$189 or $39 plus 16,000 Frequent Flier Miles? Pricing in Combinations of Currencies to Lower Consumers Perceived Cost

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1 $89 or $39 plus 6,000 Frequent Flier Miles? Priing in Combinations of Currenies to Lower Consumers Pereived Cost Xavier Drèze Joseph C. Nunes* Draft last revised February 6, 2003 Xavier Drèze is Visiting Assistant Professor of Marketing at the Anderson Graduate Shool of Management, University of California, Los Angeles, CA Joseph C. Nunes is Assistant Professor of Marketing, Marshall Shool of Business, University of Southern California, Los Angeles, CA The authors would like to thank Aimee Drolet and C. W. Park for omments provided during the early stage of this paper. Both authors ontributed equally and are listed alphabetially. Questions should be direted to either Xavier Drèze at or Joseph C. Nunes at

2 ABSTRACT The rising popularity of loyalty programs and related marketing promotions has resulted in the introdution of a number of new urrenies (e.g., frequent flier miles, Hilton HHonors points, Diner s Club Club Rewards ) that people aumulate, budget, save and spend muh like traditional paper money. As onsumers are inreasingly able to pay for goods and servies suh as airline travel, hotel stays and groeries in various ombinations of urrenies, understanding how shoppers respond to we all ombined-urreny priing is beoming inreasingly important to marketers. This researh is the first to explore how onsumers evaluate transations involving ombined-urreny pries, or pries issued in multiple urrenies (e.g., $39 plus 6,000 miles). We present a formal mathematial proof outlining the onditions under whih a prie omprised of payments delivered in different urrenies an be superior to a standard, single-urreny prie by either (a) lowering the psyhologial or pereived ost assoiated with a partiular revenue objetive (i.e., prie), or (b) raising the amount of revenue olleted given a partiular pereived ost. Three studies, whih inlude having atual airline travelers evaluate and make hoies among pries issued in single and ombined urrenies, offer both experimental and empirial support. KEY WORDS: Priing, Combined-Curreny Pries, Utility Theory, Loyalty Programs, Awards Programs, Inommensurate Resoures, Mental Aounting, Frequent Flier Miles, Pereived Cost Funtion.

3 The world has a new international urreny: frequent flyer miles. The Eonomist May 2, 2002 For millions of Amerians, frequent-flier miles have beome a seond urreny. In addition to piling them up by hopping on a plane, you an get them by making phone alls, buying toys, investing in mutual funds, taking out a mortgage, or renting ars. Meanwhile, don't be tempted by airline offers to sell you a tiket for a ombination of miles and money. The deals are usually terrible. Business Week January 8, 999 Money has been around in one form or another sine at least 9000 BC, and at one time or another igarettes, attle, stones, eggs, salt and porpoise teeth eah has served as a negotiable instrument (Davies 996). To be most useful, eonomists argue that a urreny needs to be divisible, uniform and storable. Today, while almost all eonomies run on fiat money, paper notes the government says are worth something, the immense popularity of marketing promotions and loyalty programs has resulted in the introdution of several new mediums of exhange that meet these riteria. From hotels (e.g., Marriott Rewards, Hilton HHonors) to redit ards (e.g., Amerian Express Membership Rewards, Diner s Club s Club Rewards) and even sports teams (e.g., San Antonio Spurs Rewards), onsumers are aumulating assets in a variety of novel urrenies, whih they budget, save and spend muh like paper money. Undoubtedly, the most ubiquitous alternative urreny is frequent flier miles. One hundred million people around the globe, inluding one in three Amerian adults, ollet the nearly 500 billion miles distributed annually (WebFlyer.om 2002, Eonomist 2002). As of April 2002, the umulative number of unredeemed miles was estimated worldwide at lose to 8.5 trillion, whih at urrent redemption rates with no new miles being distributed would take almost 23 years to lear (Eonomist 2002). In 2000 alone, 3 million free award tikets were issued (WebFlyer.om 2002). After omparing the relevant figures with all of the notes and oins in irulation around the globe,

4 frequent-flier miles ould be onsidered the world s seond biggest urreny after the dollar, aording to the Eonomist (May 4, 2002, p. 62). While loyalty programs are growing at a swift % per year, the fastest growing segment is that of mileage onsumers, not frequent fliers, as more than 8,500 U.S. businesses from telephone ompanies to ar rental agenies distribute miles to their ustomers (Business Week 999, WebFlyer.om 2002). These miles, given to reipients who never leave the ground, aount for half of all of the miles earned (Eonomist 2002). One diret onsequene of the growing ubiquity of rewards programs is that onsumers are inreasingly able to pay for goods and servies in a ombination of urrenies, not just dollars. For example, in the summer of 2002, Hilton HHonors offered members the opportunity to exhange either 600,000 points or 0,000 points plus $4,25 for an 8-arat gold, -arat solitaire diamond ring from the program s Diamond Colletion ( Several more obsure urrenies are progressively beoming interhangeable aross programs, partiularly in ombination with frequent flier miles. A onsumer an exhange Amerian Express Rewards points (at a rate of -to-.3) or Amtrak Guest Rewards (at -to-2) for HHonors points, whih an subsequently be onverted into frequent flier miles in affiliated programs, and spent in ombination with dollars through a growing number of online malls and atalogs. One suh mall is Milepoint.om, an Internet exhange site baked by a group of prominent airlines that allows onsumers to apply frequent flier miles as partial payment towards the purhase of more than 20 million produts offered at partiipating merhants sites. MileShopper SM is an online atalog offering more than 300,000 brand name items from ompanies like Toshiba, Samsonite and Spalding for whih shoppers an apply miles for up to 30% of the ost of their purhases. For example, in May 200, the site offered $00 off any Walt Disney World resort pakage of $99 or more in exhange for 2,000 miles. Sites making similar offers at the time inluded MileSoure.om and MyPoints.om among others. 2

5 Perhaps most familiar to frequent fliers are the deals offered by the airlines themselves. Amerian Airlines AAdvantage, the first and largest frequent flier program in the world with more than 45 million members, is one of a number of programs routinely offering airline tikets for a ombination of money and miles. For example, one NetSAAver fare advertised on the airline s web site during the winter of 2003 allowed fliers to purhase any tiket normally pried at $89 for either (a) $89, or (b) a ombined-urreny prie of $39 plus 6,000 miles. Despite the growing popularity of pries issued in more than one urreny, we know of no work that examines how onsumers evaluate what we have labeled ombined-urreny priing per se. In this researh, we explore how onsumers respond to pries offered in multiple urrenies and determine the onditions under whih a ombined-urreny prie an be superior to a prie harged in a single urreny. We define superior as either (a) lowering the psyhologial ost to the ustomer assoiated with a partiular revenue objetive by the firm, or (b) raising the amount of revenue that an be olleted given a partiular psyhologial ost. Consider the following illustration. Imagine a onsumer who is indifferent between spending $500 or 25,000 miles on an airline tiket, but who would prefer paying $400 plus 5,000 miles to either single-urreny alternative. At $0.02 per mile, the ombined-urreny prie brings in the equivalent revenue to the airline, yet inflits a smaller psyhologial ost to the onsumer. It is important to note that this onsumer s preferene for the ombined-urreny prie indiates that eah mile or dollar spent is not valued equally; the disutility of paying more dollars and/or miles inreases as the payment in that urreny inreases. Aordingly, two essential requirements emerge for a ombined-urreny prie to be superior: () the onsumer does not value eah unit within a urreny equally, and (2) the pereived ost funtion for one of the urrenies is onvex for at least part of the range at issue. In the example above, it follows that the onsumer is not spontaneously onverting harges issued in one urreny into inrements of 3

6 the other urreny at a onstant rate, otherwise the flier would either: (a) be indifferent between the three hoies, or (b) if his or her exhange rate was higher (lower) than the firm s, he or she should prefer to pay exlusively in dollars (miles). Consequently, if the firm understands the basi shape of the pereived ost funtions for eah urreny (e.g., dollars and miles) within the appliable range of pries, using its own transfer funtion it an determine whether a prie that ombines urrenies would be superior to a prie issued in a single urreny. This researh proves this mathematially and demonstrates it empirially. CONCEPTUAL BACKGROUND The Value of Money and other Currenies In lassial eonomis, it is a truism that the utility of money is marginally dereasing, and therefore that utility is onave (Fennema and van Assen 999). The priniple of diminishing marginal utility (Stigler 950) provides a rational argument for dereasing utility from equivalent inremental gains, and inreasing disutility from equivalent inremental losses (a onvex pereived ost funtion in our terms). However, sine Prospet Theory (Kahneman and Tversky 979) popularized the view that people evaluate hanges in wealth relative to a referene point in muh the same way the Weber-Fehner law of psyhophysis says people respond to hanges in physial stimuli suh as light or sound, many psyhologists have ome to aept that the utility of losses is prone to diminishing marginal sensitivity (a onave ost funtion in our terms). Hene, while the onavity of utility for gains is rarely hallenged, there is still widespread debate on whether utility is onave or onvex for losses (e.g., expenditures). Historially, utility funtions have not been measured extensively (Farquhar 984), but those attempting to do so have found empirial evidene supporting both onave and onvex utility funtions for losses (Davidson, Suppes and Siegel 957, Green 963, Swalm 966, 4

7 Offier and Halter 968, Fishburn and Kohenberger 979, Tversky and Kahneman 992, Abdellaoui 2000). After reviewing the evidene on both sides, Fennema and Van Assen (999) onluded that, Hene for losses one of the most basi aspets of utility, that is, whether marginal utility is inreasing or dereasing, is as yet an unsettled question. While our work appears to support the eonomi predition, the ontradition between diminishing marginal utility and Prospet Theory s onjeture of diminishing marginal sensitivity is well beyond the sope of this paper. While Prospet Theory pertains to hanges in wealth and welfare utilizing money as its primary instrument, it does not address the issue diretly of how people respond to multiple urrenies or arriers of wealth simultaneously. Consequently, we prefer to view our findings as reinforing the idea that utility is the result of a onstrutive proess, whih undersores how ritial it is to understand the preise deision problem while studying the orresponding psyhologial mehanisms. While we don t test it expliitly in this paper, we believe goal setting may be a ommon explanation for the onvexity in the ost funtion neessary to make ombined urreny pries appealing. Heath, Larrik and Wu (999) have shown that people are willing to exert more effort as they approah their goal and less effort as they move away from a goal. Just as someone whose goal is to do 40 sit-ups would be expeted to exert more effort to do their 39 th sit-up than their 35 th, 4,000 miles would mean more to someone with 20,000 miles than to someone with 0,000 miles, when the amount needed for a free tiket is 25,000 miles. Consider that a onsumer who pays Amerian Airline s NetSAAver fare of $39 plus 6,000 miles rather than $89 reeives 0.94 ents, 0.23 ents per mile more than someone paying $39 plus 7,000 miles rather than $89, who reeives only 0.7 ents per mile. This premium is akin to effort in the situp example as someone spending 6,000 miles is muh loser to surrendering a free tiket (25,000 miles) than someone spending 7,000 miles. At the same time, Amerian offered quantity 5

8 disounts to fliers looking to buy miles so members ould reah the awards [they] want - faster than ever before. Someone in need of 0,000 miles would pay signifiantly less per mile ($250 or 2.5 ents per mile) than someone needing only,000 miles ($27.50 or 2.75 ents per mile). These buy and sell rates are onsistent with onsumers asribing a higher value to miles the loser they bring them to their goals. Reognizing that the opportunities for spending miles or points are more limited than for dollars, we would expet salient goals or referene points (e.g., hange in membership status, free flights and upgrades) to introdue onvexities into the pereived ost funtion for these alternative urrenies more readily than for money. This is not to say, however, that goals would never introdue onvexities into the pereived ost funtion for money, as would be the ase for someone saving up for a big sreen television, for whom eah dollar they arue would mean progressively more as they neared their goal. One the onsumer surpassed the savings neessary to ahieve their goal, one might expet the pereived ost funtion to beome onave, with little inremental value to eah additional dollar or mile aumulated (i.e., an S-shaped funtion). While we mention goals as one plausible mehanism for introduing onvexities into the pereived ost funtion, it is ritial to larify two important points regarding this researh up front. First, our mathematial results depend only on the pereived ost funtion being onvex for at least one of the urrenies (it an be both) for at least part of the range at issue. Seond, the underlying ause(s) for the onvexity of a pereived ost funtion whether due to goal setting, wealth effets, relativisti proessing, mental aounting and budgeting, risk aversion or some ombination of these and/or other explanations has no impat on whether an optimal ombined-urreny prie an exist or its derivation. In this researh, we do not attempt to determine why the onvexity ours; what matters is only that some region of onvexity in the 6

9 pereived ost funtion exists within the range of the expenditure for at least one of the urrenies involved. In pratie, however, for ombined-urreny pries to be truly useful to the firm, two other onditions should be met. First, the firm should possess a transfer funtion or rate at whih the firm values eah mile surrendered that it uses to optimize globally over thousands of exhanges. This value has been reported to be $0.07 (WebFlyer.om 2002), but is most often onsidered by onsumers to be $0.02, the standard selling prie for most airlines and the amount at whih Business Week (999) advised fliers to value eah of their miles. Given that the airlines redeem more than one billion miles every day, and the relatively small number of miles assoiated with any single promotion, we will assume a linear transfer funtion for ease of exposition, although a non-linear funtion an work as well. This is a reasonable assumption given the way most airlines manage their outstanding miles and in no way interferes with our goal of demonstrating how and why ombined-urreny pries an be superior from a onsumer behavior standpoint. 2 Seond, onsumers should not spontaneously onvert harges issued in one urreny into inrements of the other urreny, nor should they onvert both simultaneously into some third urreny. Work on inommensurate resoures by Nunes and Park (2003) suggests onsumers reat to hanges in alternative urrenies muh like they do for money, yet often do not spontaneously enode one urreny in terms of another (e.g., frequent flier miles in dollar terms). Those authors found onsumers made the onversion only when it was extremely easy to do so (e.g., a stable and salient exhange rate), or were extremely motivated to do so, as they might be for very large expenditures. Consequently, just as mental aounting and mental budgeting (Thaler 985, Heath and Soll 996) have demonstrated, onsumers often behave as if their money were not perfetly fungible, and assets aounted for in different urrenies are expeted to have their own mental aounts and to be similarly non-interhangeable. Reent work by 7

10 Raghubir and Srivastava (2002) suggests that even when an exhange rate between monetary urrenies is transparent and overtly provided, onsumers are still suseptible to biases in their onversions. And while experiene may attenuate a bias, it does not eliminate it. Furthermore, differenes in the aforementioned buy and sell rates, as well as among various ombined-urreny pries (see Table ) support the assumptions that: () onsumers don t always utilize the value of a mile to the seller or at some stable market rate when evaluating ombined-urreny pries, and (2) a onsumer s subjetive value for miles is likely to hange depending on the quantity to be aquired or surrendered. Taken together, previous researh and observed praties in the real world ombine to suggest that the neessary onditions exist for opportunisti sellers to use ombined-urreny pries to shift the balane of payments among urrenies (i.e., ombined-urreny priing). They an do so in order to minimize the psyhologial pain assoiated with a purhase. The rest of this paper is organized as follows. First, we present a formal mathematial proof outlining the onditions under whih a ombined-urreny prie is superior, and alternatively the onditions under whih a prie issued in one urreny is superior. In this setion, we outline how onvexity in the pereived ost funtions for one of the urrenies involved opens the door for a superior ombined-urreny prie: either by minimizing the psyhologial ost assoiated with a given revenue objetive, or by maximizing the revenue olleted given a partiular psyhologial ost. The three studies that follow demonstrate that ombined-urreny pries an be preferred by onsumers and support the preditions derived from our proofs. More speifially, in Study, results from a laboratory study suggest that a ombinedurreny prie an be preferred, partiularly for pries involving relatively small amounts of dollars and miles. Conversely, single-urreny pries are favored for relatively high pries. In 8

11 Study 2, we ask atual airline travelers to evaluate and make hoies among pries issued in single and ombined urrenies. The results illustrate how ombined-urreny pries an indeed be superior, and how preferenes shift systematially based on the magnitude of the prie. Study is limited in that respondents hose between a ombined-urreny prie and only one singleurreny alternative, and the results were aggregated aross respondents. In Study 2, we offered atual fliers a omplete range of hoies, yet pries varied by individual and the results were aggregated aross the range of pries. In Study 3, we repliate the prinipal results from Studies and 2 utilizing a within-subjets design as well as an idential, omplete menu of priing options. In addition, we apply a more rigorous test of the assumption of onvexity for at least one of the urrenies involved. The paper onludes by pointing out some of the limitations of this researh, offering some managerial impliations and suggesting avenues for future researh. COMBINING CURRENCIES TO LESSEN PERCEIVED COST In this setion, we show how non-linear valuations result in many instanes where marketers in order to seure a partiular revenue objetive with the least amount of psyhologial pain should harge pries in a mixture of urrenies (i.e., ombined-urreny priing). We also desribe situations in whih a prie harged in a single urreny is optimal. We begin by examining the ase in whih the pereived ost funtion for both urrenies is onave, followed by the ase in whih both ost funtions are onvex. We extend the disussion by desribing the ase in whih one is onave while the other is onvex, and onlude by desribing the expeted results when one urreny s pereived ost funtion is S-shaped. For simpliity and ease of exposition, we work with only two urrenies: C and C 2. We assume that the pereived ost funtion for eah inreases monotonially (giving up more miles or dollars is worse, less of either is better) and that the ompany possesses some transfer funtion 9

12 (i.e., exhange rate) for the two urrenies, whih is linear (i.e., one unit of C is worth α units of C 2 ). Without loss of generality, we an set α =. 3 The firm s target prie or revenue objetive an be desribed as a ombination of C and C 2 suh that: + 2 = r, where i 0 is the amount to be paid in urreny C i. () From the onsumer s perspetive, based on our assumption that onsumers do not onvert the two into any meaningful ommon unit of measurement, the subjetive value of and 2 vary independently. Thus, the subjetive loss or psyhologial ost (E) assoiated with surrendering some ombination of and 2 an be written as: E = f( ) + g( ) (2) 2 where f and g are stritly monotonially inreasing ontinuous funtions of and 2, respetively, defined over the interval [0, ) (i.e., f > 0 and g > 0). Further, f(0) = g(0) = 0, and f, g, f, and g exist over their whole domain. Let s assume the goal of the firm is to set a prie that seures its revenue objetive while minimizing the psyhologial ost to the onsumer. The goal ould just as easily be to maximize the revenue reeived given a fixed psyhologial ost, but pratially speaking, we expet firms to begin with established revenue objetives, not pereived values, when developing ombinedurreny pries. Thus, the firm must solve the optimization problem: Min E = f ( ) + g( ) st : = r 2 2 (3) * * A well-known mathematial result is that, for any given r, the solutions (, ) to equation (3) will be suh that: ' * ' * f ( ) = g ( ) for an interior solution, and 2 2 0

13 f ' ' (0) g ( r) > or ' ' g f r (0) > ( ) for a orner solution (see Appendix A). An interior solution will give rise to ombining urrenies, while a orner solution will give rise to a prie assessed in only one urreny. Therefore, the firm must determine when they are faing a orner solution and when they are faing an interior solution. This will depend on the subjetive valuations of onsumers (i.e., the shape of their pereived ost funtions) for urrenies C and C 2. In what follows, we show mathematially when a firm should harge a ombinedurreny prie issued in some ombination of urrenies C and C 2, rather than a prie issued in one urreny (C or C 2 alone) in order to extrat the revenue objetive, r, with the minimum psyhologial ost to the onsumer. We will assume that f(r) g(r) purely for expositional purposes, as all laims an be transposed for those situations in whih g(r) < f(r). We proeed by first examining the ase in whih the pereived ost funtions for both urrenies are onave, before proeeding to the ase in whih both are onvex. We then examine the ase in whih f is stritly onave and g is stritly onvex over [0, r], as well as the ase in whih f is stritly onave and g is S-shaped over [0, r]. CASE : Both f and g are stritly onave over [0,r] Imagine the ase of Wagner, a projet engineer who travels frequently for work and has flown more than 00,000 miles in the past year. He is living omfortably on his nearly $00,000 annual salary. Paying 5,000 miles or $50 more or less for most things is not likely to mean muh to him. In other words, whether he is buying an airline tiket using dollars or by redeeming miles, he is generally less sensitive to the marginal value attahed to hanges in both urrenies (i.e., in this ase both pereived ost funtions are onave).

14 Proposition : When both f and g are stritly onave (i.e., f >0, g >0 and f <0, g <0) we have a orner solution. The solution is (r, 0), the prie should be assessed entirely in one urreny (C ). We proeed in two steps in order to prove Proposition. First, we show that when both f and g are stritly onave, there are no interior solutions. Seond, we show that when f(r) g(r), (r, 0) is optimal. * * Step There are no interior solutions. If there were an interior solution (, 2 ) then it would be the ase that: ' * ' * f ( ) = g ( ) f " < 0 ε > 0, f ' g" < 0 ε > 0, g ( ' f ( f ( * * 2 ' ε ) > g ( ε ) + g( ' * 2 ( * 2 * * 2 + ε) < + ε) + ε) < ε) > f ( ' f ( ) * * ' f ( ) * ) + g( * * The last inequality ontradits the premise that (, ) minimizes E sine ( *, * ε + ) is a 2 * 2 ) 2 ε better solution and + * * * * ε ε = 2. Hene, no interior solutions exist when both f and g are stritly onave (QED). Step 2. If f(r) g(r) then (r, 0) is optimal. If there are no interior solutions then either (r, 0) or (0, r) is optimal. It follows that (r, 0) is optimal when f(r) g(r). Hene, when the psyhologial osts assoiated with eah urreny are stritly onave, the seller s deision is simple. For any given desired revenue, harge a prie in one urreny, the one that is valued least by the ustomer for the assoiated level of expenditure r. For any level of revenue, one urreny will always weakly dominate the other. The best urreny, however, may differ depending on the desired level of revenue, as the onavity of the ost funtions needn t be the same. In Figure, urreny 2 (C 2 ) should be used for amounts smaller than 30, the point at whih f(r) = g(r), and urreny (C ) should apply for amounts larger than 30. In other words, faed with a hoie between paying $89, $39 plus 6,000 miles, or 20,60 miles, if Wagner 2

15 behaves optimally, we d expet him to prefer to pay in either all dollars or all miles, depending on whih urreny he values less in that prie range. A orollary to this result is the following: for an individual to prefer a ombined-urreny prie to a pure payment (one made in either urreny alone), the psyhologial ost for the individual must be onvex over at least part of [0,r]. Therefore, we now look at those ases in whih the pereived ost funtion of either both, or only one urreny is onvex. CASE 2: Both f and g are stritly onvex over [0,r] Imagine Wagner plans to get engaged in a few months and begins diverting disretionary funds towards saving to buy his fianée a sizable diamond engagement ring ($9,000). Simultaneously, he begins his quest to aumulate enough miles to upgrade the ouple from oah to first lass on his honeymoon trip to Brazil (00,000 miles). Suddenly, he is more sensitive to spending either an additional $50 or 5,000 miles as relinquishing either might hinder or thwart his progress towards these goals. Wagner now attahes inreasing marginal disutility to expenditures in both urrenies. In this ase, we desribe how goals an reate inreasing marginal sensitivity, but it is easy to see how hanges in inome ould have the same effet. Proposition 2: When both f and g are stritly onvex, a orner solution will exist only if g (0) f (r). When g (0) f (r), we are in Situation, where a prie issued in a single urreny is optimal. Situation : If g (0) f (r) then (r, 0) is a orner solution Proof: g'' > 0 g'( ε ) > f '( r), ε > 0 f '' > 0 f '( r ε) < f '( r), ε > 0 g( ε) + f( r ε) > f( r) (QED) When g (0)<f (r), we are in Situation 2, where a ombined-urreny prie is optimal. Situation 2: If g (0)<f (r) there are no orner solutions 3

16 Proof: Sine g(r) > f(r), then (0, r) is not an optimal solution. Further, (r, 0) is not optimal either beause: g '(0) < f '( r) ε > 0 : g( ε ) + f ( r ε) < g(0) + f ( r) (QED) Hene, when g (0) < f (r), the optimal solution will be to use both urrenies in order to minimize the pereived or psyhologial ost (See Figure 2). In this ase, we annot tell whether Wagner would prefer paying in a single urreny, or to split his payments. He may want to preserve miles, as they are relatively harder to ome by (he reeives a regular pay hek, but flies intermittently), and favor paying in all dollars whenever he an. Or, he may not quibble about small amounts of miles if he flies often, and instead favor ombined pries that do not tax his frequent flier aount. The important point is that, unlike the onave-onave ase, even if he is behaving optimally, a ombined prie an be preferred. CASE 3: Either f or g is onave while the other is onvex over [0, r] Now let us imagine that Wagner has purhased the ring, yet is still several thousand miles short for the first lass upgrades to Brazil. His fianée s parents are paying for the wedding, so the disutility of eah dollar he spends has diminished, while the psyhologial ost of eah mile spent (taking him away from his goal) ontinues to inrease as he nears the 00,000-mile mark neessary for the upgrades for his honeymoon to Rio de Janeiro. Let us examine the ase in whih f is stritly onave and g is stritly onvex over [0,r]. When one of the two funtions is onave (f), while the other is onvex (g), there exist three possible optimal situations:. We have a orner solution (0, r g ) r : g'( r ) f '(0) 2. We have a orner solution (r f, 0) r : f '( r ) g'(0) and f ( r ) g( r ) 3. We have an interior solution in all other ases. g f g f f f 4

17 To more fully understand when eah situation might apply, examine what happens to E as r inreases. At 0, no payment is made in either urreny. If f (0) g (0), then all payments are always made in urreny C (situation 2) as f(r) < g(r) and ε 0 g'( x) dx > r r ε f '( x) dx for ε < r. This is a rather uninteresting ase. In ontrast, when f (0) > g (0), we begin in situation, where all payments are made in the seond urreny (C 2 ). As r inreases, we move to situation 3, where payments are made in some ombination of urrenies C and C 2, and finally progress into situation 2, where all payments are made in urreny C. Indeed, when r moves away from 0, the firm will be better off asking for payment in only C 2 as g'( x) < f '(0), x< rg. This will hold true until g (r g ) = f (0) (as g > 0, this annot hold indefinitely). As seen in Figure 3, after r g the firm will minimize the psyhologial ost to the onsumer by asking for payments made in a ombination of both urrenies (C and C 2 ) as f '( ε) < g'( r ε). As r inreases, the firm will redue the amount to be paid in C 2 and inrease the amount to be paid in C until r f, the point at whih the portion of the payments that are made in C 2 shrink to 0. For any amount bigger than r f, only payment in C should be requested. In this ase, Wagner may prefer to part with small amounts of miles (e.g.,,000), but prefer paying ash for a shuttle tiket rather than give up 25,000 miles, as that would seriously impat his progress towards the free first-lass upgrades. If he had aumulated the neessary miles, but not paid off the ring, we ould expet the opposite, as he would prefer to use miles and apply the equivalent sum in ash towards the ring. 5

18 CASE 4: Either f or g is S-shaped while the other is onave or onvex over [0,r] In Case 4, we examine two extensions: () the ase where f is stritly onave and g is S- shaped over [0,r] (see Figure 4), and (2) the ase where f is S-shaped and g is stritly onvex over [0, r]. When f is onave and g is S-shaped over [0, r], the form of payment will depend on the derivatives of f and g at 0. Situation : Situation 2: If f (0) g (0), then we revert to the onave-onave situation (orner solutions where payments are made exlusively in C or C 2 depending on whether f(r) is smaller than g(r)). 4 If g (0)<f (0) then we have a situation analogous to the onave-onvex ase: a. We have a orner solution: (0, r g ) r: g'( r ) f '(0) b. We have a orner solution: (r f, 0) r : f ( r ) < g( r ) and f '( r ) < g '(0) f f f f. We have an interior solution in all other ases. g When f is S-shaped and g is stritly onvex over [0, r], the solution will depend on the derivative of g at its infletion point. If g (infletion) f (0), then the situation is analogous to the onaveonvex ase where f (0)<g (0). All payments should always be harged in urreny (C ). If g (infletion) > f (0) then we have three payment shedules:. split payment inreasing in both C and C 2 (à la onvex-onvex ase) up to the point where f ( r ) =g ( 2r )= g (infletion). 2. split payment inreasing in C, dereasing in C 2 (à la onaveonvex ase) up to the point where f (r f ) =g (0). 3. payment in C only (orner solution) for r : f '( r ) < g'(0). We should also point out that when both f and g are S-shaped over [0, r], we have a situation analogous to the S-shaped-onvex ase. f f 6

19 One of the primary goals of this researh is to show that in numerous instanes, the optimal prie in terms of minimizing the pereived ost to the onsumer entails setting a prie that mixes C and C 2, the two urrenies involved. This ould easily our when the amount harged in C falls in the onave region of its S-shaped pereived ost funtion and the harge in C 2 falls in the onvex region. In Study, we illustrate how the subjetive value that onsumers asribe to differing amounts of an individual urreny (i.e., money, miles) appears not to be linear, resulting in a situation where both interior and orner solutions an exist at different points over the range of pries for the same two urrenies. STUDY As desribed earlier, given two urrenies, if the onsumer s pereived ost funtion inludes a onvex region for one urreny, the firm an impose the minimum psyhologial ost assoiated with a partiular revenue objetive through the use of a ombined-urreny prie. With this in mind, Study is designed to illustrate two key points. First, for dollars and frequent flier miles, we show that an interior solution an exist suh that onsumers prefer a ombinedurreny prie. We expet to see signs of inreasing marginal disutility for miles and/or money when this type of priing struture is preferred. Seond, we show that a orner solution an also exist, where a prie in one urreny or the other dominates. Method Subjets. Partiipants in this study were 670 undergraduate business students enrolled in an introdutory marketing ourse at a major West Coast university. Of the 670 students, 363 or 58% of partiipants reported possessing an ative frequent flier aount ontaining miles. We limited our analysis to these partiipants responses in an attempt to insure 7

20 that our results would only reflet hoies from airline loyalty program members with experiene olleting miles. 5 Stimuli and design. Partiipants ompleted a senario-based, paper and penil study in whih they were asked to imagine they were purhasing an airline tiket with either dollars or frequent flier miles. At the onset of the experiment, eah respondent was asked whether he or she had a frequent flier aount, and if so to indiate how many miles they had in their largest aount. This would allow us to ontrol for experiene with the alternative urreny. Partiipants were subsequently instruted to disregard their personal aounts and to assume they possessed enough miles and money to aommodate whihever priing option they preferred. The ost of the tiket was either low ($250 or 25,000 miles) or high ($,000 or 00,000 miles). The base prie did not inlude a mandatory surharge, whih ould be paid in either dollars ($50) or miles (5,000). A pilot test found respondents from the same sample population valued 5,000 at approximately $50, or $0.0 per mile, whih was onsistent with our expetations. Respondents task was to hoose between priing shedules, whih inluded the surharge in either dollars or miles. The senario with miles as the base ost read as follows: You are on the phone with an airline seuring a round-trip tiket aross ountry to attend the funeral of an unle you really liked and admired. While you an t leave town for two days, you must pay for the tiket today. The prie of the tiket is 25,000 [00,000] miles. The agent on the phone tells you that in order to have your tiket request expedited, whih would be neessary to reeive your tiket in time for your departure, you will need to surrender either an additional 5,000 miles or pay $50. How would you prefer to pay? 25,000 + $50 25, ,000 miles An additional hoie senario required respondents to hoose between paying entirely in dollars or entirely in miles. The basi senario read as follows: 8

21 You are on the phone with an airline seuring a round-trip tiket aross ountry to attend the funeral of an unle you really liked and admired. While you an t leave town for two days, you must pay for the tiket today. There are two possible prie ombinations with whih you an pay for your tiket. First, you an pay $250 [$,000] for the tiket plus an extra $50 to have your tiket order expedited, whih would be neessary to reeive your tiket in time for your departure. Or you an surrender 25,000 [00,000] miles for the tiket, and an additional 5,000 miles to have your tiket expedited. How would you prefer to pay? The remaining two hoie ombinations were inluded for ompleteness, whih fored respondents to hoose between paying either $ ,000 miles or 25,000 miles + $50, and $, ,000 miles or 00,000 miles + $50. A number of the partiipants reeived more than one of the hoies, whih were rotated and ounterbalaned. If respondents possessed a linear transformation funtion between money and miles, and the exhange rate were onstant at one mile equaling one ent, they should have always be indifferent between the two priing shedules. If the pereived ost funtion were linear, and on average respondents valued eah mile at more (less) than one ent, they should always prefer to pay the prie that inludes more (less) money. Our predition, however, was that for relatively small revenue objetives or pries ($250 or 25,000 miles), respondents would prefer a ombination of miles and dollars to payments exlusively in one urreny, requiring onvexity for one of the urrenies in this range. This implies an interior solution. On the other hand, when the revenue was relatively large ($,000 or 00,000 miles), we expeted respondents to prefer paying in one urreny alone, whih would imply onavity in this region. This implies a orner solution. Note that this pattern of results would be onsistent with an S-shape pereived ost funtion for miles or money, or both. 9

22 Results The results are summarized in Table 2. As predited for Part (the first olumn), for payments in the Relatively Low Total Cost onditions, a signifiant majority of respondents preferred the ombined-urreny pries to harges issued in a single urreny. This suggests that for expenditures involving only 5,000 miles, respondents preferred paying in miles, while for expenditures from 25,000 to 30,000 miles, respondents preferred paying the surharge in dollars. This result suggests the marginal value of miles inreases at an inreasing rate (onvexity). Conversely, in the Relatively High Total Cost onditions, respondents preferred paying in a single urreny (i.e., $,050 and 05,000 miles respetively), implying the inremental 5,000 miles is worth more alone than when added to 00,000 miles, or the value of miles inreases at a dereasing rate (onavity). These results onform to the preditions from our mathematial proofs, and are onsistent with an S-shaped pereived ost funtion for miles. If the pereived ost funtion is onvex over small amounts of miles, and the pereived ost funtion for money is assumed to be onave, we would expet an interior solution (respondents preferring to pay in bundles of money and miles) rather than a orner solution (a preferene for a prie in either solely money or miles). Indeed a ombined-urreny prie is preferred in this range. And, given that the pereived ost funtion appears onave for large amount of miles, we would expet the opposite to our in the $,000 and 00,000-mile onditions. In this range, most respondents preferred pries in one urreny alone (a orner solution). We should point out that this pattern of results is also onsistent with two S-shaped ost funtions or two onvex ost funtions, where the value of money inreases faster than that of miles. Notie that, when limited to single-urreny pries, for relatively small amounts ($300, 30,000 miles) people preferred paying entirely in dollars. Conversely, for relatively high pries ($,050, 05,000 miles), people preferred to pay using miles exlusively (See Table 2, Part 2). 20

23 This implies their valuation for dollars did inrease faster than for miles as the amount to be spent inreased. Not surprisingly then, when fored to hoose between ombined-urreny pries (See Table 2, Part 3), for relatively small amounts, subjets favored the payment omprised prinipally of dollars (75% versus 25%). The reverse was true when the ombined-urreny pries were relatively high ($,000 plus 5,000 miles versus 00,000 miles plus $50) with far more respondents preferring the priing shedule omprised prinipally of miles (85% versus 5%). While the exat turning point where people swithed from preferring to pay in dollars to paying in miles may depend on the exhange rate we utilized ($0.0), we expet the general result to hold; the exhange rate between the two urrenies among onsumers is not onstant. We should remind the reader that relativisti proessing (Nunes and Park 2003) may have affeted how respondents evaluated the surharge ($50 in addition to $250 versus $,000 and 5,000 miles in addition to 25,000 versus 00,000 miles). The hanging nature of these valuations is entirely onsistent with our hypothesizing. Reall that in our pretest, subjets valued 5,000 miles and $50 as equivalent. Yet when added to 25,000, they would prefer to surrender the $50 and retain the 5,000 miles. This suggests inreasing marginal disutility and preditably, a ombined-urreny prie is preferred. When added to 00,000 miles respondents preferred to pay the 5,000 miles, or a single-urreny prie, whih is onsistent with diminishing marginal disutility. The same pattern holds true for a ash surharge. To rule out the possibility that subjets urrent frequent flyer mile holdings influened our results, we ran a separate ANOVA for eah hoie, where the average number of miles held by those favoring one option was ompared to the average number held by those favoring the opposing option. None of these omparisons was signifiant (p-values ranging from 0.2 to 0.96; average p-value = 0.58), suggesting that their deision did not depend on the number of miles in their aounts. In addition, we ran eight separate logit models on hoie using the individual s 2

24 holdings in miles as a ovariate to determine whether holdings in miles ould predit hoie. None of the oeffiients was signifiant (p-values ranging from 0.5 to 0.96; average p-value = 0.58). Disussion The results from Study illustrate how an interior solution an exist, resulting in the ase where a ombined-urreny prie is preferred. While we annot say with ertainty whether the pereived ost funtion is onvex for miles, money or both, mathematially we have demonstrated that onvexity must exist for one or both urrenies in the low-ost ($300/30,000- mile) range. This onvexity may ontinue into the relatively high-ost range ($,050/05,000- mile), although the preferene for single-urreny pries among most subjets is also onsistent with both funtions being onave in this range, suggesting an S-shaped pereived ost funtion for one of the urrenies, whih we suspet is miles. STUDY 2 In Study, respondents were undergraduates, albeit business students, whose relative inexperiene with transations involving miles may have affeted their deision-making. Respondents hose among prie shedules similar to what airlines offer (e.g., $89 or $39 plus 6,000 miles) and not a full range of options, whih would inlude both single-urreny pries as well as the ombined-urreny prie. In Study 2, we extend the results of Study by: () surveying members of a partiularly relevant test population; (2) allowing respondents to hoose between paying the ombined-urreny prie or paying in either of the two urrenies involved (money or miles); and (3) examining how their preferenes shift as the revenue objetive 22

25 represented by these priing options hanged. The revenue objetive or prie was determined by the atual prie of the tiket held by flier surveyed. Given our findings from Study, we hypothesized that people s preferenes for ombined-urreny pries would diminish as the revenue objetive inreased, and that those favoring a single-urreny prie would prefer paying in dollars for relatively low-pried tiked and yet in miles for relatively high-pried tikets. Reall that in Study, when limited to singleurreny pries, people preferred paying entirely in dollars for small amounts, but entirely in miles for large amounts, suggesting their valuation for miles diminished faster than for dollars as the amount to be spent inreased. Method Subjets. This experiment was run in a real world setting in an attempt to insure external validity. Partiipants were 64 passengers on ommerial flights that were sheduled to depart from a major West Coast airport (this was prior to 9-). The passengers were approahed at the airport prior to their departure and asked to partiipate voluntarily in an aademi study of airline tiket purhasing behavior. Partiipants were sreened on the basis of whether or not they maintained a frequent flier aount in whih they arued miles only those who possessed frequent flier aounts partiipated. Again, we expeted a signifiant proportion of fliers to favor a ombined-urreny prie. Stimuli and design. At the onset of the experiment, respondents were asked to reall what they had paid for the tiket that brought them to the airport at the time of the survey (all partiipants were waiting to take a flight when asked to partiipate). After they stated the prie paid in either dollars or miles (only two flyers redeemed miles), the experimenter, unbeknownst 23

26 to the respondent, onverted this amount into an equivalent prie in the opposing urreny at a rate of $0.02 per mile (e.g., $200 and 0,000 miles), as well as a ombined prie with 50 perent paid in eah urreny (e.g., $00 and 5,000 miles). For simpliity, we limited their hoies to dollars only, 50% dollars/50% miles, or miles only. The partiipant was then asked whih of three pries they would have preferred to pay if they had been offered the hoie (e.g., $200, $00 plus 5,000 miles, or 0,000 miles). Results Overall, we find that 24% of respondents preferred to pay in dollars only, 34% preferred to pay in miles only, and 42%, or the largest segment of travelers surveyed, preferred paying in a ombination of urrenies (see Figure 5a). A primary goal of Study 2 was to explore how and when people s preferenes shift among priing options (dollars only, a ombined-urreny prie, or miles only) aross the various amounts to be paid. Therefore, we examine the probability that a person surveyed would hoose a partiular priing option as a funtion of the prie paid. The data were analyzed using the ategorial modeling proedure of the SAS statistial software pakage (CATMOD), whih allowed us to fit a multinomial logit model using hoie, or the probability of hoosing a partiular priing shedule, as the dependant measure and prie as independent variable. The hoie of one payment option over another varied signifiantly with prie (χ 2 = 8.23, p < 0.00). In order to more easily interpret the results we omputed the hoie probability for tikets ranging from $0 to $2,500, the highest prie reported among those surveyed and graphed them in Figure 5b. As is lear from the figure, for small dollar amounts (Prie < approximately $300), straight dollar payments were the most likely option. For intermediate tiket values ($300 < Prie < $,200), mixed payments were preferred. Finally, for relatively more expensive tikets (Prie > 24

27 $,200), onsumers preferred to purhase the tikets using miles alone. Hene, we find support for our hypothesis, whih is onsistent with the results from Study and our general framework. We should note two aveats regarding the interpretation and generalization of these results. First, we used an exhange rate of two ents per mile. This will affet the relative attrativeness of paying in miles rather than dollars. A lower value, suh as one ent per mile, would be likely to shift the urves depited in Figure 5b to the right, suh that strit dollars payments are preferred over a larger domain, and strit miles payment are preferred over a smaller domain. We would also expet the net impat on mixed payments to be a shift to the right, but it is not possible to tell whether they would be preferred over a wider or narrower range of tiket pries without olleting more data. Seond, the only form of ombined-urreny pries we investigated were equally balaned, or a 50/50 split. It is possible that other mixtures (e.g., 80/20) would be preferred to any of the three forms tested (we investigate this further in Study 3). Hene, it is likely that the range of pries over whih a ombined-urreny prie is preferred is wider than highlighted by our experiment. Disussion First and foremost, the results from Study 2 reinfore the notion that a ombined-urreny prie an be the preferred option among onsumers. The results also suggest preferenes among ompeting prie shedules an depend on the amount onsumers intend to spend. Just as in Study, surrendering primarily dollars is preferred at the low end, while paying primarily in miles is preferred at the high end. In the middle range, ombined-urreny pries are most widely favored. In both Studies and 2, however, the results emerge from data aggregated aross deision makers. Therefore, we annot say with ertainty that the same patterns would hold at the individual level. 25

28 STUDY 3 Study 3 addresses many of the limitations of Studies and 2 by utilizing a within-subjet design in whih respondents, who were all frequent fliers with sizable mile aounts, rank ordered the exat same set of prie shedules, inluding both single-urreny prie options and several different ombined-urreny options. While we do not explore how the revenue objet affets hoie in this study, we do apply a more rigorous test of the assumption of onvexity for eah onsumer s set of preferenes. Method Subjets. Partiipants in this study were 3 full-time MBA students at a major West Coast university. Of those surveyed, 4 did not possess frequent flier aounts and were exluded from the analysis. The average number of programs in whih the remaining 99 respondents were enrolled was 2.5 (median = 3), having olleted miles for an average of 7.5 years (median = 6). At the time of the survey, they possessed an average of 58,000 miles (median = 35,000) in their largest frequent flier aount. Every one of the 99 members had at one time or another flown using a tiket seured with miles. Consequently, our analysis inludes only experiened fliers familiar with dealing in transations involving frequent flier miles. All respondents partiipated voluntarily. Stimuli and design. Respondents were first-year MBA students who were sheduled to partiipate in an overseas program at the onlusion of the spring 2002 semester in whih they would visit one or more ountries in the Asia-Paifi region. Eah had already purhased their travel pakage through the university. Their pakage prie did not separate out the harge for airfare (i.e., they did not know what they paid for their airfare), but the survey asked students to 26

29 imagine that in the future, suessive student groups (e.g., next year s lass) would be offered the opportunity to buy their tiket separately. Additionally, they were told that future groups might possibly be able to hoose from various pries omprised of payments made in frequent flier miles and/or dollars, and that the program offie would like to gauge their preferenes as an indiator for how to handle travel arrangements in the future (i.e., whih prie shedules to offer). They were instruted to assume the flier would own enough miles to over any option and that future partiipants would be able to travel on their preferred airline, no matter whih option they favored. Respondents then ranked five prie shedules in terms of their preferenes ( for most preferred prie to 5 for least preferred prie). The five prie shedules presented were: $700, $560 plus 7,000 miles, $350 plus 7,500 miles, $40 plus 28,000 miles, or 35,000 miles. A prie of $700 was entirely in line with what was atually paid by the shool for most tikets. Results The primary purpose of study 3 was to do a within-subjet test of our hypotheses. Given a series of hoies whih are equivalent to the firm in their value, if onsumers have stritly onave valuations for miles and money, they will only pik as their first hoie one of the pure prie options (i.e., all miles or all money). If they have linear valuations, they will be indifferent between all of the hoies and thus all priing options would be piked in the same proportion. The rankings olleted fall into 24 distint response profiles (See Table 3). Only seven of these profiles (profiles 2, 4, 3, 4, 7, 20, and 22; or 32 respondents) exhibit a orner solution (i.e., respondents prefer to pay in a single urreny). The other 7 profiles reveal that the majority of respondents (67 out of 99) prefer a ombined-urreny prie to paying in either all miles or all dollars. This preferene for a ombined-urreny prie demonstrates that their 27

30 pereived ost urves are not stritly onave for both urrenies. Further, if we look at the distribution of first hoies (see last line of Table 3), we have an safely rejet (p < 0.000) the possibility that these first hoies were made at random. Thus, we find support for neither the onave nor the linear valuation hypotheses; hene, there must exist some onvexity in most of our respondents pereived ost funtions. Going one step further, using the linear programming software LINDO (Shrage 997), we an hek if individual respondents rank-ordered all five pries in a way that is onsistent with two onave ost funtions, inluding those 32 who piked a single-urreny prie as their preferred option. We analyze the data by imposing only that eah ost funtion is either onave, onvex, or S-shaped without imposing any speifi funtional form (See Appendix B for a detailed desription of the methodology). We speify the restritions on eah of the utility funtions independently so that, a priori, one ould see any mix of shapes aross miles and money. If LINDO ould solve the linear program without violating any onstraints, then the profile was lassified as onsistent with a hypothesis of onavity for both miles and dollars (Y in olumn CC-CC of Table 3). For those favoring an interior solution (i.e., their first hoie was a ombined-urreny prie), their orderings learly violated the onavity restritions on both miles and dollars. In addition, we find that two profiles (7 and 22, in italis in Table 3) violated the onavity restritions on both miles and dollars. Hene, 69 out of 99 subjets (70%) expressed preferenes inonsistent with purely onave pereived ost funtions. We should point out that the data are also onsistent with a S-shaped ost funtion for miles, but many more hoie options would be required to distinguish between a onvex and an S-shaped pereived ost funtion for miles, whih for our purposes is unneessary. Further, as a testament to respondents adhering to the instrutions, and a sign that individual wealth effets do not appear to be driving hoie in this ase, the average number of miles owned by respondents 28

31 did not differ depending on whether they exhibited a orner solution or interior solution (p = 0.2). Disussion In summary, the results from this study reveal a strong preferene for an interior solution among experiened fliers, who hose from the idential, riher set of priing options. Within the range of miles and dollars utilized, we an rule out onave-onave pereived ost funtions for those two-thirds of respondents who favored a ombined-urreny prie. In addition, while a onave-onave senario ould apply to 30 of the 32 respondents who favored a orner solution, a onave-onvex senario ould apply to the entire sample. Reall from Case 3 of our mathematial proofs that even when the pereived ost funtion for one urreny is onave and the other onvex, a orner solution (preferene for paying in a single urreny) is entirely possible. This is espeially true sine we test only a disrete number of possible pries ombinations rather than the ontinuous range from 0 to 00% dollars. It is worth pointing out that while the option was the preferred priing shedule in Study 2 (it was the only ombined-urreny prie available), the same mix was the least favored option among the broader set of priing shedules available in Study 3. This highlights the importane of determining the right mix among urrenies when offing ombined-urreny prie. CONCLUSION, LIMITATIONS AND FUTURE RESEARCH The objetive of this researh was to determine the onditions under whih what we have labeled a ombined-urreny prie an be superior to a prie harged in a single urreny. In doing so, we seek to help explain the reent emergene and inreasing proliferation of ombinedurreny pries in the marketplae. Our mathematial proofs show how non-linear value funtions 29

32 result in many instanes where marketers should harge ombined-urreny pries, speifially when the pereived ost funtion for one of the urrenies is onvex within the range in question. A ombined-urreny prie in this ase ould maximize the amount of revenue olleted given a set psyhologial ost, or minimize the psyhologial ost assoiated with a given prie. Both the anedotal real-world evidene and our experimental evidene illustrate how people often prefer to pay pries omprised of payments in more than one urreny. More speifially, in Study, we offered evidene that both a ombined-urreny prie (i.e., interior solution) and a single urreny prie (i.e., orner solution) an be superior within the same population of onsumers, while simultaneously demonstrating a pattern of hoie onsistent with a onvex pereived ost funtion for one of the urrenies involved. In Study 2, we demonstrated how hoies made by atual fliers onform to the general preditions laid out in our proofs and are onsistent with the results of Study. In Study 3, we olleted more detailed individual level data, and provided more diret evidene that people who favor a ombinedurreny prie must have onvexity in the pereived ost funtion for at least one of the urrenies involved. Taken together, these studies provide onvergent evidene supporting the expeted requirements for, and benefits from, ombined-urreny priing. The studies are not without their limitations. Both studies and 2 rely on aggregate data, while studies and 3 rely on students as respondents. None of the studies speifies for whih urreny the onsumer s pereived ost funtion is onvex, and we never attempt to doument the underlying ause(s) for the shapes of the pereived ost funtions. We were areful, however, to (a) insure that the results of Study hold using the responses from only those partiipants who were frequent flier members, and to (b) qualify students in Study 3 based on their experiene aumulating and transating in miles. 30

33 In Study, respondents may have favored a single-urreny prie beause as the payment grew larger in one urreny, the pereived ost of traking a transation in the other urreny appeared larger. We reognize that the existene of transation osts, and their relative magnitude, an affet the relative attrativeness of ombined-urreny pries. This would our most often with pries that inluded extremely small amounts in one of the urrenies, and thus a firm may be well served to strategially avoid suh highly skewed offerings. While this researh highlights the importane of ombined-urreny pries and illustrates the advantages to firms that implement them well, it is also limited in the sense that it does not go into detail as to how the firm an derive a preise prie for a partiular ustomer or set of ustomers. While we test the general shape of respondents pereived ost funtions in Study 3, we did not measure these funtions with a great degree of preision. Pratially speaking, a firm ould better asertain the shape of a partiular individual s pereived ost funtion for speifi urrenies using a more omplete onjoint analysis design. This proess would be far more burdensome in terms of the time required by eah partiipant, and hene far more ostly than what we have done here. Developing a ost effetive way to do this diretly for a population or segment of interest would appear to be an important avenue for future work. Combined-urreny pries are designed to minimize the psyhologial ost assoiated with a partiular revenue objetive by taking advantage of people s inability, relutane, or lak of desire to onvert amounts assessed in one urreny into denominations of the other urreny (Nunes and Park 2003). Of ourse, important individual differenes may moderate the effetiveness of ombined urreny pries. It may be that ertain onsumers ontemplating spending miles, dollars or any mixture of two urrenies may have diffiulty realling or onstruting a value for varying amounts of either or both. Or, that for ertain onsumers, the relevant information is unavailable or inaessible. This researh did not explore the proess by 3

34 whih onsumers assess the pereived ost assoiated with various inrements of eah urreny or ompare prie shedules. Future researh may be direted towards developing a proess level model of hoie involving pries in ombined urrenies with an eye towards those fators that mediate or moderate their attrativeness. The proess onsumers utilize is likely to be affeted by the omparability of the urrenies and their knowledge or experiene with eah. In the same way that Johnson (984) suggests experts should be more likely to use within-attribute strategies for omparing alternatives, we d expet those who fly all the time to possess or onstrut some sort of exhange rate in order to make the relevant omparisons aross prie shedules. As within-attribute strategies all for omparing attributes diretly, we d expet regular fliers to ompare $39 plus 6,000 miles versus $89 by simply mathing dollars to dollars and miles to miles. Hene, they would be left to determine whether paying $50 or 6,000 miles is preferable. They might do so by applying their idiosynrati exhange rate, a well-known exhange rate (2 ents), or by onsidering how long it takes to aumulate eah (onverting units in eah into time). Conversely, non-experts (i.e., infrequent fliers) may utilize what Johnson alls an aross-attribute proess, making an overall evaluation in whih omparisons are made at a very abstrat level. This would orrespond to these onsumers simply asking themselves, What hurts more, $89 or $39 plus 6,000 miles? The latter proess seems more in line with the hoie patterns we observe, leading us to suspet our results are onsistent with the behavior of most onsumers who fly relatively infrequently. With inreased exposure and experiene, the onversion between two or more partiular urrenies ould, in theory, beome seond nature. If this were the ase, ombined-urreny pries aross these urrenies might be expeted to lose their effiay. However, the multitude of buy and sell rates in the marketplae suggests this type of flawless interhangeability is unlikely, 32

35 although future researh ould explore how firms ould further obfusate the value of alternative urrenies suh as miles or points in terms of other urrenies. Perhaps firms are already doing this intentionally through their offerings, but praties that inrease or derease the ease with whih onsumers ompare prie shedules alternatives seems ripe for work by researhers interested in priing. In this researh, we have foused on the pereived ost assoiated with surrendering various amounts of urrenies. The mathematis should apply whether one is surrendering or aquiring the amounts in question. Another interesting avenue for future researh may be to investigate any asymmetries in valuation based on whether one expets to give or reeive payments in more than one urreny. The wife of one author reently inquired as to whether giving a $00 gift ertifiate from a partiular restaurant would be pereived as more generous than a $50 restaurant ertifiate and $50 in movie passes. She was onvined that one $00 ertifiate would seem grander. Her idea did not go unnotied and we have begun exploring this question in more detail. In addition, while we have speulated that goals an ause loal onvexities in the pereived ost funtions for urrenies, we do so in the absene of wealth effets. It would be interesting to examine not only how expenditures are pereived in relation to goals, but also how asset levels in the relevant urrenies an affet deision-making. To this end, exploring how goals and asset levels interat to affet hoie seems like a partiularly relevant and important area for future researh, one that we have already begun studying. 33

36 ENDNOTES. This laim was made on its web site in July 200. At the time the airlines Milepoint.om partnered with inluded Delta Air Lines, Northwest Airlines, Continental Airlines, US Airways, Ameria West Airlines, Midwest Express Airlines, Hawaiian Airlines, Hilton Hotels, and Amerian Express Membership Rewards. Members ould spend their miles at online retailers inluding Amazon.om and Skymall, as well as suh premium retailers as Hammaher Shlemmer and The Sharper Image. 2. Most soures suggest onsumers should value miles between one and two ents per mile, whih is the exhange rate we use in our experiments. Business Week (999) reports that, onventional wisdom says a mile is worth about 2 ents - around what major airlines harge ompanies that buy mileage for inentive awards to employees or lients. In reality, airlines inlude a ontingent liability in their aounts to over the ost of unredeemed miles, whih are valued at marginal ost a lot less than what they sell them for (Eonomist 2002). For example, when a travel award level is attained for a member of United Airlines, the liability is reorded for the inremental osts of providing travel, based on the expeted redemptions. The inremental osts inlude the additional osts of providing servie to the award reipient, suh as fuel, a meal, personnel and tiketing osts, for what would otherwise be a vaant seat. As of Deember 3, 999, the estimated number of outstanding awards was approximately 7 million, of whih UAL estimated that only 5.8 million awards would ultimately be redeemed and, aordingly, reorded a liability of $75 million. Considering only those miles UAL expeted to be redeemed, the airline might be onsidered as valuing eah outstanding mile at about 2/00ths of one ent. While other miles are redeemed for goods and servies at an undislosed rate, our disussions with marketing and priing managers from various airlines indiate that mileage promotions involve so few miles, relatively speaking, that a onstant or linear valuation from the airline s perspetive is an entirely reasonable assumption. ' 3. We an always set = 2 = α2. 4. Situation is a speial ase where although g is S-shaped, its slope at the origin is steeper than the slope of f at that point (f (0) g (0)). This results in the onvex portion of g to be above f. Thus f (x) in the onvex portion of the S will always be greater than g (y) regardless of the value of y. This yields a result suh that it will never pay to split payments between C and C An analysis of the data inluding all respondents gave equivalent results. 34

37 TABLE SOME COMMON REWARDS AND THEIR VALUE IN DOLLARS ON /28/200 Reward Provider Miles Dollars Exhange Rate Palm Pilot VII Amerian Airlines/AOL Program 78,500 $227* $ Admirals lub Amerian Airlines 40,000 $300 $ Membership (add a spouse) Amerian Airlines 25,000 $50 $ $500 of losing Citibank Home Mortgage 25,000 $500 $0.02 Time Magazine Milepoint.om 900 $24.95** $0.027 Upgrade Award United Airlines 2,000 $25 $0.0625*** *Average prie on CNET.om **Subsription prie for ½ year at Time.om and prie in miles for 27 issues. ***This is UAL s selling prie for four 500-mile upgrades. 35

38 TABLE 2 Study : Perentage Preferring Pure vs. Combined-Curreny Pries Part Part 2 Part 3 Relatively Low % preferring Total Cost payment option $300 or 30,000 miles $250 + $50 30% 75% $ ,000 miles 70% (63)* 75% 25,000 miles + $50 65% 25% (59)* 25, ,000 miles 35% (63)** 25% (55)* Relatively High Total Cost $,050 or 05,000 miles $,000 + $50 79% 8% $, ,000 miles 2% (63)* 6% 00,000 miles + $50 30% b 85% (6)* 00, ,000 miles 70% (63)* 82% (63)* Note: Numbers in parentheses indiate the number of responses for eah pair. Responses exeed the number of partiipants as many responded to more than one hoie question. Pairs with * differ signifiantly at p < 0.0. Pairs with ** differ signifiantly at p <

39 TABLE 3 Study 3: Response Profiles Profile $700 & 0K $560 & 7K $350 & $0 & # of $40 & 28k 7.5K 35k Respondents Interior CC-CC Y N* N Y Y N N Y Y N Y N Y N Y N Y N Y N Y N Y N N Y N Y Y N Y N N N Y N Y N N Y Y N N N Y N Y N st Choie 8** NOTES: * To be read: 25 respondents rank ordered the 5 pries, from best to worse, as $560 & 7K, $40 & 28k, $700, 35k, $350 & 7.5K. The preferred prie bundle is an interior point. For optimal hoies, it annot our if both urrenies exhibit onave utility funtions. ** To be read: 8 out of 99 respondents hoie $700 & 0K as their preferred form of payment. 37

40 Figure : Conave Conave (Psyhologial Costs and Optimal Pries) 38

41 Figure 2: Convex Convex (Psyhologial Costs and Optimal Pries) 39

42 Figure 3: Conave Convex (Psyhologial Costs and Optimal Pries) 40

43 Figure 4: Conave S-shaped (Psyhologial Costs and Optimal Pries) 4