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Quality signaling via strikethrough prices
ARTICLE IN PRESS IJRM-01252; No of Pages 9 International Journal of Research in Marketing xxx (2018) xxx–xxx
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Quality signaling via strikethrough prices夽 Eric Schmidbauer a, * , Axel Stock b a b
Department of Economics, University of Central Florida, 4336 Scorpius St., Orlando, FL 32816, USA Department of Marketing, University of Central Florida, 4336 Scorpius St., Orlando, FL 32816, USA
A R T I C L E
I N F O
Article history: First received on November 21, 2017 and was under review for 3 months Available online xxxx Senior Editor: David Soberman Keywords: Asymmetric information Price signaling Sales prices
A B S T R A C T Why do firms often advertise their current price together with their past price? Although consumers expect high quality products to have high prices, such firms may optimally charge lower prices when faced with low production costs. Thus in markets in which quality is difficult to ascertain and costs often fall over time, for example technology products, high quality firms may face a challenge of signaling their quality through current price alone. In this paper we develop a price signaling model in which uninformed consumers draw inference not only from the current price but also the prior period’s price (the “strikethrough price”) if the firm chooses to disclose it. We find that a high quality firm benefits from using strikethrough pricing when the prior probability of high quality is relatively low while the probability of costs falling is relatively high. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Why do consumers pay attention to sales prices? Standard economic theory posits that a consumer who is familiar with a product and knows his valuation for it need only consider the current price for the product and its substitutes. However, experience shows that consumers use both current and past prices when making their purchase decisions. In particular, the practice of offering discounts relative to a posted past price appears to be attractive for companies. In 2015, for example, JC Penney settled a class action lawsuit for $50 million that claimed the retailer had artificially increased past prices and posted fake “regular” prices to make discounts look enticing to consumers.1 Notwithstanding this, 1 year later JC Penney and many of its competitors, including Kohl’s, Sears and Macy’s, were accused in a California lawsuit of engaging in the same practice again during the 2016 holiday season.2 The practice of posting a sales price together with the current price is not unique to big box retailers, with online merchants a frequent user of the practice as well.3
夽 For research assistance we thank Rachel Wilder. * Corresponding author. E-mail addresses: [email protected] (E. Schmidbauer), [email protected] (A. Stock). 1
“J.C. Penney settles suit calling its ‘discount’ prices a scam.” New York Times, by Hiroko Tabucki. November 12, 2015. “JC Penney, Sears, Macy’s, and Kohl’s sued for ‘fake’ sale pricing.” NBCnews.com, by Ben Popken. December 9, 2016. 3 “It’s discounted, but is it a deal? How list prices lost their meaning.” New York Times, by David Streitfeld. March 6, 2016. See also “Are you really getting a discount, or is it just a pricing trick?” Harvard Business Review, by Rafi Mohammed. March 23, 2016. 2
https://doi.org/10.1016/j.ijresmar.2018.03.005 0167-8116/© 2018 Elsevier B.V. All rights reserved.
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Various explanations for the use of sales prices have been explored in the marketing literature, most of them focusing on the role of the pre-sale price as a reference price (see Grewal, Krishnan, Baker, & Borin, 1998; Kalyanaram & Winer, 1995; Mazumdar, Raj, & Sinha, 2005). According to this theory a pre-sale price becomes the “perceived” price, that is the price that a consumer expects to pay for a brand or product category. Consumers judge current prices against this standard to determine whether such prices are favorable or not. Our paper departs from this paradigm by considering the uncertainty some consumers have about product quality before making a purchase. We observe that a low current price may be a signal of low quality, but it may also arise from a high quality product whose marginal cost of production has fallen. This point is especially relevant in technology markets where production costs typically fall fast after a new product is introduced. In such markets a consumer who looks to the current price alone to draw inference about a product’s quality may be unable to precisely do so since in general prices reflect many factors other than product quality, such as the costs of production and the competitive environment. We show that in this setting displaying a past price can be informative. Because a low quality firm generally enjoys a cost advantage over its high quality counterpart during a product’s introductory phase, the former would typically charge a lower price than the latter during this phase. Disclosure of a high introductory price in the subsequent mature phase can therefore signal high quality at that time. In our model a single firm has exogenous quality that is either high or low and which is fixed across two periods (the “introductory period” and “mature period”). Whereas a low quality firm always has low production costs, a high quality firm has high costs in the introductory period which may fall to low in the mature period with some probability. The firm sets a price in each period after privately observing its costs and quality. A new cohort of consumers arrives in each period, uninformed of quality but able to draw inference from prices. This includes the current period’s price and, in the mature period, the past price if the firm chooses to disclose it (which we refer to as the “strikethrough price”). The possibility of posting a strikethrough price in the mature phase provides a link between the two periods: when a firm sets its price in the introductory period it knows this may affect consumers’ quality inferences both in that period and in the subsequent period should it choose to disclose a strikethrough price. Since a new cohort of consumers arrives each period, absent this link the two periods would stand alone with the high quality firm independently price signaling in each period, a result already well understood given the state of the literature.4 However, in our model when strikethrough prices are not used the high quality firm is not always able to distinguish itself from the low quality firm in the mature phase. This is because in some cases the high quality type enjoys a cost decline and so it has the same costs as the low quality type, making separation impossible within our price-signaling framework. This aspect of the model captures the insight that consumers’ inferences about quality from price can be hindered by a volatile cost environment. The result is that consumers in the mature period form a Bayesian posterior that pools over the high and low quality types, thus disadvantaging the firm that is truly high quality. The lower the prior probability of high quality, the less favorable are consumers’ pooled beliefs, and thus the more a truly high quality firm suffers from not being able to distinguish itself from a low quality firm. We show that by truthfully disclosing its first period price in the mature period, a high quality firm is able to separate itself from the low quality firm since the prices that were charged in the introductory phase successfully “proved” the firm was of high quality then. However, once the two periods are linked by strikethrough prices in this manner the low quality firm has an additional incentive to mimick its high quality counterpart in the introductory period, since doing so would induce consumers to believe its quality was high in both periods. For this reason the high quality firm must charge a very high price in the first period to deter mimickry. The price signal is therefore frontloaded, allowing the high quality firm to charge a second period price that is not distorted. In equilibrium the low quality firm is revealed by charging its full information price in each period, and it has no incentive to use a strikethrough price. After characterizing the strikethrough equilibrium we give the necessary and sufficient conditions for such an equilibrium to exist. It is required that the benefit from being perceived as high quality not be too high, or else it is impossible to deter the low quality type from mimicking, even with the use of strikethrough prices. After performing comparative statics on the prior probability of high quality and the probability of a cost reduction across periods, we provide a characterization of model parameters such that the high quality firm receives an expected benefit from the use of a strikethrough price. We find strikethrough prices are beneficial to high quality firms when the prior probability of high quality is relatively low and the probability of a cost decline is relatively high. This is because, absent strikethrough prices, when a high quality firm’s cost declines in the mature phase it is pooled with the low quality type, and consumers’ pooled inferences will be relatively pessimistic if the prior probability of high quality is low. Thus the gain from using strikethrough prices is greater in this case. In addition, the more likely a cost decline the more often the high quality firm would be pooled with the low type in the mature phase, and thus the greater the gains from separating using a strikethrough price. 1.1. Literature review Signaling of quality through price has received considerable attention in the marketing literature (Bagwell & Riordan, 1991; Moorthy & Srinivasan, 1995; Rao & Monroe, 1989). Bagwell and Riordan (1991) have shown that in a one-period model a high price can be a signal of high quality, since a low quality firm is discouraged from mimicking a high price due to its greater profit
4 See Linnemer (2012), for example, for a one-period model in which cost differences between quality types allow for signaling even when all consumers are uninformed.
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margin. In a multi-period extension they show that if the percentage of informed consumers in the market increases over time the high quality firm can signal its quality with a smaller price distortion so that a declining price path will be observed. Our model extends Bagwell and Riordan (1991) by considering the possibility that the high quality firm’s production cost decreases over time, a characteristic of many markets, as well as the decision of the firm to reveal its past price. In this setting we identify the conditions under which the high quality firm is better off communicating its past period’s price through a strikethrough price in our two-period model. Thus, our model contributes to the signaling literature by showing that a strikethrough price can be a signal of quality. Other signals of quality that have been studied in the literature include money back guarantees (Moorthy & Srinivasan, 1995), umbrella branding (Wernerfelt, 1988), slotting allowances (Lariviere & Padmanabhan, 1997), advertising (Desai, 2000; Milgrom & Roberts, 1986; Zhao, 2000), warranties (Balachander, 2001; Gal-Or, 1989; Lutz, 1989), and product scarcity (Stock & Balachander, 2005). In addition, the signaling of price image has been studied (Simester, 1995), and even the decision of whether to introduce a new product has been studied from a signaling perspective (Schmidbauer & Lubensky, 2018). In another stream of literature related to our research, Anderson and Simester (1998) construct a model in which sale signs can indicate to consumers that they are paying relatively low prices and thus should not bother searching a competitor’s store for a better product or lower price. In their model consideration of price signaling is suppressed in favor of focusing solely on the role of sale signs. In a follow-up paper, the authors analyze the effectiveness of sale signs using empirical data from a catalog retailer and show that setting too many sale signs can actually hurt companies because they render this strategy ineffective by diluting the informational content to consumers (Anderson & Simester, 2001). Although we also study firms’ usage of information about past prices as a strategy to communicate with consumers, we focus on their ability to communicate information about product quality in a price signaling framework. Our research is also related to Armstrong and Chen (2017) who analyze several two-period models of discount pricing. In one of their models first period consumers are informed and have a high willingness to pay for quality while second period consumers are uninformed and have a low willingness to pay. They show that when a firm can choose its quality level it has incentive to choose higher quality if forced to truthfully disclose its initial price, and that this raises welfare. In contrast to Armstrong and Chen’s emphasis on the welfare consequences of quality selection in the presence of strikethrough prices, our focus is on how the firm’s pricing decision affects its profits when strikethrough pricing is possible, given its quality. In addition, we assume that consumers’ information about quality is stable across periods (in contrast to Armstrong and Chen in which early consumers are informed and later ones are uninformed) and that costs may fall over time, as in technology product markets. Finally, the literature on cheap talk and advertising should be noted. In these papers the firm is unconstrained in the claims it can make in its advertisements or product packaging. Even though lying is explicitly “free” in these models it has been shown that the firm can credibly convey some information about product quality. For example, in Gardete (2013) consumers receive an advertisement from a firm in a vertically differentiated market and then must search to learn the true quality and price. Consumers are heterogeneous such that only firms with sufficiently high quality wish to serve high-end consumers and low type consumers prefer not to search if they believe quality (and hence price) will be too high. Gardete shows there is a semiseparating equilibrium in the advertisements firms send so that consumers learn what region of the quality space the firm lies in before deciding to search. Chakraborty and Harbaugh (2014) provide another example, in which a firm makes comparative statements which are deemed credible by consumers since they puff up the product on one dimension while implicitly denigrating it on another. Our model differs from these papers by using a disclosure and signaling paradigm, namely that prior prices must be truthfully disclosed and these prices may then signal the firm’s quality due to the different effect a high strikethrough price has on a high versus low quality firm.
2. Model A monopolist is privately informed of its quality, which is fixed across two periods and high with probability s1 ∈ (0, 1) and low otherwise. In the first period the product is new to the market and thus consumers are uninformed about its quality. Consumers purchase based on their belief about product quality after observing price information. In the second period, a new cohort of consumers arrives and, for simplicity, we assume that they are also uninformed about product quality.5 The marginal cost of producing a low quality product is constant and normalized to 0, while a high quality product’s marginal cost is c > 0 in period 1 but drops to 0 in period 2 with probability (1 − s2 ) ∈ (0, 1). This assumption of equal marginal cost for low and high quality products in period 2 can be justified because the use of total quality management (TQM) techniques may enable the production of a high quality product at the same marginal cost as a low quality product (Walton, 1986). Furthermore, Srinivasan, Lovejoy, and Beach (1997) show that superior product design from the point of view of customers does not necessarily entail
5 For empirical evidence that consumers perform surprisingly little search for information before purchase and thus stay uninformed as we assume, see Hawkins and Mothersbaugh (2016). In what follows we show that different quality types may pool on price in the second period provided that no consumers are informed. However, even if some consumers are informed in later stages of the product life cycle (i.e., the second period) we show in the Appendix that the high quality seller prefers the aforementioned pooling equilibrium to separating by charging a high price as long as the proportion of informed consumers is sufficiently small and they cannot credibly identify themselves to others.
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E. Schmidbauer, A. Stock / International Journal of Research in Marketing xxx (2018) xxx–xxx Table 1 States and their prior probabilities. Marginal
Quality
Prior probability
State
Cost
Parameter
Period 1
Period 2
H H L
c 0 0
b b 0
s1 0 1 − s1
s1 s2 s1 (1 − s2 ) 1 − s1
a higher production cost. While s1 and s2 are common knowledge, the realizations are private to the firm. Demand is linear in each period and given by p = (b + bl ) − mq
←→
q=
(b + bl) − p , m
where p and q are price and quantity, respectively, m > 0 is the slope parameter, and the intercept term consists of a parameter b > 0, the probability l of high quality given all available information, and a parameter b that calibrates the benefit from being high quality. We assume b ≥ c so that high quality is welfare improving over low quality. The firm sets its price in each period. Profit maximization implies that a firm with marginal cost c0 that is believed to be high quality with probability l will set price p =
b+bl+c0 2
≡ p(l, c0 ), sell quantity q =
b+bl−c0 2m
b+bl−c 2 ≡ q(l, c0 ) and earn profits P (l, c0 ) ≡ ( 4m 0 ) . Table 1 summarizes the
possible cost and quality types, lists their prior probabilities, and introduces the notation L, H, and H that will be used henceforth. s (1−s2 ) Below we will find an equilibrium in which types H and L are pooled and so it will be useful to define r ≡ s (1−s1 )+(1−s = 1 2 1) s1 −s1 s2 given L or H . Finally, we assume that a new cohort of consumers arrives in each period so that , the probability of H 1−s1 s2 second period consumers do not know the first period price.6 However, the firm can truthfully disclose its first period price in period 2 if it chooses (its “strikethrough price” ). Implicitly, we are assuming that the expected penalty for lying about a prior price is so severe that it exceeds the gains from doing so, and thus no firm would misrepresent its past price information.7 This notion is given some support by the examples of successfully filed lawsuits cited in Footnotes 1 and 2 of the Introduction. However, one could further model the choice of firms to misrepresent past prices. If firms do not always misrepresent, then a consumer that sees a strikethrough price will believe it is truthful with some probability.8 This would lower consumers’ beliefs that a product with a strikethrough price is high quality, but if this reduction was sufficiently small we would still obtain an equilibrium with strikethrough prices since payoffs in our model are continuous in beliefs. However, such an equilibrium would not be fully separating, because low cost high quality types and lying low quality types would be pooled. We look for a perfect Bayesian equilibrium. This consists of a price in each period for each type, a binary decision to reveal the strikethrough price in period 2, and beliefs l which are formed using Bayes’ rule and depend on the current price and past price, if disclosed. Prices in each period and the decision to use a strikethrough price must be a best response given beliefs while consumers’ optimal purchasing behavior given l is already incorporated into the demand specification p = (b + bl) − mq. As discussed below, signaling games often have multiple equilibria each of which must specify beliefs for actions taken off the equilibrium path. In order to reduce the number of equilibria considered we apply the intuitive criterion (Cho & Kreps, 1987) to restrict off the equilibrium path beliefs. Finally, all proofs are given in the appendix. 3. Analysis 3.1. The case without strikethrough pricing As a benchmark we first look for a separating equilibrium when strikethrough pricing is not possible. In this case each period’s equilibrium behavior is determined independently as standard one-period price signaling models with uninformed consumers and cost differences across quality types. Since these results are well known, we state them here only briefly. To focus only on the interesting cases we will assume that the high quality firm cannot costlessly separate by implementing full information prices. In the first period separation is achieved when type L has no incentive to mimick H. Thus type H chooses its price p such that p
b+b−p m
= P(0, 0),
(1)
6 Even if the same consumers return in the second period this assumption can be justified by behavioral research showing consumers generally have poor knowledge of historical prices. See Anderson and Simester (1998) and the citations within. 7 This is in contrast to cheap talk models in which false claims can be freely made by the firm (Gardete, 2013; Chakraborty & Harbaugh, 2014). 8 For example, suppose each type of firm in our model had two subtypes: honest (which never misrepresents its strikethrough price) and dishonest (which always does). Perhaps honest subtypes perceive the expected penalty for lying to be very high while dishonest subtypes perceive it to be very low. Then the use of a strikethrough price is consistent with a high quality firm or a dishonest low quality firm.
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where P(0, 0) is L s payoff in the conjectured separating equilibrium and p b+b−p is the payoff to L from successfully mimm b+b−p icking H. In fact any p such that p ≤ P(0, 0) will achieve separation. For a given equilibrium, any prices that are not m chosen by either quality type are off the equilibrium path, and Bayes’ rule cannot be used. The Perfect Bayesian Equilibrium concept then allows arbitrary beliefs, which leads to a plethora of equilibria. To restrict the number of equilibria, we impose the intuitive criterion (Cho & Kreps, 1987). The intuitive criterion implies that if a consumer sees an out-of-equilibrium price that is dominated by the equilibrium strategy of one type of seller and not the other, then the consumer should assume that the latter implemented the strategy. In the present case, any p for which the above inequality is strict can only be supported by beliefs that fail the intuitive criterion, and for this reason we focus only on p such that it binds with equality.9 In fact line (1) gives a quadratic in p that always has two solutions, the higher of which we select since this leads to higher profits for the high type.10 Denote this solution by p∗1 and the corresponding quantity by q∗1 , and note that p∗1 > p(1, c) > p(0, 0). Thus L charges its full information price while H charges a price above its own full information price to separate from L. The analysis proceeds much the same in the second period, however now there are three types, H, H , and L. However, since s1 −s1 s2 types H and L share marginal cost of 0 they must be pooled in equilibrium with perceived quality r = 1−s . Type H can 1 s2 separate from the pooled types by selecting p such that p
b+b−p m
= P(r, 0).
(2)
Denote the higher of the two solutions by p∗2 , and its corresponding price by q∗2 . Note that p∗1 > p∗2 > p(1, c) > p(r, 0). Thus in the second period H s price again exceeds its full information price, but it is less than its first period separating price. This latter result follows since the pooled type from whom H is separating enjoys higher equilibrium payoffs (i.e., P(r, 0) > P(0, 0)) and so a less distortionary price is needed. The preceding results lead to the following proposition. Proposition 1. Suppose strikethrough prices cannot be used. Then a separating equilibrium exists in which prices p∗1 and p(0, 0) are charged by the high and low quality firms, respectively, in period 1 while in period 2 type H charges p∗2 and both types H and L charge p(r, 0). We now calculate the profits earned by the firm in this equilibrium. The low quality firm earns its full information profits in the first period and profits given the pooled quality r in period 2: PL = P(0, 0) + P(r, 0).
(3)
The high quality type’s profits can be written succinctly in terms of its own quantity and the low type’s profits. This is because the incentive compatibility constraints found in lines (1) and (2) equate the high type’s revenue to the low type’s profit in the first and second periods, respectively. The high type’s profit is thus this revenue minus its expected costs: E[PH ] = (P(0, 0) − cq∗1 ) + (P(r, 0) − s2 cq∗2 ) =PL − cq∗1 − s2 cq∗2 .
(4)
A comparison of lines (3) and (4) reveals a familiar feature of signaling models with cost differences across types: the low type earns its full information profits while the higher type earns profits lower than this due to costly signaling to achieve separation. We now proceed by performing comparative statics on the equilibrium prices and profits. Proposition 2. In the no-strikethrough equilibrium of Proposition 1, p∗1 is unaffected by s1 and s2 while p∗2 decreases in s1 and increases in s2 . In addition, profits to both the high and low quality types increase in s1 and decrease in s2 . Mathematically, dp∗1 ds2
,
dp∗2 ds1
<0,
dp∗2 ds2
> 0 , and
dPi ds1
> 0 and
dPi ds2
dp∗1 ds1
=0=
< 0 for i = L, H.
The proposition states that the first period price by H is not responsive to s1 or s2 . Intuitively, in the equilibrium without strikethough pricing the two periods are not linked so s2 has no effect on first period outcomes. In addition, s1 is not relevant to a type that has already been realized as high and must separate from L. The second period separating price p∗2 is set to deter mimicking and must increase whenever the low type’s profits from pooling in period 2 decreases (i.e., r decreases), as when s1
9
For the same reason we only focus on the p for which the corresponding expressions in lines (2) and (5) hold with equality. This is because either solution provides the same revenue (namely, P(0, 0)) but a higher price leads to lower quantity and thus lower costs. Type L s payoff is the same regardless of which solution is selected. For the same reason we select the higher of the two solutions to the corresponding expressions in lines (2) and (5). 10
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decreases or s2 increases. This also explains the comparative statics on PL and E[PH ] since an increase in the perceived pooling quality r directly benefits both types and additionally benefits H by relaxing the price signaling distortion needed to separate. We conclude this subsection by noting that the assumption of no strikethrough pricing is not necessary for the equilibrium described in Proposition 1 to exist. That is, while the proposition assumes that strikethrough prices cannot be used and then establishes the existence of a price signaling equilibrium, it can be seen that this same equilibrium exists even when strikethrough prices are an available option. This follows since in a conjectured no-strikethrough equilibrium the use of a strikethrough price is off the equilibrium path and so admits arbitrary beliefs. If consumers react to the unexpected use of a strikethrough price with sufficiently pessimistic beliefs then the firm would avoid this tactic in favor of the independent per period price signaling described in the proposition. 3.2. The case with strikethrough pricing We now allow the two periods to be linked through the use of a strikethrough price. We look for an equilibrium in which a high price in period 1 signals high quality in that period and in the next period when it is disclosed as a strikethrough price. If so then in period 2 the high quality firm will display its strikethrough price and charge its full information price. The argument proceeds similarly to that in the previous subsection. In the first period, H picks p such that L is indifferent (over two periods) to mimicking: p
b+b−p m
+ P(1, 0) = 2P(0, 0).
(5)
On the left hand side of Eq. (5), a mimicking low type earns the same revenue as H but incurs no cost in period 1 and in period 2 it is able to disclose a strikethrough price that is interpreted as proof of high quality, and so earn profits P(1, 0). On the right hand side are the low type’s equilibrium profits from charging its own full information price in each period. Line (5) is a quadratic in p that has a real solution provided √ P(1, 0) ≤ 2P(0, 0) ←→ 2P(0, 0) − P(1, 0) ≥ 0 ←→ b ≥ 1 + 2 b.
(6)
In words, the condition requires that the boost to demand from being high quality not be too high, or else a low quality firm could never be deterred from mimicking. In fact when Eq. (6) is satisfied two solutions to Eq. (5) exist, the higher of which we select (as discussed in Footnote 10). Let this price be denoted by p∗3 and its corresponding quantity q∗3 . It is apparent that p∗3 > p∗1 since 2P(0, 0) − P(1, 0) < P(0, 0) ⇐⇒ P(0, 0) < P(1, 0). In this sense when strikethrough prices are available signaling is “front loaded” into a very high first period price while second period prices are not distorted. Proposition 3. An equilibrium in which the high quality type uses a strikethrough price exists if and only if line (6) holds, in which case the high type charges price p∗3 in period 1 and displays this as a strikethrough price in period 2. A lower “sales price” is charged in the second period, either p(1, c) or p(1, 0) depending on whether costs are high or low, respectively. Finally, the low type charges its full information price in both periods and does not employ a strikethrough price. In the equilibrium second period consumers will either see no strikethough price at all (and thus infer quality is low) or see strikethrough price p∗3 (and thus infer quality is high) together with a current price of p(1, c) if costs are high or p(1, 0) if they are low.11 Interestingly, the price p∗3 does not depend on s1 or s2 . The result for s1 follows since in the separating equilibrium consumers’ posteriors will be l = 1 if p∗3 is observed, regardless of the prior, and it is posterior beliefs that affect profits. For s2 we note that it is the low quality type’s incentives that matter (as shown in line (5)) and this type always has cost 0 regardless of s2 . Profits to the firm in the strikethrough price equilibrium are as follows. The low type is revealed and simply receives its own full information profits in each period, thus PL = 2P(0, 0). As for the high quality type, in the second period it earns full information profits, which are either P(1, 0) or P(1, c) depending on whether costs fall or not. First period profits can be succinctly written using a substitution from line (5) to obtain revenue and cq∗3 for costs. Thus E PSH = (2P(0, 0) − P(1, 0) − cq∗3 ) + (s2 P(1, c) + (1 − s2 )P(1, 0)) =2P(0, 0) − s2 (P(1, 0) − P(1, c)) − cq∗3 .
(7)
11 The low type is indifferent to using a strikethrough price since its quality is revealed as low either way. For concreteness we focus on the equilibrium in which only those types with a strict incentive to use a strikethrough price do so.
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Notice that s1 does not appear in line (7) because here we are conditioning on being the high type. Next, it can be seen that a higher s2 lowers H s expected payoff, a straightforward result that higher expected costs lead to lower expected profits. Proposition 4. In the equilibrium of Proposition 3, the strikethrough price p∗3 is unaffected by s1 or s2 . Additionally, the expected profits of the high quality firm are invariant to s1 while decreasing in s2 . Mathematically,
dp∗3 ds1
=
dp∗3 ds2
=
dPH ds1
= 0 and
dPH ds2
<0.
3.3. Comparison with and without strikethrough prices In Proposition 1 we showed that an equilibrium without strikethrough prices always exists while Proposition 3 established a necessary and sufficient condition for a strikethrough equilibrium to occur. When this condition is satisfied, then, both types of equilibria exist. In this subsection we explore under what conditions profits are higher under each type of equilibrium and then discuss what equilibrium may be played when multiple exist. Profits earned by the low quality firm are the most straightforward. In the strikethrough equilibrium, the low type is separated from the high types in both periods and so L earns its full information profits in periods 1 and 2. In contrast, in the equilibrium without strikethrough prices the low type is pooled with H – the high quality firm with low costs – and thus is perceived as having quality r > 0 in that equilibrium. For this reason the low quality firm earns higher profits when strikethrough prices are not employed by H. The profit implications for the high quality firm are less clear since in order to avoid pooling with the low type it must charge a very distorted first period price. In the proposition below we show whether a high quality firm prefers the equilibrium with strikethrough or not depends on the prior probability of high quality as well as the probability of a cost reduction. In particular, each must be “low enough”. Proposition 5. There exist threshold values s¯ 1 and s¯ 2 (s¯ 1 ) below which the high quality firm’s expected profits are higher in the ds¯ equilibrium with strikethrough prices. Mathematically, the condition is (s1 , s2 ) ∈ S ≡ (s1 , s2 ) : s1 ≤ s¯ 1 , s2 ≤ s¯ 2 (s¯ 1 ) . Also, s¯ 2 < 0 . 1
See Fig. 1 for an example of what this region in (s1 , s2 ) -space might look like. The proposition states that the high type would prefer signaling with a strikethrough price to not doing so, if the prior belief that the firm is high quality and the probability that costs stay high in period 2 are low enough. The intuition for this result is as follows. First, considering its strategy from the start of the game the firm benefits more from the strikethrough price strategy the greater the chance that a cost decrease will occur. This is because if its cost decreases in period 2 the high quality firm’s full information price will be lower than in period 1, which is more attractive to mimick for the low quality firm. To reduce the necessary upward distortion in price to signal its quality in period 2 the high quality firm communicates its previous period’s high price to consumers by means of a strikethrough price. Second, if the prior belief that the firm is high quality is low, then the firm’s profit in a pooling equilibrium in period 2 is quite low. The reason is that when the consumers cannot identify the firm’s type then their willingness to pay for the product will be determined by the benefits received from the high and low quality product weighted by the pooled beliefs, which depend on the prior probability that the product is high or low quality. In order to avoid this undesirable state and to reduce the price distortion necessary in a separating equilibrium, the high quality firm uses a strikethrough price indicating the price it charged in period 1. Conversely, if the prior belief that the firm is high quality is high, then the high quality firm’s profit in the pooling equilibrium in period 2 is high enough that it prefers to pool and avoid signaling distortions to revealing its true quality. Example 1. Let b = 1, b = 2.5, c = 0.5, and m = 1. Fig. 1 shades the points in (s1 , s2 )-space such that the high quality firm earns higher expected profits in the equilibrium with strikethrough prices than without.
The findings in this section reflect that our model is tailored to a particular environment (namely, one in which costs of production may fall over time). In particular, consider a limiting case where s2 = 1 so that costs never change across periods. We find that strikethrough prices are never advantageous to the high quality firm in this case.12 Thus our model cannot provide a rationale for strikethrough prices beyond their role in clarifying a price signal in a cost declining environment, though our information economics based mechanism is complementary to other explanations that may suggest firms to implement strikethrough prices in practice. Finally, we consider equilibrium selection. When the condition in line (6) is satisfied both an equilibrium with and without the use of strikethrough prices exists. For the set of parameters outside of that identified in Proposition 5 (i.e., the unshaded region in Fig. 1; or, (s1 , s2 ) ∈ / S) both type L and H earn higher profits without the use of strikethrough prices and so for this reason
12
To see this, let s2 = 1 in line 8, substitute for q∗2 and q∗1 − q∗3 from Claim 1, note that s2 = 1 implies r = 0, and use the condition in Claim 2.
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Fig. 1. Shaded are parameter values in Example 1 for which the high type earns greater payoffs in the equilibrium in which it uses strikethrough prices than in the equilibrium in which it does not.
we may expect that equilibrium to occur.13 In contrast, for the set of parameters identified in Proposition 5 this Pareto dominance argument fails since type H benefits while L is harmed by the equilibrium with strikethrough. This makes the question of equilibrium selection more difficult and heightens the role of consumers’ expectations. As our introductory examples suggest, strikethrough pricing is a frequently used marketing tool that consumers may have come to expect. If so, a high quality firm ought to use a strikethrough price, for otherwise it will be inferred to be a low quality firm since only this type has no incentive to use strikethrough pricing according to Proposition 3. Thus consumers’ expectations that only a high quality firm will use strikethrough pricing are fulfilled. This argument then implies that strikethrough pricing will occur only when the parameters (s1 , s2 ) are in the region characterized in Proposition 5, that is when the prior probability of high quality is relatively low while the probability of costs declining is relatively high. 4. Discussion and conclusion The disclosure of a product’s prior price together with its current price is a common practice in retailing. The academic literature in marketing has proposed several explanations for the use of so-called “strikethrough prices” (Rao & Monroe, 1989), however these explanations rely on psychological theories in which a consumer benefits from a deal per se. In contrast to such existing explanations for strikethrough prices we propose a signaling rationale, showing that consumers can learn information about a product’s quality from observing past prices. In our model a company sells a product across two periods in which the production cost is initially higher for a high quality product and can decrease over time. Consumers do not directly observe quality but form beliefs based on their observation of price information revealed by the company. In a one-period setting one might expect a high quality seller to reveal its quality through a high price, as in Bagwell and Riordan (1991). Similarly, in our two-period setting we identify conditions under which a high quality seller distorts its price upwards in order to signal its quality to uninformed consumers. However, if production costs decrease in the second period the high quality seller has an incentive to decrease its price at that time, which could lead to mimickry by a low quality seller. We show that in this scenario the high quality seller may want to reveal the product’s past price to consumers and charge its full information profit maximizing price in the second period in order to reduce the cost from
13 Notwithstanding this, the equilibrium with strikethrough pricing still exists. This is because by Proposition 3 whenever line (6) is satisfied a type H firm would rather use a strikethrough price when it is expected by consumers than not use one. At the same time, Proposition 1 tells us the type H firm would rather not use a strikethrough price when it is unexpected by consumers. Furthermore, Proposition 5 states that for type H the latter no-strikethrough equilibrium is / S. Thus even though the strikethrough equilibrium is Pareto dominated, if consumers expect preferred to the former strikethrough equilibrium when (s1 , s2 ) ∈ it to be played, it still survives as an equilibrium. For similar reasons the equilibrium without strikethrough prices exists even when (s1 , s2 ) ∈ S.
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signaling quality. Anticipating the possibility of a cost decrease, the high quality seller distorts its first period price even more to be able to show a meaningful strikethrough price in the second period. In our analysis we determine that signaling with a strikethrough price in this manner is more profitable for the high quality firm when the probability of a cost decrease in the second period is high and the prior belief of high quality is sufficiently low. Anecdotal evidence indicates that strikethrough pricing is often used in technology markets where successive generations of products are regularly introduced and where production costs decrease significantly over time. For example, televisions, Blueray players and stereo equipment are often priced using this strategy. In contrast, if the prior belief about high quality is high, then our analysis suggests that strikethrough pricing may not be optimal and sellers may just use price as an independent signaling device in each period. Consistent with this result we rarely observe disruptive innovations being sold with strikethrough prices. Our analysis relies on the possibility that a high quality product’s price may fall over time and this is accomplished within our model by a probabilistic decline in the marginal cost of production between periods. However, it should be noted that in many product categories a decrease in price of a high quality product can result from other factors. For example, it may be that consumers’ willingness to pay declines over time due to a new generation of the product being launched, or because later adopters of the product are less enthusiastic about it. However, under this alternative explanation the firm does not have incentive to use strikethrough prices as long as the cost difference between high and low quality products stays the same. This is because while a decline in willingness to pay would be commonly known to all, in our model strikethrough prices are used to inform consumers about a cost decrease they cannot observe. On the other hand, if the consumers’ willingness to pay for high quality were to decrease in addition to a cost decrease of the product then the incentive for the low quality firm to mimick the high quality seller is reduced and thus, a high quality firm would be able to signal its quality with less of a price distortion. Thus, the need for strikethrough prices would decrease in this case. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijresmar.2018.03.005.
References Anderson, E. T., & Simester, D. I. (1998). The role of sale signs. Marketing Science, 17(2), 139–155. Anderson, E. T., & Simester, D. I. (2001). Are sale signs less effective when more products have them? Marketing Science, 20(2), 121–142. Armstrong, M., & Chen, Y. (2017). Discount pricing. (Tech. Rep.). University Library of Munich, Germany. Bagwell, K., & Riordan, M. H. (1991). High and declining prices signal product quality. The American Economic Review, 224–239. Balachander, S. (2001). Warranty signalling and reputation. Management Science, 47(9), 1282–1289. Chakraborty, A., & Harbaugh, R. (2014). Persuasive puffery. Marketing Science, 33(3), 382–400. Cho, I.-K., & Kreps, D. M. (1987). Signaling games and stable equilibria. The Quarterly Journal of Economics, 102(2), 179–221. Desai, P. S. (2000). Multiple messages to retain retailers: Signaling new product demand. Marketing Science, 19(4), 381–389. Gal-Or, E. (1989). Warranties as a signal of quality. Canadian Journal of Economics, 50–61. Gardete, P. M. (2013). Cheap-talk advertising and misrepresentation in vertically differentiated markets. Marketing Science, 32(4), 609–621. Grewal, D., Krishnan, R., Baker, J., & Borin, N. (1998). The effect of store name, brand name and price discounts on consumers’ evaluations and purchase intentions. Journal of Retailing, 74(3), 331–352. Hawkins, D. I., & Mothersbaugh, D. L. (2016). Consumer behavior: Building marketing strategy. McGraw-Hill Education.p.535. Kalyanaram, G., & Winer, R. S. (1995). Empirical generalizations from reference price research. Marketing Science, 14(3), G161–G169. Lariviere, M. A., & Padmanabhan, V. (1997). Slotting allowances and new product introductions. Marketing Science, 16(2), 112–128. Linnemer, L. (2012). Dissipative advertising signals quality: Static model with a continuum of types. Economics Letters, 114(2), 150–153. Lutz, N. A. (1989). Warranties as signals under consumer moral hazard. The Rand Journal of Economics, 239–255. Mazumdar, T., Raj, S., & Sinha, I. (2005). Reference price research: Review and propositions. Journal of Marketing, 69(4), 84–102. Milgrom, P., & Roberts, J. (1986). Price and advertising signals of product quality. Journal of Political Economy, 94(4), 796–821. Moorthy, S., & Srinivasan, K. (1995). Signaling quality with a money-back guarantee: The role of transaction costs. Marketing Science, 14(4), 442–466. Rao, A. R., & Monroe, K. B. (1989). The effect of price, brand name, and store name on buyers’ perceptions of product quality: An integrative review. Journal of Marketing Research, 351–357. Schmidbauer, E., & Lubensky, D. (2018). New and improved? International Journal of Industrial Organization, 56C, 26–48. Simester, D. (1995). Signalling price image using advertised prices. Marketing Science, 14(2), 166–188. Srinivasan, V., Lovejoy, W. S., & Beach, D. (1997). Integrated product design for marketability and manufacturing. Journal of Marketing Research, 154–163. Stock, A., & Balachander, S. (2005). The making of a “hot product”: A signaling explanation of marketers’ scarcity strategy. Management Science, 51(8), 1181–1192. Walton, M. (1986). The Deming management method. New York: Dodd, Mead and Co. Wernerfelt, B. (1988). Umbrella branding as a signal of new product quality: An example of signalling by posting a bond. The RAND Journal of Economics, 458–466. Zhao, H. (2000). Raising awareness and signaling quality to uninformed consumers: A price-advertising model. Marketing Science, 19(4), 390–396.
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Full Length Article
Quality signaling via strikethrough prices夽 Eric Schmidbauer a, * , Axel Stock b a b
Department of Economics, University of Central Florida, 4336 Scorpius St., Orlando, FL 32816, USA Department of Marketing, University of Central Florida, 4336 Scorpius St., Orlando, FL 32816, USA
A R T I C L E
I N F O
Article history: First received on November 21, 2017 and was under review for 3 months Available online xxxx Senior Editor: David Soberman Keywords: Asymmetric information Price signaling Sales prices
A B S T R A C T Why do firms often advertise their current price together with their past price? Although consumers expect high quality products to have high prices, such firms may optimally charge lower prices when faced with low production costs. Thus in markets in which quality is difficult to ascertain and costs often fall over time, for example technology products, high quality firms may face a challenge of signaling their quality through current price alone. In this paper we develop a price signaling model in which uninformed consumers draw inference not only from the current price but also the prior period’s price (the “strikethrough price”) if the firm chooses to disclose it. We find that a high quality firm benefits from using strikethrough pricing when the prior probability of high quality is relatively low while the probability of costs falling is relatively high. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Why do consumers pay attention to sales prices? Standard economic theory posits that a consumer who is familiar with a product and knows his valuation for it need only consider the current price for the product and its substitutes. However, experience shows that consumers use both current and past prices when making their purchase decisions. In particular, the practice of offering discounts relative to a posted past price appears to be attractive for companies. In 2015, for example, JC Penney settled a class action lawsuit for $50 million that claimed the retailer had artificially increased past prices and posted fake “regular” prices to make discounts look enticing to consumers.1 Notwithstanding this, 1 year later JC Penney and many of its competitors, including Kohl’s, Sears and Macy’s, were accused in a California lawsuit of engaging in the same practice again during the 2016 holiday season.2 The practice of posting a sales price together with the current price is not unique to big box retailers, with online merchants a frequent user of the practice as well.3
夽 For research assistance we thank Rachel Wilder. * Corresponding author. E-mail addresses: [email protected] (E. Schmidbauer), [email protected] (A. Stock). 1
“J.C. Penney settles suit calling its ‘discount’ prices a scam.” New York Times, by Hiroko Tabucki. November 12, 2015. “JC Penney, Sears, Macy’s, and Kohl’s sued for ‘fake’ sale pricing.” NBCnews.com, by Ben Popken. December 9, 2016. 3 “It’s discounted, but is it a deal? How list prices lost their meaning.” New York Times, by David Streitfeld. March 6, 2016. See also “Are you really getting a discount, or is it just a pricing trick?” Harvard Business Review, by Rafi Mohammed. March 23, 2016. 2
https://doi.org/10.1016/j.ijresmar.2018.03.005 0167-8116/© 2018 Elsevier B.V. All rights reserved.
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Various explanations for the use of sales prices have been explored in the marketing literature, most of them focusing on the role of the pre-sale price as a reference price (see Grewal, Krishnan, Baker, & Borin, 1998; Kalyanaram & Winer, 1995; Mazumdar, Raj, & Sinha, 2005). According to this theory a pre-sale price becomes the “perceived” price, that is the price that a consumer expects to pay for a brand or product category. Consumers judge current prices against this standard to determine whether such prices are favorable or not. Our paper departs from this paradigm by considering the uncertainty some consumers have about product quality before making a purchase. We observe that a low current price may be a signal of low quality, but it may also arise from a high quality product whose marginal cost of production has fallen. This point is especially relevant in technology markets where production costs typically fall fast after a new product is introduced. In such markets a consumer who looks to the current price alone to draw inference about a product’s quality may be unable to precisely do so since in general prices reflect many factors other than product quality, such as the costs of production and the competitive environment. We show that in this setting displaying a past price can be informative. Because a low quality firm generally enjoys a cost advantage over its high quality counterpart during a product’s introductory phase, the former would typically charge a lower price than the latter during this phase. Disclosure of a high introductory price in the subsequent mature phase can therefore signal high quality at that time. In our model a single firm has exogenous quality that is either high or low and which is fixed across two periods (the “introductory period” and “mature period”). Whereas a low quality firm always has low production costs, a high quality firm has high costs in the introductory period which may fall to low in the mature period with some probability. The firm sets a price in each period after privately observing its costs and quality. A new cohort of consumers arrives in each period, uninformed of quality but able to draw inference from prices. This includes the current period’s price and, in the mature period, the past price if the firm chooses to disclose it (which we refer to as the “strikethrough price”). The possibility of posting a strikethrough price in the mature phase provides a link between the two periods: when a firm sets its price in the introductory period it knows this may affect consumers’ quality inferences both in that period and in the subsequent period should it choose to disclose a strikethrough price. Since a new cohort of consumers arrives each period, absent this link the two periods would stand alone with the high quality firm independently price signaling in each period, a result already well understood given the state of the literature.4 However, in our model when strikethrough prices are not used the high quality firm is not always able to distinguish itself from the low quality firm in the mature phase. This is because in some cases the high quality type enjoys a cost decline and so it has the same costs as the low quality type, making separation impossible within our price-signaling framework. This aspect of the model captures the insight that consumers’ inferences about quality from price can be hindered by a volatile cost environment. The result is that consumers in the mature period form a Bayesian posterior that pools over the high and low quality types, thus disadvantaging the firm that is truly high quality. The lower the prior probability of high quality, the less favorable are consumers’ pooled beliefs, and thus the more a truly high quality firm suffers from not being able to distinguish itself from a low quality firm. We show that by truthfully disclosing its first period price in the mature period, a high quality firm is able to separate itself from the low quality firm since the prices that were charged in the introductory phase successfully “proved” the firm was of high quality then. However, once the two periods are linked by strikethrough prices in this manner the low quality firm has an additional incentive to mimick its high quality counterpart in the introductory period, since doing so would induce consumers to believe its quality was high in both periods. For this reason the high quality firm must charge a very high price in the first period to deter mimickry. The price signal is therefore frontloaded, allowing the high quality firm to charge a second period price that is not distorted. In equilibrium the low quality firm is revealed by charging its full information price in each period, and it has no incentive to use a strikethrough price. After characterizing the strikethrough equilibrium we give the necessary and sufficient conditions for such an equilibrium to exist. It is required that the benefit from being perceived as high quality not be too high, or else it is impossible to deter the low quality type from mimicking, even with the use of strikethrough prices. After performing comparative statics on the prior probability of high quality and the probability of a cost reduction across periods, we provide a characterization of model parameters such that the high quality firm receives an expected benefit from the use of a strikethrough price. We find strikethrough prices are beneficial to high quality firms when the prior probability of high quality is relatively low and the probability of a cost decline is relatively high. This is because, absent strikethrough prices, when a high quality firm’s cost declines in the mature phase it is pooled with the low quality type, and consumers’ pooled inferences will be relatively pessimistic if the prior probability of high quality is low. Thus the gain from using strikethrough prices is greater in this case. In addition, the more likely a cost decline the more often the high quality firm would be pooled with the low type in the mature phase, and thus the greater the gains from separating using a strikethrough price. 1.1. Literature review Signaling of quality through price has received considerable attention in the marketing literature (Bagwell & Riordan, 1991; Moorthy & Srinivasan, 1995; Rao & Monroe, 1989). Bagwell and Riordan (1991) have shown that in a one-period model a high price can be a signal of high quality, since a low quality firm is discouraged from mimicking a high price due to its greater profit
4 See Linnemer (2012), for example, for a one-period model in which cost differences between quality types allow for signaling even when all consumers are uninformed.
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margin. In a multi-period extension they show that if the percentage of informed consumers in the market increases over time the high quality firm can signal its quality with a smaller price distortion so that a declining price path will be observed. Our model extends Bagwell and Riordan (1991) by considering the possibility that the high quality firm’s production cost decreases over time, a characteristic of many markets, as well as the decision of the firm to reveal its past price. In this setting we identify the conditions under which the high quality firm is better off communicating its past period’s price through a strikethrough price in our two-period model. Thus, our model contributes to the signaling literature by showing that a strikethrough price can be a signal of quality. Other signals of quality that have been studied in the literature include money back guarantees (Moorthy & Srinivasan, 1995), umbrella branding (Wernerfelt, 1988), slotting allowances (Lariviere & Padmanabhan, 1997), advertising (Desai, 2000; Milgrom & Roberts, 1986; Zhao, 2000), warranties (Balachander, 2001; Gal-Or, 1989; Lutz, 1989), and product scarcity (Stock & Balachander, 2005). In addition, the signaling of price image has been studied (Simester, 1995), and even the decision of whether to introduce a new product has been studied from a signaling perspective (Schmidbauer & Lubensky, 2018). In another stream of literature related to our research, Anderson and Simester (1998) construct a model in which sale signs can indicate to consumers that they are paying relatively low prices and thus should not bother searching a competitor’s store for a better product or lower price. In their model consideration of price signaling is suppressed in favor of focusing solely on the role of sale signs. In a follow-up paper, the authors analyze the effectiveness of sale signs using empirical data from a catalog retailer and show that setting too many sale signs can actually hurt companies because they render this strategy ineffective by diluting the informational content to consumers (Anderson & Simester, 2001). Although we also study firms’ usage of information about past prices as a strategy to communicate with consumers, we focus on their ability to communicate information about product quality in a price signaling framework. Our research is also related to Armstrong and Chen (2017) who analyze several two-period models of discount pricing. In one of their models first period consumers are informed and have a high willingness to pay for quality while second period consumers are uninformed and have a low willingness to pay. They show that when a firm can choose its quality level it has incentive to choose higher quality if forced to truthfully disclose its initial price, and that this raises welfare. In contrast to Armstrong and Chen’s emphasis on the welfare consequences of quality selection in the presence of strikethrough prices, our focus is on how the firm’s pricing decision affects its profits when strikethrough pricing is possible, given its quality. In addition, we assume that consumers’ information about quality is stable across periods (in contrast to Armstrong and Chen in which early consumers are informed and later ones are uninformed) and that costs may fall over time, as in technology product markets. Finally, the literature on cheap talk and advertising should be noted. In these papers the firm is unconstrained in the claims it can make in its advertisements or product packaging. Even though lying is explicitly “free” in these models it has been shown that the firm can credibly convey some information about product quality. For example, in Gardete (2013) consumers receive an advertisement from a firm in a vertically differentiated market and then must search to learn the true quality and price. Consumers are heterogeneous such that only firms with sufficiently high quality wish to serve high-end consumers and low type consumers prefer not to search if they believe quality (and hence price) will be too high. Gardete shows there is a semiseparating equilibrium in the advertisements firms send so that consumers learn what region of the quality space the firm lies in before deciding to search. Chakraborty and Harbaugh (2014) provide another example, in which a firm makes comparative statements which are deemed credible by consumers since they puff up the product on one dimension while implicitly denigrating it on another. Our model differs from these papers by using a disclosure and signaling paradigm, namely that prior prices must be truthfully disclosed and these prices may then signal the firm’s quality due to the different effect a high strikethrough price has on a high versus low quality firm.
2. Model A monopolist is privately informed of its quality, which is fixed across two periods and high with probability s1 ∈ (0, 1) and low otherwise. In the first period the product is new to the market and thus consumers are uninformed about its quality. Consumers purchase based on their belief about product quality after observing price information. In the second period, a new cohort of consumers arrives and, for simplicity, we assume that they are also uninformed about product quality.5 The marginal cost of producing a low quality product is constant and normalized to 0, while a high quality product’s marginal cost is c > 0 in period 1 but drops to 0 in period 2 with probability (1 − s2 ) ∈ (0, 1). This assumption of equal marginal cost for low and high quality products in period 2 can be justified because the use of total quality management (TQM) techniques may enable the production of a high quality product at the same marginal cost as a low quality product (Walton, 1986). Furthermore, Srinivasan, Lovejoy, and Beach (1997) show that superior product design from the point of view of customers does not necessarily entail
5 For empirical evidence that consumers perform surprisingly little search for information before purchase and thus stay uninformed as we assume, see Hawkins and Mothersbaugh (2016). In what follows we show that different quality types may pool on price in the second period provided that no consumers are informed. However, even if some consumers are informed in later stages of the product life cycle (i.e., the second period) we show in the Appendix that the high quality seller prefers the aforementioned pooling equilibrium to separating by charging a high price as long as the proportion of informed consumers is sufficiently small and they cannot credibly identify themselves to others.
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E. Schmidbauer, A. Stock / International Journal of Research in Marketing xxx (2018) xxx–xxx Table 1 States and their prior probabilities. Marginal
Quality
Prior probability
State
Cost
Parameter
Period 1
Period 2
H H L
c 0 0
b b 0
s1 0 1 − s1
s1 s2 s1 (1 − s2 ) 1 − s1
a higher production cost. While s1 and s2 are common knowledge, the realizations are private to the firm. Demand is linear in each period and given by p = (b + bl ) − mq
←→
q=
(b + bl) − p , m
where p and q are price and quantity, respectively, m > 0 is the slope parameter, and the intercept term consists of a parameter b > 0, the probability l of high quality given all available information, and a parameter b that calibrates the benefit from being high quality. We assume b ≥ c so that high quality is welfare improving over low quality. The firm sets its price in each period. Profit maximization implies that a firm with marginal cost c0 that is believed to be high quality with probability l will set price p =
b+bl+c0 2
≡ p(l, c0 ), sell quantity q =
b+bl−c0 2m
b+bl−c 2 ≡ q(l, c0 ) and earn profits P (l, c0 ) ≡ ( 4m 0 ) . Table 1 summarizes the
possible cost and quality types, lists their prior probabilities, and introduces the notation L, H, and H that will be used henceforth. s (1−s2 ) Below we will find an equilibrium in which types H and L are pooled and so it will be useful to define r ≡ s (1−s1 )+(1−s = 1 2 1) s1 −s1 s2 given L or H . Finally, we assume that a new cohort of consumers arrives in each period so that , the probability of H 1−s1 s2 second period consumers do not know the first period price.6 However, the firm can truthfully disclose its first period price in period 2 if it chooses (its “strikethrough price” ). Implicitly, we are assuming that the expected penalty for lying about a prior price is so severe that it exceeds the gains from doing so, and thus no firm would misrepresent its past price information.7 This notion is given some support by the examples of successfully filed lawsuits cited in Footnotes 1 and 2 of the Introduction. However, one could further model the choice of firms to misrepresent past prices. If firms do not always misrepresent, then a consumer that sees a strikethrough price will believe it is truthful with some probability.8 This would lower consumers’ beliefs that a product with a strikethrough price is high quality, but if this reduction was sufficiently small we would still obtain an equilibrium with strikethrough prices since payoffs in our model are continuous in beliefs. However, such an equilibrium would not be fully separating, because low cost high quality types and lying low quality types would be pooled. We look for a perfect Bayesian equilibrium. This consists of a price in each period for each type, a binary decision to reveal the strikethrough price in period 2, and beliefs l which are formed using Bayes’ rule and depend on the current price and past price, if disclosed. Prices in each period and the decision to use a strikethrough price must be a best response given beliefs while consumers’ optimal purchasing behavior given l is already incorporated into the demand specification p = (b + bl) − mq. As discussed below, signaling games often have multiple equilibria each of which must specify beliefs for actions taken off the equilibrium path. In order to reduce the number of equilibria considered we apply the intuitive criterion (Cho & Kreps, 1987) to restrict off the equilibrium path beliefs. Finally, all proofs are given in the appendix. 3. Analysis 3.1. The case without strikethrough pricing As a benchmark we first look for a separating equilibrium when strikethrough pricing is not possible. In this case each period’s equilibrium behavior is determined independently as standard one-period price signaling models with uninformed consumers and cost differences across quality types. Since these results are well known, we state them here only briefly. To focus only on the interesting cases we will assume that the high quality firm cannot costlessly separate by implementing full information prices. In the first period separation is achieved when type L has no incentive to mimick H. Thus type H chooses its price p such that p
b+b−p m
= P(0, 0),
(1)
6 Even if the same consumers return in the second period this assumption can be justified by behavioral research showing consumers generally have poor knowledge of historical prices. See Anderson and Simester (1998) and the citations within. 7 This is in contrast to cheap talk models in which false claims can be freely made by the firm (Gardete, 2013; Chakraborty & Harbaugh, 2014). 8 For example, suppose each type of firm in our model had two subtypes: honest (which never misrepresents its strikethrough price) and dishonest (which always does). Perhaps honest subtypes perceive the expected penalty for lying to be very high while dishonest subtypes perceive it to be very low. Then the use of a strikethrough price is consistent with a high quality firm or a dishonest low quality firm.
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where P(0, 0) is L s payoff in the conjectured separating equilibrium and p b+b−p is the payoff to L from successfully mimm b+b−p icking H. In fact any p such that p ≤ P(0, 0) will achieve separation. For a given equilibrium, any prices that are not m chosen by either quality type are off the equilibrium path, and Bayes’ rule cannot be used. The Perfect Bayesian Equilibrium concept then allows arbitrary beliefs, which leads to a plethora of equilibria. To restrict the number of equilibria, we impose the intuitive criterion (Cho & Kreps, 1987). The intuitive criterion implies that if a consumer sees an out-of-equilibrium price that is dominated by the equilibrium strategy of one type of seller and not the other, then the consumer should assume that the latter implemented the strategy. In the present case, any p for which the above inequality is strict can only be supported by beliefs that fail the intuitive criterion, and for this reason we focus only on p such that it binds with equality.9 In fact line (1) gives a quadratic in p that always has two solutions, the higher of which we select since this leads to higher profits for the high type.10 Denote this solution by p∗1 and the corresponding quantity by q∗1 , and note that p∗1 > p(1, c) > p(0, 0). Thus L charges its full information price while H charges a price above its own full information price to separate from L. The analysis proceeds much the same in the second period, however now there are three types, H, H , and L. However, since s1 −s1 s2 types H and L share marginal cost of 0 they must be pooled in equilibrium with perceived quality r = 1−s . Type H can 1 s2 separate from the pooled types by selecting p such that p
b+b−p m
= P(r, 0).
(2)
Denote the higher of the two solutions by p∗2 , and its corresponding price by q∗2 . Note that p∗1 > p∗2 > p(1, c) > p(r, 0). Thus in the second period H s price again exceeds its full information price, but it is less than its first period separating price. This latter result follows since the pooled type from whom H is separating enjoys higher equilibrium payoffs (i.e., P(r, 0) > P(0, 0)) and so a less distortionary price is needed. The preceding results lead to the following proposition. Proposition 1. Suppose strikethrough prices cannot be used. Then a separating equilibrium exists in which prices p∗1 and p(0, 0) are charged by the high and low quality firms, respectively, in period 1 while in period 2 type H charges p∗2 and both types H and L charge p(r, 0). We now calculate the profits earned by the firm in this equilibrium. The low quality firm earns its full information profits in the first period and profits given the pooled quality r in period 2: PL = P(0, 0) + P(r, 0).
(3)
The high quality type’s profits can be written succinctly in terms of its own quantity and the low type’s profits. This is because the incentive compatibility constraints found in lines (1) and (2) equate the high type’s revenue to the low type’s profit in the first and second periods, respectively. The high type’s profit is thus this revenue minus its expected costs: E[PH ] = (P(0, 0) − cq∗1 ) + (P(r, 0) − s2 cq∗2 ) =PL − cq∗1 − s2 cq∗2 .
(4)
A comparison of lines (3) and (4) reveals a familiar feature of signaling models with cost differences across types: the low type earns its full information profits while the higher type earns profits lower than this due to costly signaling to achieve separation. We now proceed by performing comparative statics on the equilibrium prices and profits. Proposition 2. In the no-strikethrough equilibrium of Proposition 1, p∗1 is unaffected by s1 and s2 while p∗2 decreases in s1 and increases in s2 . In addition, profits to both the high and low quality types increase in s1 and decrease in s2 . Mathematically, dp∗1 ds2
,
dp∗2 ds1
<0,
dp∗2 ds2
> 0 , and
dPi ds1
> 0 and
dPi ds2
dp∗1 ds1
=0=
< 0 for i = L, H.
The proposition states that the first period price by H is not responsive to s1 or s2 . Intuitively, in the equilibrium without strikethough pricing the two periods are not linked so s2 has no effect on first period outcomes. In addition, s1 is not relevant to a type that has already been realized as high and must separate from L. The second period separating price p∗2 is set to deter mimicking and must increase whenever the low type’s profits from pooling in period 2 decreases (i.e., r decreases), as when s1
9
For the same reason we only focus on the p for which the corresponding expressions in lines (2) and (5) hold with equality. This is because either solution provides the same revenue (namely, P(0, 0)) but a higher price leads to lower quantity and thus lower costs. Type L s payoff is the same regardless of which solution is selected. For the same reason we select the higher of the two solutions to the corresponding expressions in lines (2) and (5). 10
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decreases or s2 increases. This also explains the comparative statics on PL and E[PH ] since an increase in the perceived pooling quality r directly benefits both types and additionally benefits H by relaxing the price signaling distortion needed to separate. We conclude this subsection by noting that the assumption of no strikethrough pricing is not necessary for the equilibrium described in Proposition 1 to exist. That is, while the proposition assumes that strikethrough prices cannot be used and then establishes the existence of a price signaling equilibrium, it can be seen that this same equilibrium exists even when strikethrough prices are an available option. This follows since in a conjectured no-strikethrough equilibrium the use of a strikethrough price is off the equilibrium path and so admits arbitrary beliefs. If consumers react to the unexpected use of a strikethrough price with sufficiently pessimistic beliefs then the firm would avoid this tactic in favor of the independent per period price signaling described in the proposition. 3.2. The case with strikethrough pricing We now allow the two periods to be linked through the use of a strikethrough price. We look for an equilibrium in which a high price in period 1 signals high quality in that period and in the next period when it is disclosed as a strikethrough price. If so then in period 2 the high quality firm will display its strikethrough price and charge its full information price. The argument proceeds similarly to that in the previous subsection. In the first period, H picks p such that L is indifferent (over two periods) to mimicking: p
b+b−p m
+ P(1, 0) = 2P(0, 0).
(5)
On the left hand side of Eq. (5), a mimicking low type earns the same revenue as H but incurs no cost in period 1 and in period 2 it is able to disclose a strikethrough price that is interpreted as proof of high quality, and so earn profits P(1, 0). On the right hand side are the low type’s equilibrium profits from charging its own full information price in each period. Line (5) is a quadratic in p that has a real solution provided √ P(1, 0) ≤ 2P(0, 0) ←→ 2P(0, 0) − P(1, 0) ≥ 0 ←→ b ≥ 1 + 2 b.
(6)
In words, the condition requires that the boost to demand from being high quality not be too high, or else a low quality firm could never be deterred from mimicking. In fact when Eq. (6) is satisfied two solutions to Eq. (5) exist, the higher of which we select (as discussed in Footnote 10). Let this price be denoted by p∗3 and its corresponding quantity q∗3 . It is apparent that p∗3 > p∗1 since 2P(0, 0) − P(1, 0) < P(0, 0) ⇐⇒ P(0, 0) < P(1, 0). In this sense when strikethrough prices are available signaling is “front loaded” into a very high first period price while second period prices are not distorted. Proposition 3. An equilibrium in which the high quality type uses a strikethrough price exists if and only if line (6) holds, in which case the high type charges price p∗3 in period 1 and displays this as a strikethrough price in period 2. A lower “sales price” is charged in the second period, either p(1, c) or p(1, 0) depending on whether costs are high or low, respectively. Finally, the low type charges its full information price in both periods and does not employ a strikethrough price. In the equilibrium second period consumers will either see no strikethough price at all (and thus infer quality is low) or see strikethrough price p∗3 (and thus infer quality is high) together with a current price of p(1, c) if costs are high or p(1, 0) if they are low.11 Interestingly, the price p∗3 does not depend on s1 or s2 . The result for s1 follows since in the separating equilibrium consumers’ posteriors will be l = 1 if p∗3 is observed, regardless of the prior, and it is posterior beliefs that affect profits. For s2 we note that it is the low quality type’s incentives that matter (as shown in line (5)) and this type always has cost 0 regardless of s2 . Profits to the firm in the strikethrough price equilibrium are as follows. The low type is revealed and simply receives its own full information profits in each period, thus PL = 2P(0, 0). As for the high quality type, in the second period it earns full information profits, which are either P(1, 0) or P(1, c) depending on whether costs fall or not. First period profits can be succinctly written using a substitution from line (5) to obtain revenue and cq∗3 for costs. Thus E PSH = (2P(0, 0) − P(1, 0) − cq∗3 ) + (s2 P(1, c) + (1 − s2 )P(1, 0)) =2P(0, 0) − s2 (P(1, 0) − P(1, c)) − cq∗3 .
(7)
11 The low type is indifferent to using a strikethrough price since its quality is revealed as low either way. For concreteness we focus on the equilibrium in which only those types with a strict incentive to use a strikethrough price do so.
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Notice that s1 does not appear in line (7) because here we are conditioning on being the high type. Next, it can be seen that a higher s2 lowers H s expected payoff, a straightforward result that higher expected costs lead to lower expected profits. Proposition 4. In the equilibrium of Proposition 3, the strikethrough price p∗3 is unaffected by s1 or s2 . Additionally, the expected profits of the high quality firm are invariant to s1 while decreasing in s2 . Mathematically,
dp∗3 ds1
=
dp∗3 ds2
=
dPH ds1
= 0 and
dPH ds2
<0.
3.3. Comparison with and without strikethrough prices In Proposition 1 we showed that an equilibrium without strikethrough prices always exists while Proposition 3 established a necessary and sufficient condition for a strikethrough equilibrium to occur. When this condition is satisfied, then, both types of equilibria exist. In this subsection we explore under what conditions profits are higher under each type of equilibrium and then discuss what equilibrium may be played when multiple exist. Profits earned by the low quality firm are the most straightforward. In the strikethrough equilibrium, the low type is separated from the high types in both periods and so L earns its full information profits in periods 1 and 2. In contrast, in the equilibrium without strikethrough prices the low type is pooled with H – the high quality firm with low costs – and thus is perceived as having quality r > 0 in that equilibrium. For this reason the low quality firm earns higher profits when strikethrough prices are not employed by H. The profit implications for the high quality firm are less clear since in order to avoid pooling with the low type it must charge a very distorted first period price. In the proposition below we show whether a high quality firm prefers the equilibrium with strikethrough or not depends on the prior probability of high quality as well as the probability of a cost reduction. In particular, each must be “low enough”. Proposition 5. There exist threshold values s¯ 1 and s¯ 2 (s¯ 1 ) below which the high quality firm’s expected profits are higher in the ds¯ equilibrium with strikethrough prices. Mathematically, the condition is (s1 , s2 ) ∈ S ≡ (s1 , s2 ) : s1 ≤ s¯ 1 , s2 ≤ s¯ 2 (s¯ 1 ) . Also, s¯ 2 < 0 . 1
See Fig. 1 for an example of what this region in (s1 , s2 ) -space might look like. The proposition states that the high type would prefer signaling with a strikethrough price to not doing so, if the prior belief that the firm is high quality and the probability that costs stay high in period 2 are low enough. The intuition for this result is as follows. First, considering its strategy from the start of the game the firm benefits more from the strikethrough price strategy the greater the chance that a cost decrease will occur. This is because if its cost decreases in period 2 the high quality firm’s full information price will be lower than in period 1, which is more attractive to mimick for the low quality firm. To reduce the necessary upward distortion in price to signal its quality in period 2 the high quality firm communicates its previous period’s high price to consumers by means of a strikethrough price. Second, if the prior belief that the firm is high quality is low, then the firm’s profit in a pooling equilibrium in period 2 is quite low. The reason is that when the consumers cannot identify the firm’s type then their willingness to pay for the product will be determined by the benefits received from the high and low quality product weighted by the pooled beliefs, which depend on the prior probability that the product is high or low quality. In order to avoid this undesirable state and to reduce the price distortion necessary in a separating equilibrium, the high quality firm uses a strikethrough price indicating the price it charged in period 1. Conversely, if the prior belief that the firm is high quality is high, then the high quality firm’s profit in the pooling equilibrium in period 2 is high enough that it prefers to pool and avoid signaling distortions to revealing its true quality. Example 1. Let b = 1, b = 2.5, c = 0.5, and m = 1. Fig. 1 shades the points in (s1 , s2 )-space such that the high quality firm earns higher expected profits in the equilibrium with strikethrough prices than without.
The findings in this section reflect that our model is tailored to a particular environment (namely, one in which costs of production may fall over time). In particular, consider a limiting case where s2 = 1 so that costs never change across periods. We find that strikethrough prices are never advantageous to the high quality firm in this case.12 Thus our model cannot provide a rationale for strikethrough prices beyond their role in clarifying a price signal in a cost declining environment, though our information economics based mechanism is complementary to other explanations that may suggest firms to implement strikethrough prices in practice. Finally, we consider equilibrium selection. When the condition in line (6) is satisfied both an equilibrium with and without the use of strikethrough prices exists. For the set of parameters outside of that identified in Proposition 5 (i.e., the unshaded region in Fig. 1; or, (s1 , s2 ) ∈ / S) both type L and H earn higher profits without the use of strikethrough prices and so for this reason
12
To see this, let s2 = 1 in line 8, substitute for q∗2 and q∗1 − q∗3 from Claim 1, note that s2 = 1 implies r = 0, and use the condition in Claim 2.
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Fig. 1. Shaded are parameter values in Example 1 for which the high type earns greater payoffs in the equilibrium in which it uses strikethrough prices than in the equilibrium in which it does not.
we may expect that equilibrium to occur.13 In contrast, for the set of parameters identified in Proposition 5 this Pareto dominance argument fails since type H benefits while L is harmed by the equilibrium with strikethrough. This makes the question of equilibrium selection more difficult and heightens the role of consumers’ expectations. As our introductory examples suggest, strikethrough pricing is a frequently used marketing tool that consumers may have come to expect. If so, a high quality firm ought to use a strikethrough price, for otherwise it will be inferred to be a low quality firm since only this type has no incentive to use strikethrough pricing according to Proposition 3. Thus consumers’ expectations that only a high quality firm will use strikethrough pricing are fulfilled. This argument then implies that strikethrough pricing will occur only when the parameters (s1 , s2 ) are in the region characterized in Proposition 5, that is when the prior probability of high quality is relatively low while the probability of costs declining is relatively high. 4. Discussion and conclusion The disclosure of a product’s prior price together with its current price is a common practice in retailing. The academic literature in marketing has proposed several explanations for the use of so-called “strikethrough prices” (Rao & Monroe, 1989), however these explanations rely on psychological theories in which a consumer benefits from a deal per se. In contrast to such existing explanations for strikethrough prices we propose a signaling rationale, showing that consumers can learn information about a product’s quality from observing past prices. In our model a company sells a product across two periods in which the production cost is initially higher for a high quality product and can decrease over time. Consumers do not directly observe quality but form beliefs based on their observation of price information revealed by the company. In a one-period setting one might expect a high quality seller to reveal its quality through a high price, as in Bagwell and Riordan (1991). Similarly, in our two-period setting we identify conditions under which a high quality seller distorts its price upwards in order to signal its quality to uninformed consumers. However, if production costs decrease in the second period the high quality seller has an incentive to decrease its price at that time, which could lead to mimickry by a low quality seller. We show that in this scenario the high quality seller may want to reveal the product’s past price to consumers and charge its full information profit maximizing price in the second period in order to reduce the cost from
13 Notwithstanding this, the equilibrium with strikethrough pricing still exists. This is because by Proposition 3 whenever line (6) is satisfied a type H firm would rather use a strikethrough price when it is expected by consumers than not use one. At the same time, Proposition 1 tells us the type H firm would rather not use a strikethrough price when it is unexpected by consumers. Furthermore, Proposition 5 states that for type H the latter no-strikethrough equilibrium is / S. Thus even though the strikethrough equilibrium is Pareto dominated, if consumers expect preferred to the former strikethrough equilibrium when (s1 , s2 ) ∈ it to be played, it still survives as an equilibrium. For similar reasons the equilibrium without strikethrough prices exists even when (s1 , s2 ) ∈ S.
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signaling quality. Anticipating the possibility of a cost decrease, the high quality seller distorts its first period price even more to be able to show a meaningful strikethrough price in the second period. In our analysis we determine that signaling with a strikethrough price in this manner is more profitable for the high quality firm when the probability of a cost decrease in the second period is high and the prior belief of high quality is sufficiently low. Anecdotal evidence indicates that strikethrough pricing is often used in technology markets where successive generations of products are regularly introduced and where production costs decrease significantly over time. For example, televisions, Blueray players and stereo equipment are often priced using this strategy. In contrast, if the prior belief about high quality is high, then our analysis suggests that strikethrough pricing may not be optimal and sellers may just use price as an independent signaling device in each period. Consistent with this result we rarely observe disruptive innovations being sold with strikethrough prices. Our analysis relies on the possibility that a high quality product’s price may fall over time and this is accomplished within our model by a probabilistic decline in the marginal cost of production between periods. However, it should be noted that in many product categories a decrease in price of a high quality product can result from other factors. For example, it may be that consumers’ willingness to pay declines over time due to a new generation of the product being launched, or because later adopters of the product are less enthusiastic about it. However, under this alternative explanation the firm does not have incentive to use strikethrough prices as long as the cost difference between high and low quality products stays the same. This is because while a decline in willingness to pay would be commonly known to all, in our model strikethrough prices are used to inform consumers about a cost decrease they cannot observe. On the other hand, if the consumers’ willingness to pay for high quality were to decrease in addition to a cost decrease of the product then the incentive for the low quality firm to mimick the high quality seller is reduced and thus, a high quality firm would be able to signal its quality with less of a price distortion. Thus, the need for strikethrough prices would decrease in this case. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijresmar.2018.03.005.
References Anderson, E. T., & Simester, D. I. (1998). The role of sale signs. Marketing Science, 17(2), 139–155. Anderson, E. T., & Simester, D. I. (2001). Are sale signs less effective when more products have them? Marketing Science, 20(2), 121–142. Armstrong, M., & Chen, Y. (2017). Discount pricing. (Tech. Rep.). University Library of Munich, Germany. Bagwell, K., & Riordan, M. H. (1991). High and declining prices signal product quality. The American Economic Review, 224–239. Balachander, S. (2001). Warranty signalling and reputation. Management Science, 47(9), 1282–1289. Chakraborty, A., & Harbaugh, R. (2014). Persuasive puffery. Marketing Science, 33(3), 382–400. Cho, I.-K., & Kreps, D. M. (1987). Signaling games and stable equilibria. The Quarterly Journal of Economics, 102(2), 179–221. Desai, P. S. (2000). Multiple messages to retain retailers: Signaling new product demand. Marketing Science, 19(4), 381–389. Gal-Or, E. (1989). Warranties as a signal of quality. Canadian Journal of Economics, 50–61. Gardete, P. M. (2013). Cheap-talk advertising and misrepresentation in vertically differentiated markets. Marketing Science, 32(4), 609–621. Grewal, D., Krishnan, R., Baker, J., & Borin, N. (1998). The effect of store name, brand name and price discounts on consumers’ evaluations and purchase intentions. Journal of Retailing, 74(3), 331–352. Hawkins, D. I., & Mothersbaugh, D. L. (2016). Consumer behavior: Building marketing strategy. McGraw-Hill Education.p.535. Kalyanaram, G., & Winer, R. S. (1995). Empirical generalizations from reference price research. Marketing Science, 14(3), G161–G169. Lariviere, M. A., & Padmanabhan, V. (1997). Slotting allowances and new product introductions. Marketing Science, 16(2), 112–128. Linnemer, L. (2012). Dissipative advertising signals quality: Static model with a continuum of types. Economics Letters, 114(2), 150–153. Lutz, N. A. (1989). Warranties as signals under consumer moral hazard. The Rand Journal of Economics, 239–255. Mazumdar, T., Raj, S., & Sinha, I. (2005). Reference price research: Review and propositions. Journal of Marketing, 69(4), 84–102. Milgrom, P., & Roberts, J. (1986). Price and advertising signals of product quality. Journal of Political Economy, 94(4), 796–821. Moorthy, S., & Srinivasan, K. (1995). Signaling quality with a money-back guarantee: The role of transaction costs. Marketing Science, 14(4), 442–466. Rao, A. R., & Monroe, K. B. (1989). The effect of price, brand name, and store name on buyers’ perceptions of product quality: An integrative review. Journal of Marketing Research, 351–357. Schmidbauer, E., & Lubensky, D. (2018). New and improved? International Journal of Industrial Organization, 56C, 26–48. Simester, D. (1995). Signalling price image using advertised prices. Marketing Science, 14(2), 166–188. Srinivasan, V., Lovejoy, W. S., & Beach, D. (1997). Integrated product design for marketability and manufacturing. Journal of Marketing Research, 154–163. Stock, A., & Balachander, S. (2005). The making of a “hot product”: A signaling explanation of marketers’ scarcity strategy. Management Science, 51(8), 1181–1192. Walton, M. (1986). The Deming management method. New York: Dodd, Mead and Co. Wernerfelt, B. (1988). Umbrella branding as a signal of new product quality: An example of signalling by posting a bond. The RAND Journal of Economics, 458–466. Zhao, H. (2000). Raising awareness and signaling quality to uninformed consumers: A price-advertising model. Marketing Science, 19(4), 390–396.
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