Optimal Pricing with Speculators ...
MANAGEMENT SCIENCE Vol. 56, No. 1, January 2010, pp. 25���40 issn 0025-1909 eissn 1526-5501 10 5601 0025 informs �� doi 10.1287/mnsc.1090.1075 �� 2010 INFORMS Optimal Pricing with Speculators and Strategic Consumers Xuanming Su Haas School of Business, University of California, Berkeley, Berkeley, California 94720, firstname.lastname@example.org Tis his paper studies a monopolist firm selling a fixed capacity. The firm sets a price before demand uncertainty resolved. Speculators may enter the market purely with the intention of resale, which can be profitable if demand turns out to be high. Consumers may strategically choose when to purchase, and they may also choose to purchase from the firm or from the speculators. We characterize equilibrium prices and profits and analyze the long-run capacity decisions of the firm. There are three major findings. First, the presence of speculators increases the firm���s expected profits even though the resale market competes with the firm. Second, by facilitating resale, the firm can mimic dynamic pricing outcomes and enjoy the associated benefits while charging a fixed price. Third, speculative behavior may generate incentives for the seller to artificially restrict supply, and thus may lead to lower capacity investments. We also explore several model extensions that highlight the robustness of our results. Key words: dynamic pricing speculation resale strategic customer behavior competition History: Received January 7, 2009 accepted July 21, 2009, by Martin Lariviere, operations management. Published online in Articles in Advance September 28, 2009. 1. Introduction Many items are available only in limited quantities. Examples include tickets to a Broadway show, seats at a basketball match, and ���hot��� electronic gadgets such as Apple���s iPhone and Nintendo���s Wii video game console. Because of capacity constraints, there is often insufficient supply to meet demand. When scarcity arises, consumers unable to buy over regular chan- nels may be willing to turn to online resellers and Internet auction sites (e.g., eBay). Often, these con- sumers end up paying a significant price premium. Because there is a lucrative arbitrage opportunity, speculative behavior naturally emerges. Unlike ���true��� consumers, speculators make purchases purely with the intention of reselling them at a profit. The objec- tive of this paper is to introduce a tractable modeling framework that captures such speculative resale, and to understand its implications for the firm. Although ticket scalping has an unglamorous his- tory, the Internet resale industry has steadily risen and become increasingly acceptable with the growth of companies such as StubHub (a subsidiary of eBay) and TicketsNow (owned by Ticketmaster). The total revenue from online ticket sales is estimated to reach $4.5 billion by 2012, which is a significant increment over the $22 billion in ���regular��� sales by U.S. live music and sporting event industries (see Mulpuru and Hult 2008). These figures are not surprising because online resellers may charge a staggering price premium. For example, even though their face value rarely exceeds $5,000, courtside tickets to the National Basketball Association Finals may be priced as high as $35,000 each (see McGinn 2008). Even the free (but limited) admission tickets to Barack Obama���s inau- guration were put up for sale, although these post- ings were soon removed (see Colker 2008). Scalpers also tried to profit from reselling tickets to Michael Jackson���s memorial service, and many questioned the morality behind their actions (see Gundersen and Breznican 2009). Given rampant speculation, it is not surprising that Ticketmaster, a long-time exclusive provider of tickets to many major live entertainment events, began to introduce its own resale program (see Smith and Silver 2006). However, speculation is not always profitable: eBay estimates that about 45% of the tickets it has brokered are at or below face value (see Johnson 2007). As another example, consider the widespread short- age of Nintendo Wii game consoles in 2007 (see Kane and Wingfield 2007). Although already into the sec- ond year of launch, consumers were unsuccessful at locating the Wii console at local retailers for many months. As December approached, many began to turn to other alternatives and ended up paying sub- stantially higher prices from Internet resellers. On eBay auctions, average selling prices for the Wii con- sole remained consistently above $350 from November 2007 to January 2008, occasionally reaching $450, even 25
Su: Optimal Pricing with Speculators and Strategic Consumers 26 Management Science 56(1), pp. 25���40, �� 2010 INFORMS though the selling price is $249 at retail stores. Because this is a lucrative transaction for resellers, it is not surprising that retailers may also wish to play a part. Amidst the consumer frenzy, some retailers were hoarding their inventory from consumers and instead selling them on eBay at a ���Buy It Now��� price of $399. Some other retailers chose to increase margins by bundling the much sought-after Wii console with a number of other items such as games and accessories (see Kuchera 2007). Is Nintendeo simply underpric- ing the Wii at $249? Why don���t they increase produc- tion quantities? Our paper sheds new light on these questions. We study the following model in this paper. There is a monopolist seller with a fixed capacity. We con- sider two time periods. In the first period, there is a deterministic number of consumers in the market. (These are consumers who, for example, purchase sea- son passes or submit preorders.) In the second period, a random number of new consumers arrive. In addi- tion, there is a large pool of ���bargain hunters��� who are willing to purchase all remaining units at a lower price. There is also a large number of potential spec- ulators who may buy in the first period to sell in the second. Therefore, in the first period, the seller sells to consumers and speculators, and in the sec- ond, the seller and speculators jointly serve as sup- pliers. The seller sets a price at the start of the first period (this fixed price applies in both periods), and the resale price in the second period is competitively determined by the speculators. Note that resale may be profitable if demand is sufficiently large (then spec- ulators can resell units at a sufficiently high price). We assume free entry: Speculators enter the market until each earns zero expected profit. Therefore, equi- librium prices and speculative behavior are endoge- nously determined. We obtain three main results. First, we show that speculative resale can benefit the seller. The intuition is as follows. With an active resale market, the seller indirectly benefits because speculators ���place their bets��� up-front. As speculators purchase units before realizing their resale value, the seller not only collects more revenue earlier but also shifts some risk of hav- ing leftover inventory to the speculators. However, the downside is that speculators on the resale market compete directly with the firm and may undercut its price. Note that the seller can use the price to con- trol the equilibrium volume of speculative activity: As the price is increased, fewer speculators will enter the market, and in the extreme case, the seller can charge a sufficiently high price to completely shut specula- tors out of the market. We find that in many cases, the seller���s optimal price leads to some positive amount of speculative resale. Our results suggest that specula- tive behavior in equilibrium may have been implicitly encouraged by the seller. Our second main result is that speculative resale can serve as a proxy for dynamic pricing. The prac- tice of revenue management has been successful in a wide variety of applications, but it may not be feasi- ble in some contexts where equity and fairness across consumers are important considerations and the seller has to charge a fixed price. In such cases, we show that the seller can still enjoy some of the benefits of dynamic pricing by creating (or at least accommodat- ing) resale mechanisms. Effectively, the resale market becomes a mechanism that dynamically adjusts prices to match demand conditions. This increased flexibil- ity extracts consumer surplus, and some of the result- ing earnings are channeled back to the seller through increased sales to speculators. Therefore, speculators serve as market makers that help the seller achieve a form of ���disguised��� dynamic pricing. Interestingly, we find that speculators play a completely different role if the seller directly implements dynamic pric- ing. In that case, speculators act as competitors, and it is optimal for the seller to price them out of the market. Finally, we investigate the seller���s long-run capac- ity decision. We find that the seller is less inclined to make capacity investments in the presence of poten- tial speculative behavior. This is because a tight capac- ity level intensifies scarcity, which helps to sustain profitability on the resale market, and thus gener- ates speculative demand. In fact, there are situations where the seller will not expand even if doing so were costless. This result suggests that although specula- tive resale can improve profits, it may also discourage capacity investments. The remainder of this paper is organized as fol- lows. Section 2 provides a literature review. Sec- tion 3 introduces the model. Section 4 provides an equilibrium analysis. Section 5 discusses the analogy between speculative resale and dynamic pricing. Sec- tion 6 studies long-run capacity decisions. Section 7 describes several model extensions. Section 8 con- cludes. All proofs are presented in the appendix. 2. Literature Review This paper is most closely related to the recent lit- erature on strategic consumer behavior in operations management. In this literature, consumers form expec- tations about future market conditions and strategi- cally respond to them. Specifically, a group of papers study the scenario where consumers may strategically time their purchases in anticipation of future price changes. These papers (e.g., Aviv and Pazgal 2008, Elmaghraby et al. 2008, Jerath et al. 2007, Levin et al. 2009, Ovchinnikov and Milner 2005, Su 2007) analyze optimal dynamic pricing strategies when consumers strategically wait for markdowns. A more complete
Su: Optimal Pricing with Speculators and Strategic Consumers Management Science 56(1), pp. 25���40, �� 2010 INFORMS 27 review appears in the survey by Shen and Su (2007). There is another set of papers that focuses on how strategic consumers anticipate future availability as driven by firms��� inventory decisions these expecta- tions of availability influence their buy-or-wait deci- sion. For example, see Liu and van Ryzin (2008a, b), Su and Zhang (2008), Cachon and Swinney (2009), Lai et al. (2009), and Yin et al. (2009). Unlike the above, our current work studies a different type of strate- gic behavior. Whereas the above papers study strate- gic waiting behavior in anticipation of price changes, we additionally study strategic speculative behavior in anticipation of potential resale profits. There is a number of related papers that study eco- nomic mechanisms used to sell a fixed capacity when there is demand uncertainty. Harris and Raviv (1981) use a mechanism design approach to analyze a pri- ority pricing scheme when selling to a fixed num- ber of buyers with unknown valuations. Lazear (1986) studies a clearance sales mechanism. DeGabra (1995) shows that creating scarcity can induce buying fren- zies before consumers learn their valuations. Xie and Shugan (2001) consider advance selling to consumers who are uncertain of their valuations at the time of purchase. Dana (1998) studies how to use advance purchase discounts to screen consumers with differ- ent levels of uncertainty. Gale and Holmes (1993) and Dana (1999b) consider a model with two different products (e.g., two flights with different departure times), and consumers are uncertain over their rela- tive preferences. When there is limited capacity, Png (1989) points out that offering reservations before con- sumers learn their valuations insures them against the possibility of being rationed, and Alexandrov and Lariviere (2007) show that it can be optimal to offer reservations for free. Whereas most of the papers above focus on valuation uncertainty, Dana (1999a) considers aggregate demand uncertainty and stud- ies a mechanism where a limited number of units are available at each price and lower-priced units are sold first. (This is similar to Wilson 1988, who does not consider demand uncertainty.) Our paper also considers aggregate demand uncertainty, and more importantly, a key driver of our results is strategic speculation, which is absent in the models above. There has been some research that studies specula- tion and resale in markets with limited capacity. Three different approaches have been used, and our model differs from all of them. First, there is a stream of work on ticket scalp- ing see Courty (2003a) for a survey. In this literature, scalpers exploit arbitrage opportunities and make def- inite profits by buying and then reselling units. For example, Swofford (1999) assumes that scalpers are less risk averse than the seller and earn a guaran- teed risk premium by serving as middlemen Courty (2003a) assumes that consumers who arrive later have higher valuations so that scalpers make sure prof- its by reselling to them and Karp and Perloff (2005) assume that scalpers are able to perfectly price dis- criminate and extract maximal consumer surplus. In contrast, speculation is a risky prospect in our model: Because of aggregate demand uncertainty, speculators may ���flip��� the unit for a profit as intended, but they may also incur losses. In our model, the uncertainty faced by speculators is an essential ingredient, and speculators make zero expected profit in equilibrium. We further explore the distinction between arbitrage (certain profits) and speculation (possible but uncer- tain profits) in ��7. Next, there are some papers that consider resale markets as a medium for units to change hands between consumers. For example, Courty (2003b) and Geng et al. (2007) develop models where a fixed group of consumers face valuation uncertainty, and con- sumers who turn out to have low valuations can later resell to consumers with high valuations. However, our model admits a separate population of specula- tors who have no use for the unit, but make pur- chases because of potential resale profits. Further, we consider free entry of speculators, so the equilibrium volume of speculative transactions is endogenously determined. Finally, speculators play yet another different role in some other papers. Png (1989) studies a setting where consumers make reservations before learning their valuations he argues that sellers should not compensate consumers who end up with low valua- tions, because otherwise speculators with no use for the unit may simply show up to claim the compen- sation. Similarly, Su and Zhang (2009) suggest that if available guarantees (e.g., sellers compensate con- sumers when products are out of stock) are exces- sively generous, speculators may have an incentive to prowl stores for out-of-stock products. In the papers above, speculators do not ���speculate��� per se: They merely constrain the seller���s actions. Because the seller would take care to prevent such behavior, these speculators do not actively participate in the market in equilibrium. However, in our model, speculative resale not only emerges in equilibrium, but also has important implications for the seller. 3. Model In this model, there are three groups of agents. On the supply side, there is a monopolist seller. On the demand side, there are consumers. Finally, there are speculators who have no use for the product they buy it with the hope of reselling it at a higher price. We describe these three groups of agents in the fol- lowing list.