Measuring Heterogeneous Reservation Prices for Product Bundles

This paper develops a model for capturing continuous heterogeneity in the joint distribution of reservation prices for products and bundles. Our model is derived from utility theory and captures both within-and among-subject variability. Furthermore, it provides dollarmetric reservation prices and individual-level estimates that allow the firm to target customers and develop customized and nonlinear pricing policies.Our experiments show that, regardless of whether the products are durables or nondurables, the model captures heterogeneity and predicts well. Models that assume homogeneity perform poorly, especially in predicting choice of the bundle. Furthermore, the methodology is robust even when respondents evaluate few profiles.Self-stated reservation prices do not have any informational content beyond that contained in the basic model. The direct elicitation method appears to understate (overstate) the variation in reservation prices across consumers for low-priced (high-priced) products and bundles. Hence this method yields biased demand estimates and leads to suboptimal product-line pricing policy.The optimization results show that the product-line pricing policy depends on the degree of heterogeneity in the reservation prices of the individual products and the bundle. A uniformly high-price strategy for all products and bundles is optimal when heterogeneity is high. Otherwise, a hybrid strategy is optimal.

[1]  W. K. Vickery,et al.  Counter-Speculation Auctions and Competitive Sealed Tenders , 1961 .

[2]  William Vickrey,et al.  Counterspeculation, Auctions, And Competitive Sealed Tenders , 1961 .

[3]  M. Degroot,et al.  Measuring utility by a single-response sequential method. , 1964, Behavioral science.

[4]  R. Kirk.  Experimental Design: Procedures for the Behavioral Sciences , 1970 .

[5]  Janet L. Yellen,et al.  Commodity Bundling and the Burden of Monopoly , 1976 .

[6]  C. Granger,et al.  The Pricing of New Products , 1979 .

[7]  G. W. Milligan,et al.  An examination of the effect of six types of error perturbation on fifteen clustering algorithms , 1980 .

[8]  Jordan J. Louviere,et al.  Design and Analysis of Simulated Consumer Choice or Allocation Experiments: An Approach Based on Aggregate Data , 1983 .

[9]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Yoram Wind,et al.  Conjoint Analysis of Price Premiums for Hotel Amenities , 1984 .

[11]  Richard Schmalensee,et al.  Gaussian Demand and Commodity Bundling , 1984 .

[12]  Arthur Lewbel,et al.  Bundling of substitutes or complements , 1985 .

[13]  Ronald M. Harstad,et al.  Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study , 1987 .

[14]  M. Whinston,et al.  Multiproduct Monopoly, Commodity Bundling, and Correlation of Values , 1989 .

[15]  K. B. Monroe.  Pricing: Making Profitable Decisions , 1990 .

[16]  Ward Hanson,et al.  Optimal bundle pricing , 1990 .

[17]  Nicholas Economides,et al.  Mixed Bundling in Duopoly , 1993 .

[18]  S. Chib,et al.  Bayesian analysis of binary and polychotomous response data , 1993 .

[19]  R. Venkatesh,et al.  A Probabilistic Approach to Pricing a Bundle of Products or Services , 1993 .

[20]  Luc Leruth,et al.  Why firms may prefer not to price discriminate via mixed bundling , 1993 .

[21]  M. Salinger.  A Graphical Analysis of Bundling , 1995 .

[22]  J. Kagel,et al.  Handbook of Experimental Economics , 1997 .

[23]  J. Kagel.  7. Auctions: A Survey of Experimental Research , 1995 .

[24]  S. Chib,et al.  Understanding the Metropolis-Hastings Algorithm , 1995 .

[25]  André de Palma,et al.  Discrete Choice Theory of Product Differentiation , 1995 .

[26]  Charles B. Weinberg,et al.  Pricing a Bundle of Products or Services: The Case of Nonprofits , 1996 .

[27]  Xiao-Li Meng,et al.  POSTERIOR PREDICTIVE ASSESSMENT OF MODEL FITNESS VIA REALIZED DISCREPANCIES , 1996 .

[28]  A. Rukhin.  Bayes and Empirical Bayes Methods for Data Analysis , 1997 .

[29]  Peter E. Rossi,et al.  Marketing models of consumer heterogeneity , 1998 .

[30]  J. M. Villas-Boas.  Product Line Design for a Distribution Channel , 1998 .

[31]  T. Gruca,et al.  Industrial Pricing: Theory and Managerial Practice , 1999 .

[32]  Vijay Mahajan,et al.  A Conjoint Analysis-Based Procedure to Measure Reservation Price and to Optimally Price Product Bundles , 1999 .

[33]  Praveen K. Kopalle,et al.  The Role of Market Expansion on Equilibrium Bundling Strategies , 1999 .

[34]  Yannis Bakos,et al.  Bundling and Competition on the Internet , 1999 .

[35]  Preyas S. Desai.  Quality Segmentation in Spatial Markets: When Does Cannibalization Affect Product Line Design? , 2001 .

[36]  Z. John Zhang,et al.  Augmenting Conjoint Analysis to Estimate Consumer Reservation Price , 2002, Manag. Sci..

[37]  B. Skiera,et al.  Measuring Consumers' Willingness to Pay at the Point of Purchase , 2002 .

[38]  W. Kamakura,et al.  Optimal Bundling and Pricing Under a Monopoly: Contrasting Complements and Substitutes from Independently Valued Products , 2003 .