استراتژی رقابتی زمانی که مصرف کنندگان با قیمتهای مرجع تحت تاثیر قرار میگیرند

The article presents a model that analyzes the optimal strategy of multi-product firms when consumers are affected by reference prices. Generally, the stronger the consideration of reference prices is, the more intensified the competition is and the lower are the prices and profits. In some cases it becomes optimal to sell the good for which consideration of reference prices is stronger at a negative markup. The model offers several practical implications, for example, suggesting that firms should usually avoid focusing advertisements on the price differences between the firm and its competitors.

An important consideration of consumers when making purchase decisions is the perceived fairness of prices, which in turn depends on a comparison between the firm’s prices and some reference prices. Kahneman, Knetsch, and Thaler (1986a, p. 729–730), for example, write “A central concept in analyzing the fairness of actions in which a firm sets the terms of future exchanges is the reference transaction, a relevant precedent that is characterized by a reference price or wage…” A rich literature studies price fairness perceptions and reference prices, and how these are determined (see for example Bolton et al., 2003, Kahneman et al., 1986b, Thaler, 1985 and Urbany et al., 1988). Rajendran and Tellis (1994) write that “An emerging consensus in marketing is that consumers respond to price relative to some standard or reference price” and argue that not only past prices in the store but also other prices in the store can serve as reference prices. Maxwell (2002) finds in two studies that consumers’ perceptions of price fairness and consequently their willingness to purchase are affected not only by the price itself but also by the process in which that price has been determined. Dodonova and Khoroshilov (2004), who examine empirical data from the auction website Bidz.com, provide additional evidence for the importance of reference prices. They find that people bid more for the same item when its posted “buy now” price is higher, suggesting that the reference “buy now” price affects buyers’ valuation of a good.1Briers, Pandelaere, and Warlop (2007) suggest that even deciding how much to donate to charities is affected by reference prices. Heidhues and Koszegi (2008) assume that consumers are loss averse relative to a reference point that is provided by their expectations and build a model that analyzes the impact of this on demand and equilibrium prices. Trautmann and Traxler (2010) study whether reserve prices serve as reference prices in online auctions of virtual football players. Karle and Peitz (2012) study how contextual consumer loss aversion affects firm strategy in duopoly, when some consumers are initially uniformed about their tastes and form a reference point that consists of an expected match-value and price distribution. Rosato (2013) presents a model with consumers who have a reference point that is affected by their expectations about consumption value and price. He shows that limited-availability sales can cause consumers to make an ex-ante unfavorable purchase. Another psychological issue that has implications for pricing is the utility that consumers may derive from finding a good bargain, beyond the utility that can be obtained from using the money saved for additional consumption. Darke and Freedman (1995), for example, find that subjects enjoyed bargains regardless of any financial gain, implying that non-financial motives might also be involved. In addition, they report that bargains acquired through skill were not enjoyed more than bargains achieved because of luck, suggesting that achievement motives could not explain why subjects enjoyed bargains when there was no associated financial gain. Xia and Monroe (2010) suggest that perceptions of price fairness share many similarities with transaction value (consumers’ psychological satisfaction from taking advantage of a good deal), but also have important differences. In three studies that address these differences they show that a “bad deal” is usually perceived to involve an unfair price, but a “good deal” is not necessarily perceived to offer the fairest price. The psychological evidence mentioned above has important implications for optimal pricing strategy in general and in particular for pricing of multi-product firms. However, models of multi-product firms’ pricing (e.g., DeGraba, 2006 and Doraszelski and Draganska, 2006) have not yet considered these implications.2 The purpose of this article is therefore to model how incorporating reference prices affects optimal pricing in the presence of multiple goods, thus contributing to the literature on pricing of multi-product firms. The article also contributes to the growing literature that addresses the effects of psychological biases on industrial organization and firm strategy.3 In the model presented below, two multi-product retailers compete by choosing prices and take into account that consumers are affected by reference prices. Each firm offers two goods, L and H, where L is the good with the lower cost. Consumers are interested in either one good or both. When considering the reference prices consumers may pay more attention to the reference price of the expensive good, or they may consider more the reference price of the cheap good (e.g., because the same absolute price difference creates a larger percentage difference when the price is lower). The model allows for both possibilities; the former corresponds to k > 1 and the latter to k < 1. The extent to which consumers care about reference prices in general is captured by the parameter g. In equilibrium both firms choose the same markups. For most parameter values the markups are decreasing in g: more consideration of reference prices by consumers leads to more aggressive competition, lower prices and lower profits. This result has practical implications for firms, as it suggests that firms should generally not encourage consumers to think about reference prices. This implies that advertisements that focus on the price differences between the firm and its competitors may be dangerous, because they may intensify the price competition in the market and erode profits. Another result shows that when consumers pay more attention to the reference price of one of the goods, the competition for this good intensifies. As a result, the markup on L decreases and the markup on H increases if k < 1, and the opposite happens when k > 1 (compared to the equilibrium without consumers who buy both goods). A practical implication of the model is that the firm should take into account in its pricing decisions for which of its goods consumers are particularly affected by reference prices. Generally, these goods should be priced very competitively, especially if consumers who buy these goods also buy other goods on the same shopping trip. In some cases firms present the behavior of loss-leader pricing. One of the two goods is sold for a price that is lower than its cost. This attracts also consumers who buy both goods, and the gain from their purchases of the second good justifies the loss on the first good. Only the good for which the consideration of reference prices is stronger may have a negative markup in equilibrium. Moreover, negative markups are only possible for a sufficiently high level of g. The rest of the paper proceeds as follows. Section 2 presents the model. The next section analyzes the model and derives several results. The last section concludes, discusses some practical implications, and suggests ideas for future research. Appendix A includes the proofs of the propositions and Appendix B presents numerical results.

The article presents a model that analyzes the optimal pricing strategy of multi-product retailers who take into account that consumers are affected by reference prices. This behavior is consistent with the findings of many studies, and can result for example from a desire to avoid prices that are perceived as unfair or from utility that consumers derive when they find a good bargain (beyond the utility from using the money saved for additional consumption). The model uses competing retailers, each offering two goods, L and H, where L is the good with the lower cost. Consumers are interested in either one good or both. When considering the reference prices consumers may pay more attention to the reference price of the expensive good (e.g., because they care more about it because it is more expensive), or they may focus more on the reference price of the cheap good (e.g., because the same absolute price difference creates a larger percentage difference when the price is lower). The model allows for both possibilities; the former corresponds to k > 1 and the latter to k < 1, where k = 1 captures the case where the reference prices of the two goods have the same effect. In addition, the extent to which consumers care about reference prices in general is captured by g. A few main results are summarized below. In equilibrium both firms choose the same markups. When k = 1, and for most parameter values also when k ≠ 1, the markups are decreasing in g. That is, the more consumers consider reference prices, the more intensified the competition is and the lower are the prices and profits. This idea also applies to the differences between the two goods: when consumers pay more attention to the reference price of one of the goods, the competition for this good intensifies. Consequently, compared to the equilibrium without consumers who buy both goods, the markup on L decreases and the markup on H increases if k < 1, and the opposite happens when k > 1. Moreover, the markup on L is increasing in k and the markup on H is decreasing in k. The model also yields, for certain parameter values, the behavior of loss-leader pricing. One of the two goods is sold at a negative markup, because doing so attracts also consumers who buy both goods, and the gain from their purchase of the other good suffices to justify the loss on the first good. Only the good for which the consideration of reference prices is stronger is a candidate to have a negative markup in equilibrium. Moreover, negative markups are only possible for a sufficiently high level of g, and in particular without consideration of reference prices (g = 0) negative markups are not optimal. Several results have practical implications. For example, the model shows that more consideration of reference prices by consumers intensifies competition, reducing markups and profits. This suggests that firms are generally better off not encouraging consumers to think about reference prices. Consequently, firms should be careful when they consider focusing advertisements on the price differences between the firm and its competitors. This may intensify the price competition between the firms and erode profits. However, this conclusion may be sensitive to the assumption that the firms are symmetric. It is possible that when the firms’ costs are asymmetric, the firm that enjoys lower costs (for example due to purchasing from the suppliers in larger quantities and getting a quantity discount, or due to more efficient operations) will have an incentive to focus advertisements on price differences, being able to offer lower prices than its competitor due to lower costs. An analysis of firms with asymmetric costs and the interaction between the desire to advertise prices when your costs are lower and the desire to avoid intensified competition on the other hand is an interesting direction for future research. Moreover, empirical work that looks at advertisements and examines how often firms use price comparisons in their ads and in what cases they do so can be very interesting. Another implication of the model is that the firm should observe for which of its goods consumers are particularly affected by reference prices, and take this into account when pricing these goods. In general, these goods should be priced very competitively (i.e., with lower markups compared to goods for which consumers are not affected by reference prices, other things being equal), especially if consumers who buy these goods also buy other goods on the same shopping trip. In addition, the profit being maximized when k < 0.5 means that if the firms can affect for which goods reference prices will be more prominent, the firms are better off choosing the cheap goods. When many consumers buy more than one good, it may become optimal to price the goods for which the reference prices are the most prominent below cost, in accordance with the practice of loss-leader pricing. Other studies of loss leaders that do not consider the impact of reference prices obtain different predictions on loss leaders. For example, Lal and Matutes (1994) suggest that products with lower reservation prices are more natural candidates to become loss-leaders. They also report that their model is consistent with the rationale that products that are purchased frequently and those with high storage costs should be used as the loss leaders. In the model of Hess and Gerstner (1987), the loss leader is the good for which consumers compare prices between stores, and are willing to return to the store a second time to get it if necessary, whereas the goods that yield the profit to the stores are the impulse goods that consumers buy on sight without price comparison between stores. DeGraba (2006) suggests that lower margins (possibly creating loss leaders) should be set on goods that are purchased mostly by more profitable customers. That is, in his model loss leaders are a way to create price discrimination in the presence of customer heterogeneity that makes some customers more profitable than others (e.g., larger customers). Interesting directions for future research include the development of models with more than two firms or more than two goods, in case these can yield further interesting insights that are not captured with a simpler model of two firms and two goods. Such models may allow, for example, to analyze what happens when the consumer, due to cognitive limitations, can consider reference prices only for some goods but not for others.7 If the number of goods is large but consumers only remember reference prices for a small set of goods (that is identical across consumers), we may get the result that the firms will compete strongly for this small set of goods while enjoying higher margins in the goods for which consumers do not consider reference prices. In the experimental direction, it is interesting to explore what makes the behavior of considering reference prices stronger. Are people more inclined to consider reference prices for some goods, for example more expensive goods or goods that are purchased more frequently? Do people give more weight to reference prices when they have readily available reference prices, such as list prices of books or MSRP (Manufacturer’s Suggested Retail Price) of cars? Can firms affect to what extent consumers will consider reference prices, for example by focusing their ads on prices?