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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 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. American Marketing Association is collaborating with JSTOR to digitize, preserve and extend access to Journal of Marketing Research. 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 de- velopment and empirical investigation they consider a season ticket bundle for a series of entertainment performances such as sports games and music/dance con- certs. 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 com- ponents (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 sepa- rately). They apply their model to price a planned series of music/dance perfor- mances. 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 sep- arately. *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? 494 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 approach that 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.
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