.g. Glaeser and Ujhelyi 2010, Hattori and Higashida 2012). They suggest that the socially optimal level of false advertising 4 Some examples include the eects of high-pressure sales tactics (Armstrong and Zhou 2013), the misuse of commissions for advice-giving intermediaries (Inderst and Ottaviani 2009) and the regulation of cancellation and refund rights (Inderst and Ottaviani 2013). 4

5 can be positive because the associated increase in consumption can oset the distortion from imperfect competition. Other papers resolve the credibility issue by maintaining consumer rationality but introducing the eects of legal penalties in ways more related to our paper. Closest is Piccolo et al (2014) who examine a duopoly model with homogeneous consumers where one rm has a good product and the other has a bad product. Unlike us, they focus only on fully pooling and separating equilibria. They nd that a zero punishment can maximise consumer surplus. They further state that such a result cannot emerge in a monopoly (p.19) because instead, the authority would always prefer to eradicate false advertising. By using our richer monopoly framework with heterogeneous consumers and the use of semiseparating equilibria, we provide a very dierent conclusion for a range of welfare measures. In other closely related work, Corts (2013, 2014a, 2014b) studies fully pooling and separating equilibria in a monpoly setting. He takes a dierent focus by assuming that the rm must choose whether or not to become informed of its own product quality. The ndings suggest that nite penalties may be optimal because they induce the rm to make socially-valuable unsubstantiated claims. 5 As a last note, our model also relates to a number of papers in the communication literature that study equilibrium lying and persuasion under full rationality (e.g. Kartik 2009, Kamenica and Gentzkow 2011). Of most relevance is Kartik (2009) which oers a general treatment of lying costs in a standard cheap-talk setting. Our paper allows for policy-related lying costs within a specic advertising context with optimal pricing. The paper now proceeds as follows. In Section 2, we outline the model before Section 3 provides some preliminary results for the case of known quality. Section 4 analyzes the full game equilibria and performs a range of comparative statics for the optimal level of punishment in regard to a variety of welfare objectives. Section 5 concludes. All omitted proofs are available in Appendix A. 2 Model A monopolist sells one product to a unit mass of consumers. The monopolist is privately informed about its product quality q. Specically, the product is of low quality L with probability x (0, 1), and of high quality H with probability 1 x. Average ex ante quality can then be dened as q = xl+(1 x)h. For our main analysis we assume that marginal cost is independent of product quality, and normalized to zero. Each consumer has unit demand and is willing to pay q + ε for a product of quality q, where ε is a consumer's privately 5 In some broader work, Barigozzi et al (2009) study false comparative advertising rather than false quality advertising. Finally, one other strand of literature shows how false advertising can be credible when consumers' preferences are heterogeneous over quality (e.g. Chakraboty and Harburgh 2010 and Gardete 2013). However, this literature does not examine the eects of policy. 5

6 known match with the product. This match is drawn independently across consumers using a distribution function G(ε) with support [a, b]. The associated density g(ε) is strictly positive, continuously dierentiable, and has an increasing hazard rate. The monopolist sends a publicly observable advertisement or `report' r {L, H} at no cost. A report r = z is equivalent to a claim My product is of quality z. Note that this binary report space is without loss because there are only two rm types and reports are costless. False advertising is dened as the use of a high quality report r = H when the monopolist has a low quality product, q = L. A regulator is able to verify any advertising claim, and impose a penalty φ on the rm if the advertising is false. The penalty can either be considered as a deadweight loss (such as the administrative costs of removing the advertising) or as a ne that goes straight to the regulator. However, any nes are not used to directly compensate consumers. 6 For our main analysis, we assume that the regulator can costlessly choose any level of punishment, φ 0, in order to maximize its objective function. 7 During the paper we consider three dierent regulatory objectives: the maximization of consumer surplus, total welfare, and prot. The timing of the game is as follows. At stage 1 the regulator publicly commits to a penalty φ for false advertising. At stage 2 the monopolist privately learns its product quality. It then announces a price p and makes an advertising claim r {L, H}. At stage 3 consumers decide whether or not to buy the product, taking into account both the penalty φ and the rm's choice of price and claim. Finally at stage 4 the regulator veries the advertising claim, and nes the rm φ if it made a false claim. The solution concept is Perfect Bayesian Equilibrium (PBE). 3 Benchmark with known quality As a preliminary step towards solving the model, we rst consider a benchmark case in which the rm is known to have quality q. Quality claims are then redundant as truthtelling will be weakly optimal, with r(q) = q. The rm's only task is then to choose a price p. An individual consumer buys the product if and only if ε p q, such that demand equals D(p q) = 1 G(p q). Therefore the rm chooses its price to maximize p [1 G (p q)]. It is then immediate that: 6 Allowing nes to be directed back to consumers is equivalent to the approach taken within the product liability literature. This generates a range of dierent issues, which are not the focus of our paper. See Daughety and Reinganum (2013) for more. 7 One practical application of φ is in terms of an expected punishment where there is some exogenous level of punishment F, but where the regulator varies the probability m of monitoring adverts, such that φ = mf. 6

7 Lemma 1. Suppose the rm is known to have quality q. The rm's optimal price, p (q), is increasing in q and satises: where q = b and q = a + 1/g(a). 0 if q q ( ) p 1 G(p (q) = (q) q) if q q g(p (q) q), q a + q if q q (1) The interpretation of Lemma 1 is straightforward. When q q quality is so low that the rm would make zero sales even if it priced at marginal cost. The market is therefore inactive, and we normalize the rm's price to zero without loss of generality. When instead q (q, q) the rm optimally sells to some but not all consumers, such that p (q) satises the usual monopoly rst order condition. After dierentiating this rst order condition, one nds dp (q) dq = 1 σ 2 σ where dp (q)/ q is the level of quality-pass-through, and where σ(d) = D D /[ D ] is the curvature of the inverse demand function (see Aguirre et al 2010, and Weyl and Fabinger 2013). It then follows that dp (q)/dq [0, 1) because logconcavity of demand implies σ 1. Intuitively, an increase in quality q produces a parallel rightward shift in the inverse demand curve. The rm optimally responds to this both by charging a higher price, and by selling to strictly more consumers. Finally if q q quality is so high that the rm prefers to sell to the entire market. Price then equals the willingness-to-pay of the marginal consumer a + q, and hence increases one-for-one with quality. 8 (2) Henceforth to avoid some uninteresting cases, we assume that q + b > 0 such that a product of average quality makes strictly positive prot. The prot earned by a rm of known quality q can then be written as π (q) = p (q) [1 G (p (q) q)] (3) It is straightforward to show that π (q) is increasing and convex in q, given our assumption that 1 G(.) is logconcave. Finally consumer surplus can be expressed as v (q) = ˆ b+q p (q) [1 G (z q)] dz (4) When q q no consumer buys the product and so v (q) = 0. When q q all consumers buy and p ( q) = a + q, such that v (q) = v ( q) = b [1 G (z)] dz which is independent of a 8 The threshold q is nite if and only if consumers' idiosyncratic matches are bounded from below, a <. 7

8 quality. However when q (q, q) the market is partially covered, and it is easily veried that v (q) is both positive and strictly increasing in q. Further, by making use of equation (2), one can also note that consumer surplus is convex in quality if and only if dσ(d) dd σ(d) > 2 D (5) Thus if condition (5) holds, consumer surplus behaves as in Figure 1. Condition (5) is equivalent to an assumption used within a recent literature on third-degree price discrimination which requires that price is `not too convex' in quality 9. The condition is satised by many common demand functions, including all those with constant or decreasing passthrough. Bulow and Peiderer (1983) characterize a rich class of constant passthrough demand functions, which include linear, exponential, and constant elasticity. Fabinger and Weyl (2012) show that the AIDS demand function has decreasing passthrough. Finally, certain parameterizations of increasing passthrough demand functions can also satisfy the condition, including the normal and quadratic. The condition (5) is also preserved under arbitrary truncations of the match distribution, G(.). Figure 1: Equilibrium Consumer Surplus, v (q) b a v (q) [1 G (z)] dz q q q 4 Privately-known quality Henceforth we assume that the rm is privately informed about its quality. A high quality rm may then try to signal its type. As is typical in signaling games, there exists a large 9 Specically, Cowan (2012) and Chen and Schwartz (2013) use an equivalent condition which ensures that consumer surplus is convex in a rm's marginal cost. Weyl and Fabinger (2013) formally establish the relationship between cost- and quality-passthrough. 8

9 number of Perfect Bayesian Equilibria (PBE), because consumers can attribute any oequilibrium claim (or price) to the low-quality type. We approach the equilibrium selection issue in the following way. Firstly, we restrict attention to equilibria in which a high-type always makes a truthful claim r(h) = H. This allows us to focus on the incentives of a low-type to engage in false advertising. Secondly, we restrict consumer beliefs to depend only on the rm's claim, and thus to be independent of the rm's price. The rationale for doing this is as follows. Notice that conditional on making a high claim and charging a price p, the payos of the low- and high-type dier only by the expected punishment φ because the types have the same marginal cost. In other words, the preferences of the two types are perfectly aligned with respect to the price they charge. It therefore seems unnatural that consumers should infer anything from the rm's price. To explore this further, let qh e E (q r = H) denote consumers' belief about quality following a high claim. Given our second restriction, the rm optimally charges p (qh e ) when it makes a high claim (irrespective of its actual type). Interestingly this is also the unique price selected by Mailath et al's (1993) Undefeated Equilibrium renement. 10 Specically, notice that conditional on its claim, a rm's pricing decision can be viewed as a special type of signaling `game', where forward induction renements like D1 and the Intuitive Criterion have no bite because the two seller types have identical preferences over price. However, the `game' does have a unique (pure strategy) Undefeated PBE, in which both types pool on the price p (qh e ). After applying our equilibrium restrictions, we derive the following result. Proposition 2. Suppose a high type always sends a truthful claim, and that consumer beliefs depend only the rm's claim. There is a unique PBE equilibrium (up to o-path beliefs 11 ), in which: i) A high-type rm claims r = H and charges p (q e H ) ii) A low-type rm randomizes. With probability y it claims r = H and charges p (q e H ). With probability 1 y it claims r = L and charges p (L). iii) The probability that the low type uses false advertising, y, is determined as follows: - When φ φ 1 π ( q) π (L), y = 1 - When φ φ 0 π (H) π (L), y = 0 - When φ (φ 1, φ 0 ), y (0, 1) and uniquely solves π (q e H) φ = π (L) (6) 10 See Mezzetti and Tsoulouhas (2000) for a formal denition, and also for a development of the renement. 11 Note that when φ < φ 1 the claim r = L is o-path, and a range of beliefs Pr (q = L r = L) lead to the same equilibrium play. 9

10 iv). Consumer beliefs about the rm's type are Pr (q = H r = L) = 0 and Pr (q = H r = H) = Expected quality when the rm makes a high claim is q e H (y ) = 1 x 1 x + xy xy 1 x + xy L + 1 x 1 x + xy H (7) This is also the unique Undefeated Equilibrium outcome of the game. Proposition 2 characterizes a natural semi-pooling equilibrium, in which false advertising arises probabilistically. A low quality rm has the following tradeo when choosing its advertising claim. Firstly if the rm reports truthfully with r = L, consumers correctly infer that its product is of low quality. Consumers then demand 1 G (p L) units from the rm, such that it optimally charges a low price p (L) and earns a low prot π (L). Secondly, if a low quality rm engages in false advertising and claims r = H, it attracts an expected punishment φ, but also prompts the rational consumers to Bayesian update and raise their expectations of the quality of the product to q e H (y ) = xy 1 x + xy L + 1 x 1 x + xy H > L (8) where y is the (equilibrium) probability that a low type makes a false claim, and where we henceforth simplify notation by writing qh e (y ) as qh e. Therefore by making a false claim, a low quality rm persuades consumers to overestimate its product quality and therefore use a higher demand curve 1 G (p qh e ), such that the rm can charge a higher price p (qh e ), and earn a higher prot π (qh e ). However, such false advertising never systematically deceives consumers because their beliefs are correct on average due to the additional possibility that the high report comes from a high type. The precise equilibrium characterization depends upon how strong the level of regulation is, as measured by the size of φ. If φ π ( q) π (L) policy is `weak'. The low type always uses false advertising (i.e. y = 1), because the regulatory punishment from doing so is very small. The equilibrium has full pooling, with both types claiming r = H and charging a price p ( q). Advertising is completely uninformative, and therefore when faced with a high claim, consumers just maintain their prior, q e H = q. On the contrary if φ π (H) π (L) policy is `strong'. The low type never uses false advertising (i.e. y = 0), because if it did, the regulator would punish it very severely. Therefore policy enables the two types to perfectly separate: the low type claims r = L 10

11 and charges p (L), whilst the high type claims r = H and charges p (H). Advertising is perfectly informative, and consumers fully believe any high claim i.e. q e H = H. Finally and perhaps most interestingly, if φ (φ 1, φ 0 ) policy is `moderate'. In equilibrium the low type makes a false claim with probability y (0, 1), as dened by (6). This ensures that the low type is indierent between lying and telling the truth, and is therefore willing to randomize between the two. The equilibrium now has partial separation: sometimes the low type separates by claiming r = L and charging p (L), but other times it pools with the hightype, by using false advertising to claim r = H and charge p (qh e ). Consequently advertising claims are only partially informative. Randomization by the low type is an essential feature of the equilibrium. For example there does not exist an equilibrium with full separation: given the associated consumer beliefs qh e = H, a low type would do better to deviate and use false advertising to get π (H) φ, rather than tell the truth and get π (L). Similar reasoning shows that there does not exist an equilibrium with full pooling. When policy is either `strong' or `weak' the low-type has a strict preference for truthtelling and lying respectively, such that small changes in φ have no eect on its behavior. However when policy is `moderate', changes in φ act to lower the level of false advertising: Lemma 3. A rm is less likely to engage in false advertising when the level of regulation is stronger; y is weakly decreasing in φ. When policy is `moderate' the low-type is indierent about whether or not to use false advertising. In this case an increase in the punishment φ implies that in order to maintain indierence, the gains from lying π (qh e ) π (L) must increase. In other words, consumers must be more condent of high quality when they observe a high claim. Since consumers are rational and use Bayesian updating, this can only happen if a high claim is indeed more believable with a lower level of equilibrium lying, y. Overall, as noted in the introduction, our equilibrium characterization provides an attractive, smooth unication of some broad areas of related literature. On the one hand when φ φ 1, any punishments are ineective, and advertising is close to being cheap talk. Low types always engage in false advertising and the model involves a full pooling equilibrium with no information transmission. On the other hand, when φ φ 0, punishments are strong and the low type has no incentive to engage in false advertising. As such, advertising becomes fully veriable, and the model reduces to a simple model of full disclosure with quality unraveling. However, the novelty of our equilibrium arises in the intermediate region, where adverts are partially veriable. Here, the low type engages in false advertising with an in- 11

12 terior probability, and consumers rationally allow advertisements to inuence their beliefs. 4.1 The Eects of Policy on Consumer Surplus We now move on to consider the eects of policy on a variety of welfare measures, starting with consumer surplus. In light of Proposition 2 we can write expected consumer surplus as E(v) = x(1 y )v (L) + (xy + 1 x)v (q e H) (9) In words, with probability x(1 y ) the rm sends a low report, consumers correctly infer quality to be low, face the associated price, p (L), and receive the associated surplus v (L). With complementary probability 1 x+xy the rm sends a high report, consumers correctly infer an updated expected quality of qh e, face the associated price, p (qh e ), and receive the associated surplus, v (qh e ). Hence, E(v) is simply a convex combination of v (L) and v (qh e ). Before providing a more intuitive explanation below, we rst note some immediate eects from a marginal increase in the probability of false advertising, y. As y increases, i) consumers are less likely to receive a low claim, via a reduction in x(1 y ), and ii) consumers correctly lower their resulting expectations of quality for any product with a high claim, q e H. Equivalently, a small increase in y induces a mean-preserving contraction in consumers' posterior belief about the rm's quality. Assume that condition (5) holds i.e. v (q) is convex for intermediate qualities. Figure 1 then suggests that there are three distinct cases of interest. Firstly when qh e < q, Jensen's inequality implies that consumers benet from having a more dispersed posterior, such that a small increase in y lowers E(v). Secondly though, when L < q q e H it is easy to see that E (v) is increasing in y as consumers are actually made better o by a small increase in lying. Thirdly when q L, E (v) = v ( q), such that regulation has no eect on consumer surplus. In light of these results, it is then straightforward to prove: Proposition 4. Suppose the policymaker seeks to maximize consumer surplus, and that condition (5) holds. a) When H q the policymaker uses a tough policy φ φ 0 to induce y = 0. b) When q < q < H the policymaker uses a moderate policy φ = π ( q) π (L) to induce y = (H q)(1 x) (0, (H q)(1 x)+ q q 1), such that qe H = q. c) When L < q q the policymaker uses a weak policy φ φ 1 to induce y = 1. d) When q L the policymaker is indierent over all φ. Proposition 4 provides a range of demand and parameter conditions where a consumeroriented policymaker may choose not to do completely eradicate false advertising by setting 12

13 a very high penalty. To understand its insights, observe that an increase in y produces two eects. On the one hand, consumers are more likely to receive a false ad and so be persuaded to buy a potentially low quality product at an inated price. On the other hand, the increase in lying reduces consumers' quality expectations for a product with a high claim and so induces any such product to have a lower price. In more detail, one can write E(v) = x [v (L) v (q y H L)] e (1 x + xy )D(p (qh) e qh) e p (qh e ) qh e (10) y q e H The rst term is a direct `persuasion' eect. Conditional on the rm having a low quality product with probability, x, a marginal increase in lying replaces the surplus that the consumer would have received if the rm had told the truth, v (L), with the surplus associated with false advertising, v (qh e L) = v (qh e ) (qe H L) D (p (qh e ) qe H ). To explain this latter surplus, note that after observing such a false ad with price, p (qh e ), the consumers expect a quality of qh e and so purchase D (p (qh e ) qe H ) units. However, as quality is actually low, they receive (qh e L) utils less than they anticipated on each unit purchased. This eect harms consumers by prompting them to pay too much and to potentially buy too many units of a low-quality product, as represented by the shaded area in Figure 2. The eect is equivalent to a formalization of the loss in consumer surplus caused by persuasive advertising, as identied in the seminal paper by Dixit and Norman (1978). However, as noted in the introduction, our false advertising `persuasion' eect arises from a change in consumers' beliefs rather than their preferences. The second term in (10) is a `price' eect. An increase in y lowers the probability that a high-claim is true, q e H / y < 0. Therefore, with the probability that the rm uses a high claim, (1 x + xy ), the rm is now forced to set a lower price, p (qh e ), which results in higher associated consumer surplus. Proposition 4 can then be understood in terms of these two eects. In most cases, the persuasion eect dominates such that the policymaker should eradicate false advertising. However, in other cases, the price eect can dominate. 12 For instance, consider the case where L < q. Here, from Section 3 we know that dp (q) /dq is larger when a market is covered. It then turns out that when q qh e such that the high-claim market is covered, the price eect dominates; while the direct eect dominates if q > qh e. Hence, a consumeroriented policymaker should reduce false advertising as much as possible, subject to the 12 In one nal case, when q L, the two eects exactly cancel. Intuitively all consumers buy irrespective of the claim. They pay either a + L following a low claim, or a + qh e following a high claim, but the average price paid is a + q, which is unaected by policy. 13

14 Figure 2: The Direct Loss in Consumer Surplus from an Increase in False Advertising P 1 G(p q e H ) p (q e H ) 1 G(p L) p (L) 1 G(p (L) L) 1 1 G(p (q e H ) qe H ) Q constraint that the high-claim market remains uncovered. 13 We now consider how the other parameter values aect optimal policy. First, given our discussion of the two eects above, one may suspect that the optimal level of lying is likely to be larger when demand exhibits a higher level of quality-pass-through, p q(q) = 1 σ, as this 2 σ would enhance the size of the price eect. However, this need not be true, because a higher level of quality-pass-through also acts to enhance the size of the persuasion eect. Indeed, by noting that v q(q) = D(p (q) q)[1 p q(q)], one can rewrite the two eects in (10) as E(v) y [ ˆ qh e ( ) ( )] = x 1 p z(z) D(z)dz (qh e L) D(p (qh) e qh) e 1 p qh e (qe H) L (11) Moreover, when demand exhibits a constant cost-pass-through coecient, with p q(q) = P for all relevant q, as in the case of linear, exponential or constant elasticity demand, then optimal policy can actually be independent of the magnitude of the cost-pass-through coecient. Second, consider how the values of the other market variables, x, H and L aect optimal policy. When L q, the authority is indierent. However: Corollary 5. Suppose L < q. A consumer-oriented policymaker is more tolerant of false 13 Finally, for completeness, consider the case of homogeneous consumers with a = b = 0. Then p (q) = q and q = q = 0 such that i) v (q) = 0 and ii) p q(q) = 1 for all q 0. Contrary to our results, it then follows that the persuasion eect always equals the price eect and so a consumer-surplus orientated policymaker is indierent over φ for all cases. However, the results under a prot or total welfare objective do not dier from our later ndings for heterogeneous consumers. 14

15 advertising when products are better (L and H are higher) and when the probability of a low-quality type, x, is smaller. Through its control of φ, the policymaker should allow the low-type to engage in a higher level of false advertising when product quality levels are higher, or when the probability of a low type is smaller. Intuitively, under these conditions, the high-claim market is closer to being covered and so the policymaker permits more false advertising in order to lower the associated price. 4.2 The Eects of Policy on Prots To start with, consider the eects of policy on the prots earned by each individual rm type. A high-type always tells the truth and consequently earns E (π H ) = π(qh e ). A low-type tells the truth with probability 1 y and earns π (L), but also lies with probability y, to earn a prot π (qh e ) with expected punishment φ. This gives an overall expected payo for a low-type of E (π L ) = y [π (qh e ) φ] + (1 y )π (L). One can then show the following. Lemma 6. A high-type seller's prot is increasing in φ and reaches its maximum at φ φ 0. A low-type seller's prot is decreasing in φ and reaches its maximum at φ = 0. This result is very intuitive. Stronger regulation that eradicates false advertising benets a high-type, because it causes consumers to update more optimistically upon seeing a high claim. However, stronger regulation hurts a low-type, because it (weakly) reduces the prot that can be earned by lying and mimicking a high-type. We now turn to the eects of policy on `ex ante' expected equilibrium prots, E (Π) = xe (π L ) + (1 x) E (π H ). After some simple manipulations, E (Π) can be shown to be piecewise linear: π ( q) xφ if φ < φ 1 E (Π) = π (L) + (1 x) φ if φ [φ 1, φ 0 ] (12) xπ (L) + (1 x)π (H) if φ > φ 0 Intuitively, when φ < φ 1 the low-type lies with probability one such that qh e = q. Both types then earn π ( q), but the low-type also incurs an expected penalty φ. When instead φ [φ 1, φ 0 ], the low-type is indierent between lying and telling the truth, such that by equation (6), π (qh e ) φ = π (L). This then allows us to write E (π L ) = π (L) and E (π H ) = π (L)+φ. Finally when φ > φ 0 the types fully separate, with the high-type earning π (H), the low-type earning π (L), and no punishments being incurred. It then follows that: 15

16 Proposition 7. Suppose the policymaker seeks to maximize ex ante expected prots. a) When L < q the policymaker uses a tough policy φ φ 0 to induce y = 0. b) When q L the policymaker is indierent between a tough policy with φ φ 0 to induce y = 0, and a very weak policy with φ = 0 to induce y = 1. This can be understood from equation (12) which implies that in order to maximize ex ante expected prots, the rm should never pay the penalty in equilibrium - a rm-oriented regulator would either set φ = 0 and allow full pooling, or set φ > φ 0 and induce full separation. Given that π (q) is convex in q, it is straightforward to see that full separation is (weakly) dominant. Interestingly, Proposition 7 implies that from an ex ante perspective the monopolist itself always (weakly) prefers higher punishments. Hence, if the monopolist could credibly commit to eective self-regulation in some way, then it would weakly prefer to commit not to use false advertising. Also note that the monopolist's preferred level of punishment (weakly) coincides with that of consumers in some circumstances, namely when L q or H < q. However, in the remaining circumstances, the monopolist prefers a level of punishment that is strictly higher relative to the levels preferred by consumers. This (mis-) alignment between the rm's and the consumers' preferences is picked up in the next subsection. 4.3 The Eects of Policy on Total Welfare Finally, we examine the impact of policy on expected total welfare. We assume that the expected punishment, φ, is in the form of a ne such that it is as valuable to the government as to the rm, and so acts as a simple welfare transfer. Expected total welfare can then be written as E(T W ) = x (1 y ) [v (L) + π (L)] + (1 x + xy ) [v (q e H) + π (q e H)] (13) Now denote ye(v) and y E(π) as the optimal level of false advertising for a policymaker with a consumer surplus or prot objective, respectively, (as solved for in Propositions 4 and 7). We may then state the following: Proposition 8. Suppose the government seeks to maximize total welfare, and that condition (5) holds. a) When H q the optimal policy induces y = ye(v) = y E(π) = 0. b) When L < q < H, there exists an ˆL ( ) q q, q such that the optimal policy induces y y E(π) = = 0 if L < ˆL (0, 1] if L > ˆL y E(v) 16

17 c) When L q total welfare is the same for all y [0, 1]. Surprisingly, Proposition 8 shows that under certain conditions a welfare-maximizing policymaker permits false advertising. In particular, it chooses to do this whenever the product qualities L and H are relatively large. The intuition behind Proposition 8 is as follows. In cases outside market coverage, a monopolist uses its market power to restrict output below the socially ecient level. False advertising then changes this output distortion in two ways. Firstly it raises consumers' expectation of a lying low type's product quality, enabling it to expand its output. Secondly, it lowers consumers' expectation of a high type's product quality, and thus causing it to reduce its output. The net eect of these two output changes depends crucially on the level of market coverage. When qh e q the market is not fully covered. A small reduction in false advertising is then benecial for welfare, E(T W )/ y < 0, because a unit of output is more socially valuable when it is produced by the high type. However when qh e > q > L, the rm sells to all consumers when it makes a high claim. Consequently a small change in y has no eect on the output produced by a high type, nor on its contribution to total surplus. Instead, an increase in y i) increases the probability of a low type claiming r = H and generating surplus v (qh e )+π (qe H ) (qe H L)14, and ii) decreases the probability that it claims r = L and generates surplus v (L) + π (L). Let (L) be the dierence between these two surpluses: (L) = v (qh) e + π (qh) e v (L) π (L) (qh e L) (14) There then exists a unique ˆL such that (L) > 0 when L > ˆL, and (L) < 0 when L < ˆL. It is then straightforward to prove that de(t W )/dy is strictly positive (negative) when L is above (below) ˆL. In other words, the output expansion induced by false advertising is socially benecial if and only if L is relatively large. Intuitively when L is large, the socially optimal output of a low type is also large and so false advertising is benecial since it brings the rm's actual output closer to the social optimum. However when L is small, the optimal level of output for a low type is also small and so false advertising is detrimental since it increases the rm's output by so much that most of the additional units are valued at less than marginal cost. Now return to Proposition 8. When H q the policymaker clearly chooses to fully eliminate false advertising. Recalling our earlier results, the policymaker thus implements the outcome preferred by both consumers, ye(v), and rm, y E(π). Next suppose that q < q < H. At y = 1 the market is not fully covered and so, from above, the policymaker reduces y until qh e just hits q; after this, the policymaker either stops intervening if L > ˆL, or entirely eliminates false advertising if L < ˆL. Finally suppose that L < q q, such that 14 On average a high report generates surplus v (qh e ) + π (qe H ). However when the rm's quality is actually low, each unit of output is worth qh e L less to consumers than the average. 17

18 a rm reporting r = H always sells to the entire market. Given the above discussion, the policymaker chooses y = 0 if L < ˆL, and chooses y 15 = 1 if L > ˆL. In these last two cases, the preferred level of lying for the rm, ye(π), is mis-aligned with the consumers' preferred level, ye(v). Depending upon parameters, the policymaker implements either the rm-optimum or the consumer-optimum. Thus policy is (weakly) too lenient for the rm and (weakly) too strong for consumers. Finally, consider the case where some of the punishment, φ, is `lost' and does not contribute to total welfare. Here, the analysis is messier but qualitatively similar to that in Proposition 8. In particular it is clear that: Remark 9. Suppose that a fraction τ > 0 of the punishment is lost from total surplus. There still exists parameters such that a welfare-maximizing policymaker strictly prefers to allow false advertising. To illustrate, consider the case where L < q q. When there is no welfare loss, τ = 0, Proposition 8 showed that the optimal policy induces y = 1, with φ = 0. However, when τ > 0, it becomes even more attractive for a welfare-maximizing authority to set φ = 0. 5 Conclusions This paper has analysed the eects of consumer protection policy on false advertising. Despite its prevalence and importance, false advertising has previously remained under-studied as an equilibrium phenomenon. However, by using standard tools, we have shown how it can arise in equilibrium and how policy can be used to inuence the level of false advertising and market welfare. Moreover, the paper has further shown the conditions under which imperfect, rather than perfect, regulation can be optimal for consumers and society due its eect in counteracting rms' market power. 15 When L q the rm sells to every consumer regardless of its report. False advertising thus has no eect on the rm's output, or the surplus that it generates. 18

19 Appendix A: Proofs Proof of Lemma 1. (i) If q q demand is zero at any strictly positive price, so prot is (weakly) maximized at p = 0. (ii) If q > the rm's price must satisfy p a + q otherwise q it could increase p, still sell to all consumers, and strictly increase its prot. Provided p [a + q, b + q] we can dierentiate the prot function p [1 G(p q)] with respect to p and get a rst order condition g (p q) 1 p 1 G (p q) = 0 (15) ( ) (a) When q q, q the lefthand side of (15) is strictly positive at p = a + q, strictly negative as p b, and strictly decreasing in p given our assumption of a logconcave density. Hence there is a unique p that solves equation (15). Since the lefthand side of (15) is weakly increasing in q and decreasing in p q, but strictly decreasing in p, it readily follows that p (q)/ q [0, 1). (b). When q q the lefthand side of (15) is strictly negative at all p > a + q and hence p = a + q. Proof of Proposition 2. It is straightforward to show that this is a valid PBE and we therefore omit a formal proof. Instead, we begin by showing that this is the unique PBE (up to o-path beliefs) in which r(h) = H and consumer beliefs are price-independent. Dene βh e = Pr (q = H r = H) and βe L = Pr (q = H r = L). (a) Beliefs must satisfy Bayes' rule where possible. Therefore xing y, βh e = 1 x. 1 x+xy Moreover βl e = 0 if y < 1. However Bayes' rule places no restrictions on βl e if y = 1. (b) Prices must maximize prots given consumer beliefs. Therefore any rm claiming r = L must charge p (ql e ), and any rm claiming r = H must charge p (qh e ), where q e H = (1 β e H) L + β e HH and q e L = (1 β e L) L + β e LH (c) The high type should prefer to report r = H. This is clearly true because, from part (b), it will earn π (ql e ) if it reports r = L, but earn π (qh e ) > π (ql e ) if its reports r = H. (d) The low type's report should be optimal. (i) Using (b), there is an equilibrium with y = 0 if and only if φ π (H) π (L). (ii) Using (b), there is an equilibrium with y = 1 if φ π ( q) π (ql e ). We know from (a) that Bayes rule doesn't restrict qe L in this instance, however we also know that ql e L. So with the appropriate o-path beliefs, an equilibrium with y = 1 exists for all φ π ( q) π (L). (iii) Using (b) an equilibrium with y (0, 1) requires that equation (6) hold. Notice that since qh e [ q, H], equation (6) cannot hold for φ / [φ 1, φ 0 ]. However (6) does have a unique solution for any φ [φ 1, φ 0 ], with y = 0 when φ = φ 0, and y = 1 when φ = φ 1. 19

20 (e) Summing up then, there is a unique PBE (up to o path beliefs). Next we show that this PBE is also the unique PBE consistent with the Undefeated Equilibrium renement being used to select a price when r = H. Consider the signaling game played between the rm and consumers following a claim r = H. Suppose that a fraction β (0, 1) of the rms sending the claim r = H are telling the truth. Dene q β = βh + (1 β)l. Following the denition in Mezzetti and Tsoulouhas (2000; p. 674), consider a proposed equilibrium and a price p which is not chosen in this equilibrium, but which is chosen in another equilibrium by a set of rm-types T. If each member of T prefers the alternative equilibrium to the proposed one, with at least one strict preference, then after observing price p in the proposed equilibrium, consumers' belief should satisfy E (q {r, p} = {H, p}) = L + (H L) β m (q H ) β m (q H ) + (1 β) m (q L ) (16) where m(q) = 0 for all types q / T, and m(q) = 1 for all types q T 1 where T 1 is the set of rm-types that strictly prefer the alternative equilibrium. We focus on pure strategy pricing so we need only consider pooling and separating equilibria. In any pooling equilibrium p the payos of the two types are respectively p [1 G (p q β )] φ and p [1 G (p q β )]. It is also straightforward to show that in any separating equilibrium the payos of the two types are respectively π (L) φ and π (L). It is immediate that p = p (q β ) is the unique Undefeated Equilibrium. After a deviation to p (q β ) from any other putative equilibrium, consumers believe the rm is high quality with probability β, such that the deviating rm's prot increases; hence the putative equilibrium is defeated. Moreover p (q β ) cannot be defeated since there is no other equilibrium which delivers higher prot to either rm-type. Finally, given that rms charge p (q β ) after claiming r = H, and given that β must be consistent with Bayes rule, it is straightforward to show that only the lying behavior in part iv) of the proposition is possible. Proof of Lemma 3. This follows directly from Proposition 2. a) y = 1 when φ φ 1. b) y (0, 1) and satises equation (6) when φ (φ 1, φ 0 ). Recall that π (qh e ) / qe H > 0, and note that equation (8) implies dqh e /dy < 0. Totally dierentiating equation (6) then gives y / φ < 0. c) Finally y = 0 when φ φ 0. Proof of Proposition 4. Given Lemma 3 we can rst solve for the optimal y, and then use Proposition 2 to nd the φ needed to implement it. Using equations (8) and (9) we can write that E(v) y [ = x v (qh) e v (L) dv (qh e ) ] (qh e L) dq (17) 20