A Probabilistic Approach to Pricing a Bundle of Products Or Services Author(S): R

A Probabilistic Approach to Pricing a Bundle of Products or Services Author(s): R. Venkatesh and Vijay Mahajan Reviewed work(s): Source: Journal of Marketing Research, Vol. 30, No. 4 (Nov., 1993), pp. 494-508 Published by: American Marketing Association Stable URL: http://www.jstor.org/stable/3172693 . Accessed: 07/11/2011 11:11

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http://www.jstor.org R. VENKATESHand VIJAYMAHAJAN*

The authors propose a probabilistic approach to optimally price a bundle of products or services that maximizes seller's profits. Their focus is on situations in which consumer decision making is on the basis of multiple criteria. For model development and empirical investigation they consider a season ticket bundle for a series of entertainment performances such as sports games and music/dance concerts. In this case, they assume consumer purchase decisions to be a function of two independent resource dimensions, namely, available time to attend performances and reservation price per performance. Using this information, the model suggests the optimal prices of the bundle and/or components (individual performances), and corresponding maximum profits under three alternative strategies: (a) pure components (each performance is priced and offered separately), (b) pure bundling (the performances are priced and offered only as a bundle), and (c) mixed bundling (both the bundle and the individual performances are priced and offered separately). They apply their model to price a planned series of music/dance performances. Results indicate that a mixed bundling strategy is more profitable than pure components or pure bundling strategies provided the relative prices of the bundle and components are carefully chosen. Limitations and possible extensions of the model are discussed.

A Probabilistic Approach to Pricing a Bundle of Products or Services

Bundling, the strategy of marketing two or more prod- ternative strategies to offer her or his products or ser- ucts and/or services as a "package" at a special price vices (Schmalensee 1984): (Guiltinan 1987), is a pervasive practice in the marketing 1. Pure components:The seller prices and offers the com- of and services. Examples include vacation products ponentproducts/services as separateitems, not as bun- packages, assortments of food products (e.g., cookies), dles. season tickets for entertainmentperformances, computer 2. Pure bundling:The seller prices and offers the compo- hardware and software combinations, and meal specials nent products/servicesonly as a bundleand not as in- in restaurants. dividualitems. In these situations, in general, a seller faces three al- 3. Mixed bundling:The bundle as well as the individual componentproducts/services are priced and offered separately. *R. Venkatesh is a doctoral candidate and Vijay Mahajan is John P. Harbin Centennial Chair Professor in Business and Associate Dean To evaluate the desirability of these alternative strat- for Research, both in the Department of Marketing at The University egies, the seller must address the following four ques- of Texas at Austin, College of Business Administration. The authors tions: thank Ajay Kohli, R. Preston McAfee, and Lynne Stokes of The Uni- versity of Texas at Austin; Rajeev Kohli and Donald R. Lehmann of * What are the optimalprices of the bundle and/or com- Columbia University; Robert P. Leone of Ohio State University; Elliot undereach strategy? three JMR ponents Maltz of University of Southern California; anonymous * Correspondingly,what are the levels of profits? reviewers; and the JMR editor for their helpful comments. Financial * of the marketis attracted the Research Whichportion(s) potential (are) support for this research was provided by University undereach Institute at The University of Texas at Austin. strategy? * How sensitive are profitsto variationsin price levels?

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Journalof MarketingResearch Vol. XXX (November 1993), 494-508 PRICINGA BUNDLEOF PRODUCTSOR SERVICES 495

Addressing the four questions simultaneously is cru- specific approaches for designing and pricing bundles. cial for a manager to understandthe stakes that he or she Of these articles, faces by following any of the three strategies. Each strat- and Wind have a different of the market and therefore (a) Goldberg,Green, (1984) suggested egy taps portions conjointanalysis-based approach to developbundles for the of in revenues. No one impacts degree uncertainty hotel amenities.Their approachis appropriatefor de- strategy may always be the best. As we discuss later, signing bundlescomposed of a core productwith op- with myopic pricing, mixed bundling strategy may be tional add-ons such as automobilesand computers. less effective than pure components or pure bundling Thoughthey used conjointanalysis to captureattribute strategy. We therefore believe that an approach inte- level trade-offsto facilitateoptimal bundle design, they grating the four questions is likely to be quite useful to did not extend their approachto applicationsin which the is maximizationwith a focus on both practitioners making bundling decisions. objective profit literature on in and prices and costs. Their approachdoes not provide(1) Interestingly, bundling marketing underthe three does not focus on the scenariosof optimalprices and profits economics suggesting specific ap- alternative the of the to answer these bundlingstrategies, (2) portions proaches integratively questions (Rao marketthat are attractedunder each strategy,and (3) Most articles on 1992). published bundling primarily the sensitivityof profitsto changesin price levels. As provide theoretical rationales for the bundling concept arguedearlier, these issues are crucial to a seller and and project several contexts that are aptly suitable for necessitatean optimizationapproach that providesan- bundling. The suggested rationales for bundling include swers to these questions. price segmentation(Adams and Yellen 1976; Dansby and Furthermore,as pointedby Kohliand Mahajan (1991, Conrad 1984; Hanson 1987; Stigler 1968), price dis- p. 348), "currentconjoint simulators do not extend to crimination (Adams and Yellen 1976; Burstein 1960; (1) assessingthe profitabilityof a new product,and (2) from a new Paroush and Peles 1981; Schmalensee 1982, 1984; identifyinga price that maximizesprofit Stig- The reason is that a criterion ler 1968), restriction Hanson, and product. principal profit product range (Eppen, necessitatesestimates of fixedand variable costs for every Martin 1991), reduction in classification/processing costs feasible as Green and Klein economies product. ... Practically, suggested by (Kenney 1983), scope (Baumol, and Krieger(1989), multi-attributecost functionsare Panzar, and Willig 1988; Eppen, Hanson, and Martin difficult to estimate reliably. . . . [(This)] has been a 1991), consumers' search economies (Adams and Yellen majorimpediment in the developmentof conjointmodels 1976), and risk reduction (Hayes 1987; Liebowitz 1983). using a profit objective." Challenge remains for re- Guiltinan (1987) has provided a normative framework searchersto developconjoint analysis-based approaches for bundling that elegantly integrates most of these the- that answerthe four bundlingquestions raised earlier. oretical rationales. (b) Hansonand Martin's(1990) mixed integerlinear pro- In the motivations for some of grammingapproach is useful in identifyingthe right advocating bundling, for the contexts addressed are block of movies bundle (from a numberof predeterminedbundles) booking each of several in a marketand the add-ons for automobiles Han- segments optimal (Stigler 1968), (Eppen, priceof each bundle.However, even theirapproach does and Martin classification of diamonds son, 1991), (Ken- not integrativelyanswer the bundlingquestions posed ney and Klein 1983), and multiproductbundling of items earlier. that satisfy different needs (Gaeth et al. 1991). In con- trast to bundling, Wilson, Weiss, and John (1990) have Our purpose is to propose a probabilistic approachthat explained situations and conditions that justify "unbun- enables a seller to determine optimal prices of a bundle dling." and/or its component products/services under pure Though the aforementioned articles establish the im- components, pure bundling, and mixed bundling strat- portance and richness of the bundling concept, none pro- egies. The model also estimates the corresponding max- vide an optimization approach to practitioners to answer imum levels of profits under each strategy. Because the the practical questions that we raised earlier. Two arti- seller knows the relative stakes, he or she can choose cles that build on Adams and Yellen (1976) and evaluate the desired strategy judiciously. We highlight the por- alternative bundling strategies are McAfee, McMillan, tions of the potential market that are likely to purchase and Whinston (1989) and Schmalensee (1984). McAfee, different offerings under alternativestrategies. The model McMillan, and Whinston have demonstratedthat (mixed) can indicate the sources of gains and losses in revenue bundling is an optimal strategy provided that the reser- if the seller were to change strategies or price levels. For vation prices for the various products/services are in- example, we identify the portion of the market likely to dependently distributed in the population of consumers. buy individual items under pure components strategy, Schmalensee observed that a mixed bundling strategy but not likely to buy the bundle under pure bundling generally yields higher profits than either pure bundling (representing a loss in revenue). We accommodate dif- or pure components strategy. Neither suggests any ex- ferences in consumer preferences across product/service plicit approach to determine the optimal prices and prof- components at an individual consumer's level as well as its under the three bundling strategies. the heterogeneity across individuals constituting the po- In marketing, only two articles (Goldberg, Green, and tential market. Wind 1984; Hanson and Martin 1990) have suggested We attempt to make another important contribution. 496 JOURNALOF MARKETINGRESEARCH, NOVEMBER 1993

Bundling literature so far has addressed problems con- Given a set of n performances, the seller faces a crucial sidering essentially one underlying dimension of con- and interesting decision problem of pricing the single sumers' decision making, namely, reservation prices. (performancewise)ticket and/or the season ticket, which There are several instances in which the decision is a maximizes profits.' The absolute and relative values of function of several important dimensions, all of which the two types of tickets are crucial determinants of the may not be captured by the reservation price. For ex- seller's profits. We focus on those performances held in ample, a person's decision to go to a series of music auditoriums or stadiums as distinct from home enter- performances is not only a function of the monetary di- tainment. The following analysis considers a series of of mension (i.e., whether the price the ticket is less than music/dance performances for better clarity of presen- or equal to her or his reservation price) but also the like- tation. lihood that the has the and to person ability willingness We propose that a prospective viewer's decision to at- the time to attend alternative Sim- spare performances. tend a performance is related to two key independent in the case of tie-in sales of and ilarly, computer systems resources-time and money. Vogel (1990) has high- a consumer's decision is not a function stationery, only lighted the central role of these two dimensions in the of the reservation unit but also the price per probable entertainment An individual is expected to at- rates of the tied which is to industry. consumption good, likely tend a particular performance only if he or she has the vary across consumers. In such cases, unless the pre- and to the time to attend model these the willingness ability spend (a) scribed captures multiple dimensions, that and the to the ticket. serious limitations. in performance (b) money purchase analysis may possess By bringing For a series of we the time di- the notion of dimensions as reservation performances, capture multiple (such mension the number of an indi- and time to attend we not by likely performances prices performances), capture vidual can attend from that series. Factors such as the consumers' tastes for attributes work/ only product-related recreation of and but also constraints that determine their engagements, possibility preferences (consumers') for alternative of and unforeseen eventual choice. types entertainment, with to an in- The remainder of this article is as follows: circumstances create uncertainty regard organized the time to The next section the and dividual's ability and willingness to spare highlights conceptual analytical attendvarious over a of time. underpinnings of our model; we then apply our model performancesplanned period In view of these factors, the individual can, front, to pricing a series of music/dance performances that an up visualize a certain to attend a ethnic group is planning to organize in a medium-sized only probability particular In other the individual's to city in the southwest; analysis of results follows; and the performance. words, ability attend a is a random last section provides a discussion of the approach and specific performance event/out- come on the circumstancesthat unfold suggests possible directions for future research in bun- (that depends prior to the For a series of dling. performance). planned perfor- translated Our empirical results indicate that mixed bundling mances, this performancewise probability gets an individual can strategy is more profitable than the other two strategies. into a likely number of performances The results are consistent with the theoretical arguments attend, which is a random variable representing the time of Schmalensee (1984). More importantly, if the relative resources. The estimate on this dimension is not con- prices of the bundle and its components are carefully strained by the monetary aspect of the decision, namely, chosen, mixed bundling can effectively price-discrimi- the price of the ticket. nate among frequent and occasional consumers and in- The monetary dimension, which is independent of the crease total profits. time dimension (to be discussed following), is captured by an individual's reservation price. This is the maxi- MODEL DEVELOPMENT mum price the individual is willing and able to pay for a particular type of performance assuming that time is Conceptual Underpinnings not a constraint on the decision process. The relative at- To illustrate our approach, we consider the entertain- tractiveness of a performance for an individual is likely ment industry, which frequently makes bundling deci- to be reflected in her or his reservation price. We rec- sions at the end-consumer level. An avid follower of ognize that even among a string of seemingly related football games or music performances is often "lured" performances, an individual's reservation prices may be by deals in the form of season tickets. The bundle in this case is a series of performances organized over a certain time horizon. Purchase of a season ticket implies a tie- 'Though bundling does bear certain similarities with quantity dis- in to the package of performances (assuming that tickets count, it is different in several significant ways. A quantity discount are not easily transferable). The temporal dispersion of is a price reduction for buyers who buy large volumes of the same or service On the other a bundle is an performances adds uncertainty to the consumers' ability product (Kotler 1991). hand, assortment of different products and/or services. Bundling can in a to spare the time to attend any performance. Each con- way fulfill a consumer's variety-seeking needs. Moreover, from the sumer is also likely to have different intensities of pref- supply side, the incentive for quantity discount arises from scale econ- erence for the alternative performances in the package. omies whereas bundling yields scope economies. PRICINGA BUNDLEOF PRODUCTSOR SERVICES 497 different across different subcategories of performances. We make this assumption for model development under Our model is developed accordingly. pure components and mixed bundling strategies only. We assume that the two variables-the likely number There are likely to be several applications for which this of performances an individual can attend and her or his assumption may not be valid. For example, for a series reservationprices-are independentof each other. It may of concerts by performersof different caliber there could be argued that people with high incomes may have a be a significant and systematic difference in reservation high cost of time and less sensitivity to price (implying prices across performances even at the market level. For higher reservation prices), whereas people with low in- such situations, a generalized approach relaxing this as- comes may be more thrifty (implying lower reservation sumption is suggested in Appendix A. prices) and have a low cost of time. In other words, an The mean reservation price distribution (h(p,)) cap- argument can be made that there is an inverse relation- tures the transfer of consumer surplus (the difference be- ship between the two variables. However, it is to be rec- tween an individual's reservation price for a product and ognized that though the earning member of a high-in- its actual price) and demonstratesthe motivation for bun- come family may have a high cost of time, her or his dling. To illustrate, consider an individual whose res- family members may not find it too costly to spare the ervation prices for two performances A and B are $10 time. It is also possible that people with lower wage rates and $20, respectively (with a mean reservation price of may have to work for longer hours and may not have $15) and who is willing and able to spare the time to adequate time to spare. We therefore believe that any attend both performances. If there is no season ticket and systematic negative relationship between individuals' the price of the ticket per performance is $19, then this reservation prices and the number of performances that person is likely to attend performance B only. In con- they expect to attend (considering only time-related con- trast, if only a season ticket priced at $29 is offered, the siderations) is likely to be small. One might also high- mean price per performance is $14.50. We expect the light certain situations in which a positive relationship individual to purchase the season ticket because her or between the dimensions is possible. We discuss impli- his mean reservation price ($15) for the combination of cations of such situations to our approach and possible A and B is greater than mean price per performance. The modifications to the model in the "Discussion" section. season ticket bundle thus helps to transfer the individ- Our model is appropriatefor situations in which there is ual's surplus from the more attractive performanceto the no significant relationship between the two dimensions. less attractive one and enhances seller's revenue. In this To articulatethe alternativebundling strategies, we must example, the gross utility for this viewer increases from extend the individual level responses on (a) the likely $20 to $30. number of performances to attend and (b) reservation Besides the symbols relating to the probability density prices to the market level for all individuals constituting functions mentioned earlier, we use the following sym- the potential market. This extension yields three distri- bols: butions: M = market size * the function of the f(z), probabilitydensity (pdf) likely n = number of performances numberof performancespotential consumers can attend, P, = of a ticket (to be which gives the proportionof the potentialmarket that optimal price single deter- expects to spare the time to attenddifferent numbers of mined) performances,assuming that price is not a constraint; Pb = optimal price of the season ticket (to be deter- * the pdf of performancewisereservation price, which mined) g(ps), = representsthe proportionof consumerswilling to pay dif- Ej expenditure to organize the fh performance ferentprices for theirtickets assumingthat they are willing to sparethe time to attend; We commence the discussion of the rationale of con- * h(p,,), the pdf of a derivedmean reservation price, which sumer decision making under alternative bundling strat- is obtainedby averagingthe reservationprices of each in- egies by considering the pure components strategy, un- dividualacross performances. der which only the single (performancewise) tickets are sold. The of the market the an individual's reservation proportion potential having Though price may change time to attend exactly i out of n performances is2 across different performances, we assume at the market level the reservationprice distributionsare the same across these performances. The basis for this assumption is that (1) Pr(i) = f(z)dz. the market is comprised of a heterogenous mix of individuals. In simple terms, though some individuals may have low reservation prices for some performances and high reservation prices for others, there are other indi- 21t could be argued that the limits of integration be i - 1/2 and i viduals who may have a reverse pattern of reservation + 1/2 on the grounds that rounding off to the nearest integer is ap- to determine the of individuals to prices for those performances. This assumption enables propriate proportion expecting spare the time for i performances. However our goodness-of-fit analysis re- us to pool the reservation price information and have the veals that the limits i and i + 1 represent the data better. We have same distribution (g(p,)) to represent each performance. accordingly used these limits. 498 JOURNALOF MARKETINGRESEARCH, NOVEMBER 1993

If P, is the price per performance, then the proportion bution. A random variable X that has a Weibull distri- of these individuals willing to pay this price for a par- bution (Johnson and Kotz 1970) has the probability den- ticular performance, assuming they expect to spare the sity function time to attend the performance, is given by

(4) fM(X)= ca-'{(X - eo)/a}c-' (2) Pr(Ps) = g(Ps)dps. *exp{-[(X - eo)/ac}, eo < X. Therefore, for viewers who expect to spare the time to attend i performances, the likely number of single tickets The cumulative distribution function is sold across all n performances is given by

(3) numberof single ticketssold (5) Fx(X) = 1 - exp{- [(X - eo)/a]c}.

= iMf f(z)dz{ g(ps)dps}. Parametersc, a, and eo determine the shape, spread, and location respectively of the distribution. It is to that this numberis the ex- The motivations for using the Weibull distribution are important recognize the pectationof single ticketssold at the segmentlevel (that following: is, from the segment that expects to spare the time to attend i performances).An individualin this segment a) The distributionsthat we consider,such as performance- drawn at random is to {i * wise reservationprice distribution,may not be symme- expected buy f., g(ps)dp,} tickets (rather than either i tickets or none at all). tric. Choosingthe Weibulldistribution provides the flex- to accommodatea wide of distributionsof Under the pure bundling strategy only the season tick- ibility range ets are offered. Let the bundle that fetches the max- differentskewness and kurtosis. For example, parameter price values of c = 1 and = 0 a conventional imum be An individual who to eo give decaying profits Pb. expects attend distribution.Parameter value of c = 3.6 i is to the season ticket bundle exponential pro- performances likely buy vides a good approximationof the normaldistribution; if the mean price per performance (Pb/i) is less than or and equal to her/his mean reservation price pm. The bundle b) It can be algebraicallymanipulated easily. is more attractive for those segments of the market willing to spend the time to attend a larger number of performances than others. In the following paragraphs we provide the mathe- Under mixed bundling strategy, both the season and matical development of the model for pure components, single (performancewise)tickets are on sale. In this case, pure bundling and mixed bundling strategies. The lo- the seller is free to price the tickets differently than under cation, spread and shape parameters of f(z), g(p,), and the earlier two strategies. Because both the season and h(pm) are (a, eo, c), (a,, e0l, cC), and (a2, eo2, c2) re- single tickets are on sale, the seller has to ensure that spectively. the price of one of the two types of tickets is not so low Pure components. As mentioned earlier, this repre- as to drastically cannibalize the sales of the other and sents the strategy under which only single (performance- reduce profits. An individual who expects to have the wise) tickets are offered. If P, is the price per perfor- time to attend i performances is likely to prefer a season mance, the profits from holding n performances are ticket priced at Pb over several single tickets priced at P, each if (Pb/i) is less than P, and the mean reservation price pm. The relative prices of the season and single (6) rr= - eoi)/aic1- tickets are crucial to minimize the harmful effects of f zf(z)(c,/a,){(ps cannibalization on profits. The prices have to be simultaneously, not sequentially, optimized. This issue is dis- - - cussed further later on in this article. exp [-{(p, eo,)/ai}clMpdpsdz Ej. j=1 Analytical Underpinnings As z and In this section we propose the functional forms of the p, are independent three distributionswith probabilitydensity functions f(z), g(p,), and h(pm) mentioned earlier and the rationale for our choice. Subsequently we provide the mathematical (7) T = zf(z)dz development of our model separately for pure components, pure bundling, and mixed bundling strategies. The probability density functions that we assume for E. the three distributions are those of the Weibull distri- Sexp[-{(Pl,- eo)/a,}c']MPs,- j=1 PRICINGA BUNDLEOF PRODUCTSOR SERVICES 499

For maximum profits, ur, the optimal price equation3 is If ir denotes the profit as before,

n (8) Ps{Ps - eol,-' = al'/cl. (12) 7 = PrMPb - Ej j=1 If reservation prices can vary from zero to a maximum value, then = 0. In that case, equation 8 simplifies For maximum the is to yield the optimaleoj single (performancewise)ticket price profits, optimal price equation4

n = = (9) P, al/cil/c'. (13) Prob(X i) Prob(Y> [Pb/il) i= 1 the estimates of and of the Knowing parameters a, c, [1 - Pb c2 (ia2})c2 [Pb - ieo2l2-1] = 0 performancewise reservation price distribution (g(p,)), we can determine price P, from equation 9 which, when With the substituted in equation 7 gives the maximum profits for estimates of parameters (a, c) of time distri- the pure components case. (We explain parameter esti- bution and (a2, c2) of mean reservation price distribution, mation in a later section.) we can numerically determine the optimal season ticket Pure bundling. Under this strategy, the seller offers price Pb from equation 13 and the corresponding maxi- only season tickets. The appropriate distribution to use mum profits from equation 12. is the mean reservation price distribution. If Pb is the Mixed bundling. The seller adopting the mixed bun- price of a season ticket (to be determined), and X and Y dling strategy offers both single (performancewise) tick- are the random variables the number of ets and season tickets at and denoting per- prices Ps Pb apiece respec- formances a person can attend and the person's mean tively. As explained earlier, an individual expecting to reservation price, respectively, then the proportionof the attend i performancesis likely to choose the season ticket market to the season ticket is over several tickets if willing buy single (performancewise) (Pb/i) < P, and if the mean reservation price exceeds (Pb/i). On the other hand, even if (Pb/i) < Ps, if the mean reser- (10) Pr = Prob(X = i) Prob (Y ?> [Pb/il) vation price is less than or equal to (Pb/i), then this person is expected to purchase several single tickets. If, however, (Pb/i) Ps, then the individual can exclude the option of purchasing- the season ticket and purchase (11) Pr = {exp[-({(i + 1) -eo}/a)cl several single tickets on the basis of available time and reservation prices exceeding the single (performance- ticket Let and Z be the random vari- - exp[-({i - eo}/a)c]} {exp[-{(Pb/i wise) prices. X, Y, ables representing the number of performances an indi- - eo2)/a2}c21}. vidual can attend, the person's mean and performancewise reservation prices respectively. Then at the aggregate (market) level, the objective function is 3Let the mean numberof performancesfor which consumersare willing and to sparethe time be n+ 1 4For maximum profits, z* = f zf (z)dz. diT dP, - 0 = MP, + MP . Therefore, dPb dPb dP, IT = That P, + P 0 z* M P, {exp[-{(P, - e -,)/a}c']} - is, dP = j=I Ej. dPr n For maximumprofits, rm,,, = Prob(X = i) - dPb exp{-([(Pb/i) e,,21/a2)} dTrr i=, - = 0 = z* M P,{exp[-{(P, - e,,)/a,}']}(-c,) dPl, -(-c2)([(Pb/i) - /[ia2). eo2/a2)-'(l Therefore,the optimalprice equationis - [(Ps - eoi)/al]•-'(l/a,) + z* M {exp[-{(P, - Prob (X = i) Prob (Y e-,)/aj•']} - [Pb/i]) If P, < oo,then {exp[-{(P, - e,,)/a,1a']} $ 0. - Pb - = 0. By simplification, S[1 C2(01/{ia2}){Pb ieo22-] This equationcan be solved numericallyto yield the optimalbundle P,{P, - e,}•'-' = a?'/c, price Pb. 500 JOURNALOF MARKETINGRESEARCH, NOVEMBER 1993

n (14) maximizer = Prob(X= i) (18) = Xklog Xk i= 1 I 1k=1 I k=1I *M{mi [Prob(Y > (Pb/i)) Pb S - - s' logXk + Prob(Y< (Pb/i)) Prob([Z> PJ] If is different from I[Y< (Pb/i)]) i PJ] eo zero, we replace each Xk by (Xk - eo). With these estimates, we are in a position to use the model. + (1 - Prob(Z i - mi) P,) P,} E, - j=1 EMPIRICALINVESTIGATION The model we propose can be applied to actual situ- (15) suchthat mi = 1 if (Pb/i) < Ps ations in which consumers' bundle purchase decisions = 0 otherwise. are on the basis of multiple criteria. We demonstrate ap- plication of our model in the context of a series of music/ In other words, dance performances to be organized by an Asian Indian classical music/dance association in a medium-sized city in the southwest. We need to that we could (16) maximizer = Prob(X= i) emphasize have as well applied our model to numerous other contexts, such as orchestra mov- - symphony performances, SM{mi [exp{- [(Pb ieo2)/ia2]c2}Pb ies, and sports games with very little change in our approach. + (1 - exp{-[(Pb - ieo2)/ia2]c2}) The relevant population for our study is comprised of * exp{-[(P, - nearly 1000 individuals, excluding students, belonging eol)/al]c'}iPs] to the Asian Indian community living in this southwest- + - - (1 mi) exp{-[(P, eol)/al]cI}iP)} ern city. Their annualhousehold income is typically higher than $36,000. We mailed questionnaires and self-addressed business reply envelopes to 360 respondents on the basis of a list an j=1 supplied by organization representing the Asian Indian community. We avoided any subject to choice rule 15. This choice rule, contingent explicit references to our pricing model to reduce bias on the values of Pb and P, that are yet to be determined, in feedback on reservation prices. The respondents were necessitates that we resort to a numerical search to iden- also informed that ten music/dance performances of uni- at tify the simultaneous optimal values of Ps and Pb* formly high standardwere scheduled to be performed regular monthly intervals. ESTIMATIONOF PARAMETERS We divided the ten performances into five groups of two each on the basis of the of The we need to estimate to use our model performances type per- parameters in our concurredwith our are those of the functions formance.5Respondents pretest probability density f(z), g(p,), basis of between the alternative and that are assumed to have Weibull distinguishing perfor- h(pm) distribu- mances. information on time and venue of these tions. Specific was to enable to an- The Weibull 4 performances provided respondents distribution, represented by equations swer on the number of were and has three and For questions performances they 5, parameters, namely, a, c, eo. to the time to attend and the distributions that take values from is zero likely spare money they zero, eo (John- were to as as son and Kotz 1970). If the values commence from a cer- willing pay precisely possible. The first (see B) related tain nonzero level, eo is taken as the minimum of the set important question Appendix to the respondents' ability and willingness to spare the of random variables from s observations X,, , Xk ...... , time to attend the performances. We highlighted to the X, relating to the subject distribution where Xk is the re- respondents the uncertainty that exists on this dimen- sponse from the kth respondent and s is the sample size. Using the probability density function of a Weibull distribution (mentioned earlier), and knowing eo = 0 (i.e., distribution varies from zero at the lower end), the max- 5Indian classical music consists of two major types: (a) Hindustani imum likelihood estimates and Kotz for music, which has its roots in Northern India and includes well known (Johnson 1970) musicians such as Pandit Ravi Shankar, and (b) Carnatic music, which a and c are given by has a South Indian base and is popularized by stalwarts such as M. S. Subbulakshmi. Indian classical dance is of several types such as ) Bharatanatyam, Kathak, Kuchipudi, and Odissi. The five categories (17) c = s-'I (X that we considered are Hindustani music-vocal and instrumental, 'k= 1 Carnatic music-vocal and instrumental, and classical dance. PRICINGA BUNDLEOF PRODUCTSOR SERVICES 501 sion. On the basis of their past experience of their will- the population of the ethnic group. The questionnaire did ingness and ability to spare the time for performances not seek the identity of the respondents to facilitate more similar to the ones planned, their expected obligations honest feedback. and future time commitments, respondents were asked In all, 119 questionnaires were received representing to indicate the probable number of performances they a response rate of about 33%. Of these, 31 question- thought they could attend in the planned series. They naires were returned blank (consistent with our instruc- were specifically asked not to be influenced by the price tions) leaving 88 useful responses. of the tickets in providing their response to this question. The following questions may now be raised to facil- Respondents were also asked the maximum prices they itate data analysis and interpretation: were to for each willing pay per person per performance * Do we satisfy the assumptionsunderlying our model and of the five performance types, assuming they had the data? time to attend. We stated the exact categories of per- * How well do the parameterestimates fit the data? formances and listed the exemplar musicians/dancers * What are the answersto the four questionsraised in the under each category. They were free to choose different introduction? prices (including zero) for different performances to accommodate their heterogeneity in preferences across Validity of Assumptions performances. Table 1 summarizes the results of our tests to validate It is to be recognized that certain performances may the assumptions underlying the applicabilityof the model not appeal to the tastes of certain respondents irrespec- in the context of the Asian Indian music/dance perfor- tive of the caliber of the performers. In other words, mances. even isolating the influence of price of the ticket, the Our analysis requires there be no significant non-re- consideration set for each respondent is probably a sub- sponse bias in our sample. Consistent with this assump- set of the total number of performances. Therefore, un- tion, we did not observe significant differences between der the question on reservation prices, we also sought earlier and later respondents on (a) the probable number for each type of performance whether respondents would of performances they could attend on the basis of time- be willing to attend excluding the price factor. On the related considerations alone (p = .36), and (b) reser- basis of each individual's response to this part of the vation prices (p = .81). This gives us some confidence question, we had to shrink the preceding response, that the responses are representative of the sample we namely, the probable number of performances the in- contacted. dividual can attend (on the basis of time related consid- To test our assumption that reservation prices across erations alone). For example, suppose an individual ex- types of performances are not significantly different, we pects a priori that he or she can spare the time to attend used a repeated measures ANOVA on reservation prices all ten performances for the broad category planned. across the five types of performances. It did not indicate However, considering the specific menu of perfor- significant differences (p = .18). This validates our as- mances, if this person believes he or she is not willing sumption that the types of performances are comparable to attend four out of ten performances even if they are on reservationprices at the marketlevel even though they free of charge (purely because of lack of taste for those may vary at an individual level. We pooled the perfor- subcategories of performances), then the likely number mancewise reservation price information to have one of performances that this individual will attend on the distribution representing reservation price per perfor- basis of time considerations alone is shrunk from ten to mance for all types of performances. Had this assump- six. tion been violated, we would have used the more general We also asked for the number of persons likely to ac- procedure suggested in Appendix A.6 company the respondents for each type of performance. Our approach assumes that the expected number of Our purpose was to check whether the reservation prices performances individuals can attend on the basis of time- were independent of the number of persons accompa- related considerations alone is independent of their res- nying them. To appreciate the need for this check, con- ervation prices. In line with this assumption, the corre- trast individuals who are accompanied by several family lation between the two variables was not significant (p members with others who go with fewer people. If the = .40). ticket prices are perceived to be a sizable portion of the Last, we had assumed that reservation prices of in- families' entertainmentbudget, the reservationprices may dividuals are independent of the number of persons ac- exhibit a systematic negative relationship with the number of accompanying individuals. In that case, we would have to weigh the reservation price information suitably 6As the organizers perceived some uncertainty regarding the avail- to estimate the appropriatemarket level distribution. ability of certain performers, we could only provide an exemplary list Respondents who had no interest whatsoever in Indian of performers in our questionnaire and not an accurate list of actual If we had the exact list of we would have classical music/dance were requested to return the performers. performers, ques- performed the more appropriate test of checking whether the reser- tionnaires without filling them out. Using this informa- vation prices are significantly different across performers rather than tion, we could estimate the potential market size given across the five types of performances. 502 JOURNALOF MARKETINGRESEARCH, NOVEMBER 1993 Table 1 VALIDITYOF ASSUMPTIONSUNDERLYING THE PROPOSED MODEL FOR THE ASIAN INDIAN MUSIC/DANCE PERFORMANCES

Is assumption Assumption F-value p valid? * There are no significant differences between earlier and later respondents on * number of performances they can attend based on time-related considerations alone .83 .36 Yes * reservation prices (money) .06 .81 Yes * There are no significant differences in reservation prices across types of performances 1.59 .18 Yes * Individuals' reservation prices are independent of the number of performances they can attend .70 .40 Yes * Reservation prices of individuals are independent of number of companions .07 .80 Yes

companying them to performances. Reservation prices the chi-squarevalues from Weibull fits are markedlylower of individuals were not significantly related to the num- than those from normal fits for all three distributionswith ber of their companions (p = .80). probability density functions f(z), g(ps), and h(p,,).The Weibull distribution is more than the normal Parameter Estimates and Goodness Fit appropriate of distribution in this case. It is relevant to note that several The parameter estimates of Weibull distributions and studies in bundling such as Schmalensee (1984) assume chi-square values are given in Table 2. To assess the a normal distribution of reservation prices. Normality as- goodness of fit of the Weibull distributions, we need to sumption may reduce the efficiency of results when the evaluate the chi-square values. For a given number of distributions such as ours are skewed. The ability of the degrees of freedom, a lower chi-square value is indica- Weibull distributionto captureboth symmetricand skewed tive of a better fit. The p values represent the probability patterns provides a major encouragement for its usage. of the data coming from the assumed distributions. Typ- We correctedthe size of the potentialmarket from 1000 ically, p values greater than .05 are considered non-sig- to 750 on the basis of the proportion of respondents in- nificant and adequate to accept the stated distributions. dicating they had no interest in the planned series of per- As Table 2 indicates, we had non-significant chi-square formances. Drawing from the cultural association's past values for the Weibull distributions when fitted to data experience for similar performances, the cost per per- on performancewise reservation prices (p > .10), mean formance was assumed to be $1,200. The model can, reservation prices (p > .90), and the likely number of however, accommodate different costs across perfor- performancesthat individualscan attend (p > .10). These mances. results suggest that Weibull distributions describe these Prices and data very well. Optimal Profits To highlight the shape of the fitted Weibull distribu- Applying the model to the data yields the results in tions, we provide their plot in Figure 1. The three dis- Table 3. Mixed bundling is the most attractive of the tributions have moderate to pronounced skewness. How strategies. The optimal prices under this option are $14 do Weibull fits compare with normal fits? For our data, for the single ticket and $55 for the season ticket, yield-

Table 2 WEIBULLPARAMETER ESTIMATES FOR THE ASIAN INDIAN MUSIC/DANCE PERFORMANCES

chi-square Weibull Parameter/Estimates Weibull Normal Distribution a eo fit fit Performancewise Reservation Price 15.08 0 2.38 8.7a 20.0 Mean Reservation Price 7.46 6 1.41 3.8b 13.7 Number of Performances to Attend 5.42 0 2.66 10.la 13.2

ap > .10 bp > .90 PRICINGA BUNDLEOF PRODUCTSOR SERVICES 503

Figure 1 PROBABILITYDENSITY FUNCTIONS OF ESTIMATEDWEIBULL DISTRIBUTIONS

PDFOF LIKELYNUMBER OF PERFORMANCESTO ATTEND

0.2

0.18

0.16

0.14

00.12 Z 0.1 0.08 a. 0.06

0.04

0.02

0 1 2 3 4 5 6 7 8 9 10 11

LikelyNumber of Performances

PDFOF PERFORMANCEWISERESERVATION PRICE PDFOF MEANRESERVATION PRICE

0.07 0.1

0.09 0.06 0.08

0.05 0.07

0 004 Z 0.05.06 o0.04 S0.03 0.02 0.03 0.02 0.01 0.01

0 0 I I I I • I 0 3 6 9 12 15 18 21 24 27 30 0 t-----3 6 9 12 15 18 21 24 27 30

PerformancewiseReservation Price in $ MeanReservation Price in $

ing a total profit of approximately$13,620. At these price confidence intervals do not overlap across the three bun- levels, 620 single tickets and 308 season tickets are ex- dling strategies. There is a clear hierarchy in the relative pected to be sold for the series of performances. The attractivenessof the three strategies. These provide strong profits are about 32% higher than those under pure com- evidence for the superiority of mixed bundling strategy ponents strategy ($10,330 by selling approximately 2233 over pure components and pure bundling strategies. single tickets at $10 apiece) and about 95% higher than Sources Gains and Losses in Revenues profits from pure bundling ($6,980 throughsales of nearly of 542 season tickets at $35 per ticket). We carried out the Another important issue is the source of revenues from jackknife procedure to estimate the variance of the profit different portions of the markets under each strategy and estimates. We provide a 95% confidence interval for the gains and losses in revenues as we shift from one strat- profits estimated under each strategy in Table 3. The egy to another. 504 JOURNALOF MARKETINGRESEARCH, NOVEMBER 1993 Table 3 OPTIMALPRICES AND PROFITSFOR ALTERNATIVE BUNDLING STRATEGIES

Optimal Price ($) Number of Tickets Sold Bundling Single Season Single Season Net Strategy Ticket Ticket Tickets Tickets Profits($)* Pure components -single tickets only 10 N.A. 2,233 N.A. 10,330 (9,910-10,870) Pure bundling -season tickets only N.A. 35 N.A. 542 6,980 (6,700-7,350) Mixed bundling (Simultaneous Optimization) -single/season tickets 14 55 620 308 13,620 (13,190-14,130) Mixed bundling (Sequential Optimization -Suboptimal) -single/season tickets 12 35 296 525 9,920 -single/season tickets 10 55 1,398 175 11,610 N.A.= Not Applicable * = Lower and upper bounds for 95% confidence interval are given in parentheses.

Under the pure components strategy, with the optimal ucts," the season ticket and single ticket priced at $55 single ticket price P, (equal to $10), we are able to attract and $14, respectively. It is interesting to note that these all consumers with reservation prices above this price for prices are different from those under pure components a given performance provided the individual consumers ($10 for the single ticket) and pure bundling ($35 for the are willing to spend the time to attend. However, in the season ticket) strategies. Availability of both types of process, the organizers are "subsidizing"consumers with tickets enables sellers to resort to price segmentation.7 higher reservationprices for specific performances,which Potential consumers who expect to attend four or more translates as the "consumer surplus." Moreover, those performances and whose mean reservation prices are potential consumers who expect to spare the time to at- higher than the mean performance prices are likely to tend a large number of performances but are not willing prefer the season ticket at $55 each over several single or able to pay at the single ticket rate represent another tickets. Others are likely to buy single tickets at $14 per source of opportunity loss under pure components strat- performance (if the price is less than or equal to their egy. reservationprice for the performancesfor which they end Pure bundling typically captures a portion of potential up having the time). At these price levels, the seller's consumers with low mean reservation prices but who ex- profits are the highest. The extent of harmful cannibal- pect to attend a large number of performances. The op- ization of the two types of tickets is lower than under timal season ticket price Pb is $35. The gains, compared any other price combination. to come from those con- pure components strategy, to Price - sumers who are willing and able to spare the time to Sensitivity of Profits Changes Importance of Simultaneous attend a large number of performances at less than the Optimization single ticket prices under pure components. The gain from It is apt to note that mixed bundling should involve a each new consumer is equal to the bundle price. The simultaneous optimization of the single (performance- switch from pure components to pure bundling results in wise) and season ticket prices to maximize profits. If the two sources of losses in revenue: (a) some consumers under pure components strategywho expect to attendonly a few performances and, hence, do not feel inclined to 7What accounts for the differences in prices of the same types of tick- the season ticket and consumers who would have ets across alternative strategies? The problem in pure bundling, for buy (b) is that to low to attract a attended a number of example, prices may have be kept enough large performances anyway by sizable proportion of the market that expects to spare the time for a buying single tickets and are now reaping the advantage few performances only. Introduction of single tickets under mixed of buying season tickets. In our example, pure bundling bundling takes care of this category of customers by offering single emerges as a less attractive strategy than pure compo- tickets at a price higher than that under pure components but lower nents under conditions. than the average price per performance under pure bundling. With optimal pricing this segment taken care of, those willing to attend a larger number of The power of mixed bundling lies in its ability to act performances need not be offered the season ticket at $35 any longer as a price discrimination device. We have two "prod- (which is why the season ticket price increases to $55). PRICINGA BUNDLEOF PRODUCTSOR SERVICES 505 price of, for example, the season ticket were the same price discrimination device only when the prices are op- under pure bundling and mixed bundling strategies, the timized simultaneously. "low-priced" season ticket would have drastically re- Limitations and Future Research Directions duced the effectiveness of the single ticket, making mixed bundling irrelevant. Our approach does not consider certain relevant situ- To clarify this point, we refer the reader to Table 3, ations that form the limitations of this article and provide which gives the profits from mixed bundling when the the opportunity for further research. For example, we (a) prices are optimized simultaneously and (b) prices restricted our attention to a monopolist organizing the are optimized sequentially, that is, the single ticket price series of performances. The model does not have com- is optimized given the optimal season ticket price is as petitors who may strategically interact with the pricing under pure bundling strategy (i.e., $35). The second case decisions of the focal seller. Bundle pricing with mul- has a sequentially optimized single ticket price of $12 tiple criteria in the presence of closely competing alter- and a profit of $9,920, lower than that under pure com- natives (such as another series of Asian Indian music ponents ($10,330). It illustrates that the advantages of performances staged in parallel by another association) mixed bundling can be undermined by myopic pricing. is likely to be an interesting extension. When the single ticket price is as under pure components Our choice of a distributional approach facilitated the ($10), the sequentially optimized season ticket price (for analytical development of the results. Distributions rep- ten performances) turns out to be $55, yielding a profit resenting the market may occasionally be multimodal, of $11,610, less than the profits under mixed bundling requiring certain modifications in the proposed ap- with simultaneousoptimization of single and season ticket proach. If trade-offs between the multiple dimensions are prices. In this case also the effectiveness of mixed bun- relevant and important, conjoint analysis-based ap- dling strategy is reduced. proaches can be quite attractive. Challenges remain for These figures underline the importance of simulta- researchers to develop and expand alternative ap- neous optimization of single and season ticket prices. In proaches such as conjoint-basedtechniques to answer the mixed bundling, the single ticket "skims" the segment four bundling questions addressed here. that did not want to buy the season ticket because of time In modeling the time dimension, we contended that constraints and achieves price discrimination. individuals may not be able to spare the time to attend even for the like the most. The DISCUSSION performances they primary reason is that the individuals may not foresee, up Our primary objective has been to propose an ap- front, factors such as inclement weather, work pres- proach to integratively answer four issues (across pure sures, and unknown, alternative entertainmentprograms components, pure bundling, and mixed bundling strat- that may constrain them from sparing the time to attend egies) that are crucial to the seller: (a) optimal prices of the offered performances. A counter argument is that the bundles and/or their components, (b) correspondingprofit probability of attending alternative performances is in- levels, (c) sources of revenues as well as gains and losses fluenced purely by the attractiveness of the performance. in revenue if the seller changes from one bundling strat- However, for contexts such as ours, an individual faces egy to another, and (d) price sensitivity of profits. We a nonzero probability that he or she cannot attend even have addressed a buyer's purchase decision contingent if the performance is perceived to be highly attractive. on meeting two criteria, such as reservation prices for It may be more appropriate to model the attractiveness alternative performances and available time to attend of the performance as a moderating factor that motivates performances in the context of entertainment perfor- the individual to manage the external uncertainties to an mances. We have empirically tested our approach using extent and correspondingly change the individual's prob- an actual bundling problem. The approach can be ex- ability to spare the time to attend. tended to situations involving more than two criteria as For a series of entertainmentperformances such as the well. We believe our model represents a refinement over one we consider, an important exception in which lack other alternatives thus far that have modeled the problem of appeal has an overriding influence on allocated time considering only one relevant dimension, such as res- is for performances for which an individual has no mo- ervation prices. Though a unidimensional approach may tivation to spare the time even when admission is free. be adequate for several situations, it is likely to be in- Our approach accommodates this adjustment (as dis- adequate for problems such as the one considered here. cussed earlier). An alternativeapproach to model the time Our empirical results are consistent with Schmalensee dimension is to consider an individual level probability (1984), who maintainsmixed bundling is better than pure of sparing the time to attend alternative performances as bundling and pure components. However, the extent of a composite of the probability in the manner we have advantage is determined by the ingenuity of fixing the defined, together with another component that is mono- price of the bundle relative to that of the components. tonically related to attractiveness of the performances for Suboptimal pricing leads to extensive cannibalization of the individual. This requires explicitly modeling a pos- one "product"by anotherand may make the idea of mixed itive relationship between the time dimension and res- bundling irrelevant. Mixed bundling can be an effective ervation prices because the latter is clearly a measure of 506 JOURNALOF MARKETINGRESEARCH, NOVEMBER 1993 the attractiveness of alternative performances for the in- the marketlevel the reservationsprice distributions are not sig- dividual. As discussed earlier, in certain situations one nificantlydifferent. In certaincases, some performancesmay be may also expect a negative relationship between reser- perceivedby most consumersto be significantlysuperior or inferiorto others. It be more to the vation prices and allocated time. To model situations in may appropriate price single tickets from to performance. which the correlations (positive or negative) between di- differently performance Relaxing our earlier does not have an impacton mensions is and sizable, assumption important bundling approaches pure bundlingstrategy since the mean reservationprice dis- need to be developed that consider these relationships tributioncan accommodatethis variation.The modificationhas using multivariate distributions. an impact only underpure componentsand mixed bundling For certain situations in which individuals have no un- strategies. certainty in allocating time for performances that they For situationsin which the marketas a whole perceivesper- find the most appealing, our approachwill understatethe formancesto be widely different,we assumethe distributions profits and number of single tickets sold and overstate differ from one anotheron their location parameter(eo) but their dif- the numberof season tickets sold. The advantageof mixed patterns(shape and variance)are not significantly over is ferent. Let the performancewith the lowest reservationprice bundling strategy pure components strategy likely be the first be the extentto which rather limited under such circumstances. performanceand , n to be the - 12,.*... are shifted fromthe We do not side constraints such as the remaining(n 1) performances away capture supply first performance.If we subtractthese values from the cor- of the auditorium or stadium that alter the capacity may respondingreservation prices, we wouldhave distributionsthat optimal solutions. Research that considers the capacity arenot significantlydifferent, enabling us to use the samepro- constraint may examine several interesting issues such cedureas before with the following modifications. as (a) yield management (that is, offering several price For the purecomponents case, equation7 representingprof- tiers for single/season tickets) with more effective price its from holding the n performanceswould changeto discrimination than the approach we suggest and (b) optimization with the of to Fur- objective selling capacity. r = f zf(z)dz thermore, on the cost side, though we accommodate dif- (19) ferences across we do not treat costs "product"offerings, n as variable with the number of units sold. The advantage - M - is akin to scope economies and can be incorporated. exp[-{(P, eol)/a,}c] Ps* Ej Marketing of bundles represents a means of reducing the j=1 seller's risk, especially when the competing alternatives are likely to be strong. The seller might offer special (20) whereP* = P, + [( (n - 1) . prices for consumers who are willing to purchase tickets , well in advance of the performance(s). Future bundling researchcan bundle their risk Note that is a linearfunction of The of optimize prices recognizing P* Ps. optimalprice reducing capacity. (single) ticketsfor the firstperformance will continueto be Ps In situations such as symphony orchestra perfor- as underequation 9. The prices for performances1 throughn are mances, consumers may have the option of choosing from given by the vector multiple season ticket bundles offering admission to dif- (21) = 1 + * 1 + ferent assortments of performances. The power of price Ps P,[1, (12/Ps), . (*InPps)]T discrimination demonstrated under the mixed bundling In the case of mixed an individual'schoice of a sea- can be further enhanced bundling, strategy by offering multiple son ticketover several ticketswill occur when < bundles. The seller's are to increase if the single (Pb/i) profits likely P* and Y > (Pb/i) whereP*s is computedsimilar to thatunder are Future research can prices optimized correctly. gen- equation20. As mentionedearlier, the valuesof underpure eralize our to bundles. Ps approach incorporate multiple componentsstrategy will differ from that under mixed bun- Bundling models can also be developed to select vi- dling. Hence, P* in equation20 will be numericallydifferent able combinations of products/services. For example, from that undermixed bundling.The objectivefunction is which set of n performancesshould the organizerschoose to maximize profits? This also relates to an earlier point n maximize = Prob = M on the "appeal" of alternative performances. Though re- (22) rr I (X i) searchers such as Hanson and Martin (1990) address similar issues for products, there is opportunity for fur- {m[Prob(Y> (Pb/i))Pb ther development in situations such as ours. ? + Pr(Y (Pb/i)) Pr([Z > P,] APPENDIX A -

Relaxing the Assumption on Similarity in Reservation Prices + (1 - mi) Prob (Z P,) iP*} Across Performances - For model developmentwe had assumedthat though an individual'sreservation price may vary acrossperformances, at j= PRICINGA BUNDLEOF PRODUCTSOR SERVICES 507

such that = 1 < (23) mi if (Pb/i) Ps* dicate your desire to attend the performances, the maximum are to if are inclined to = 0 otherwise. price you willing pay you attend them and the number of persons likely to accompany The simultaneous optimal values of P, and Pb are determined. you. You are free to indicate different amounts for different The vector of single ticket prices is computed similar to that types of performances, if you so desire. under equation 21. APPENDIX B Maximumprice Are are Numberof the Used the you you willing Summary of Questionnaire for Survey: willing to pay per persons to attend The questionnaire consisted of four parts: personper likely to accompany " Part I: Six on (a) of enter- Program/ performance performance questions viewing frequency Performer (Yes/No) ($) you tainment performances (all types/Asian Indian category), (b) money spent on tickets, (c) partic- ipation of members of household, (d) details of attending8 specific performances(including 5 Asian Indian music/dance performances).

* Part H: One question (with 8 sub-sections) on intensity of Additional Points for Data Collection and Coding: for eight different types of music/dance preference * The exact menu of performances is to be indicated under five mainstream Ameri- performances (including the first column of the table under question 9. can and three Asian Indian types). * Depending on response under the second column of the above table, the responses under question 8 have to ad- * Part III: Two questions with a lead paragraph seeking in- justed as explained in the text. formation on the two key questions relating to available time to attend performances and reser- REFERENCES vation prices. Adams, William J. and Janet L. Yellen (1976), "Commodity * Part IV: characteristics. Demographic Bundling and the Burden of Monopoly," Quarterly Journal Economics, 90 475-98. We verbatim the two mentioned under of (August), reproduce questions Baumol, William John C. and Robert D. Part III: J., Panzar, Willig (1982), Contestable Markets and the Theory of Industry For questions 8 and 9 assume that 10 professional Indian Structure, New York: Harcourt-Brace-Jovanovich. classical music/dance performances are to be held in ... at Burstein, M. L. (1960), "The Economics of Tie-In Sales," ... Hall, the first Saturday of each month for the next 10 Review of Economics and Statistics, 42 (February), 68-73. months and musicians/dancers of a high caliber perform on Dansby, Robert E. and Cecilia Conrad (1984), "Commodity each occasion. Also assume that no other professional In- Bundling," American Economic Review, 74 (May), 377-81. dian classical music/dance performance is being organized Eppen, Gary D., Ward A. Hanson, and R. Kipp Martin (1991), by any other association/group during this period. "Bundling: New Products, New Markets, Low Risk," Sloan 8. You may not be able to attend all 10 performances due to Management Review, 1991 (Summer), 7-14. Irwin P. and time-related constraints. For example, your work commit- Gaeth, Gary J., Levin, Goutam Chakraborty, Aron ments interfere with leisure time on certain M. Levin (1991), "Consumer Evaluation of Multi-Product may your per- Bundles: An Information formance or be attracted to a different Integration Analysis," Marketing days you may pro- Letters, 2 47-58. Based on (January), gram. your past experience, expected obligations Goldberg, Stephen, Paul E. Green, and Yoram Wind (1984), and future time indicate the number commitments, of per- "Conjoint Analysis of Price Premiums for Hotel Ameni- formances (out of ten) you may be able to attend. Do not ties," Journal of Business, 57 (1), S111-S132. worry about the price of the ticket per performance to an- Green, Paul and Abba M. Krieger (1989), "Recent Contri- swer this question. butions to Optimal Product Positioning and Buyer Segmen- Provide your tation," European Journal of OperationalResearch, 41, 127- 41. a) most pessimistic estimate : performances out of 10 Guiltinan, Joseph P. (1987), "The Price Bundling of Services: A Normative Framework,"Journal of Marketing, 51 (April), b) most likely estimate : performances out of 10 74-85. c) most optimistic estimate : performances out Hanson, Ward (1987), "The Role of Bundling," of 10 Strategic working paper, Center for Research in Marketing, Univer- 9. Depending on your intensity of your preference and within sity of Chicago. the overall budget that you may have for entertainment, Hanson, Ward A. and R. Kipp Martin (1990), "Optimal Bun- you may be willing to pay a certain maximum amount for dle Pricing," Management Science, 36 (February), 155-74. each type of performances indicated below. Assuming that Hayes, Beth (1987), "Competition and Two-Part Tariffs," you have the time to attend each of the performances, in- Journal of Business, 60 (1), 41-54. 508 JOURNALOF MARKETINGRESEARCH, NOVEMBER 1993

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