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Beyond plain vanilla: Modeling joint product assortment and pricing decisions


This paper investigates empirically the product assortment strategies of oligopolistic firms. We develop a framework that integrates product choice and price competition in a differentiated product market. The present model significantly improves upon the reduced-form profit functions typically used in the entry and location choice literature, because the variable profits that enter the product-choice decision are derived from a structural model of demand and price competition. Given the heterogeneity in consumers’ product valuations and responses to price changes, this is a critical element in the analysis of product assortment decisions. Relative to the literature on structural demand models, our results show that incorporating endogenous product choice is essential for policy simulations and may entail very different conclusions from settings where product assortment choices are held fixed.

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  1. These results complement recent theoretical work by Gandhi et al. (2008) that finds the potential for substantial differences in consumer welfare and profitability effects of a merger when allowing post-merger product repositioning relative to a fixed product assortment.

  2. Information from the FTC website at Note that the FTC’s concerns related primarily to Dreyers’ super-premium brands (Dreamery, Godiva and Starbucks).

  3. It is delivered by partners of Breyers (an independent broker network) and by Dreyers’ in-house distribution arm.

  4. In the remainder of the paper we use firms and brands interchangeably.

  5. The loss of information is not severe because all we can learn from the fact that a brand always offers a particular flavor is that the cost of offering that flavor is smaller than the lowest incremental variable profit across periods from offering it, which would only yield an upper bound on such costs.

  6. While our model readily accommodates cost shifters that are brand-flavor specific, our application to ice cream does not require this additional generality, see Section 4.1 for details.

  7. Recall from Section 2.1 that in our multi-product firm setting we also may have multiple equilibria of the pricing game.

  8. Some brands, like Breyers, replaced their 4 pint packages with 3.5 pint ones without changing the unit price. This strategy of increasing the per-ounce price is fairly common among manufacturers of frequently purchased consumer packaged goods because it is not as obvious to consumers as a change in the unit price.

  9. Because it is difficult to determine how their flavors map to the other brands’ vanilla offerings based on the names, we include the private label and other brands in the outside good.

  10. Dreyer’s ice cream is sold under the brand name Edy’s in the Midwestern and Eastern United States after Kraft (the makers of Breyers) raised objections in 1985.

  11. We tried several alternative definitions for M. In general, definitions based on ice cream consumption, which include non-supermarket ice cream sales (e.g., sales in ice cream parlors and specialty stores) were too broad to produce reasonable empirical results. Different definitions based on supermarket sales did, however, yield similar estimates to those reported here.

  12. For comparison purposes, we have also estimated a homogeneous logit demand model. To make this specification more flexible, we replaced the brand and flavor constants by brand-flavor constants.

  13. The data for one of the markets, Little Rock, AR, was suspect because Dreyers was not at all present for a couple of quarters. For this reason we could not back out marginal cost as described, and we drop this market from the analysis.

  14. The main advantage of estimating the parameters sequentially is savings in computing time. The computationally expensive component of the estimating problem is the product choice stage, in particular since we bootstrap standard errors. The separate estimation of the fixed cost, price, and demand sides reflects the information available to firms at different stages of the model. We assume, for example, that firms learn their competitors’ flavor choices before making a price choice. As such, estimating the parameters separately yields consistent, albeit inefficient parameter estimates.

  15. Results available from the authors upon request.


  • Anderson, S., de Palma, A., & Thisse, J. (1992). Discrete choice theory of product differentiation. Cambridge, MA: MIT.

    Google Scholar 

  • Bajari, P., Hong, H., Krainer, J., & Nekipelov, D. (2006). Estimating static models of strategic interaction. NBER Working Paper No. W12013.

  • Berry, S. (1994). Estimating discrete-choice models of product differentiation. RAND Journal of Economics, 25, 242–262.

    Article  Google Scholar 

  • Berry, S., Levinsohn, J., & Pakes, A. (1995). Automobile prices in market equilibrium. Econometrica, 63, 841–890.

    Article  Google Scholar 

  • Berry, S., Levinsohn, J., & Pakes, A. (2004). Differentiated products demand systems from a combination of micro and macro data: The new vehicle market. Journal of Political Economy, 112(1), 68–104.

    Article  Google Scholar 

  • Berry, S., & Waldfogel, J. (2001). Do mergers increase product variety? Evidence from radio broadcasting. Quarterly Journal of Economics, 116, 1009–1025.

    Article  Google Scholar 

  • Bresnahan, T., & Reiss, P. (1987). Do entry conditions vary across markets? Brookings Papers on Economic Activity, 1987(3), 833–881.

    Article  Google Scholar 

  • Bresnahan, T., & Reiss, P. (1991). Entry and competition in concentrated markets. Journal of Political Economy, 99(51), 977–1009.

    Article  Google Scholar 

  • Caplin, A., & Nalebuff, B. (1991). Aggregation and imperfect competition: On the existence of equilibrium. Econometrica, 59, 26–59.

    Google Scholar 

  • Draganska, M., & Jain, D. (2006). Consumer preferences and product-line pricing strategies: An empirical analysis. Marketing Science, 25(2), 164–174.

    Article  Google Scholar 

  • Draganska, M., Mazzeo, M., & Seim, K. (2007). Beyond plain vanilla: Modeling product assortment choices in the ice cream market. Working Paper No. 1982R, Stanford Graduate School of Business.

  • Einav, L. (2003). Not all rivals look alike: Estimating an equilibrium model of the release date timing game. Working Paper, Stanford University.

  • Gandhi, A., Froeb, L., Tschanz, S., & Werden, G. (2008). Post-merger product repositioning. Journal of Industrial Economics, 56(1), 49–67.

    Article  Google Scholar 

  • Hajivassiliou, V., & McFadden, D. (1998). The method of simulated scores for the estimation of ldv models. Econometrica, 66(4), 863–896.

    Article  Google Scholar 

  • Heckman, J. (1978). Dummy endogenous variables in a simultaneous equation system. Econometrica, 46(6), 931–959.

    Article  Google Scholar 

  • Hotelling, H. (1929). Stability in competition. Economic Journal, 39, 41–57.

    Article  Google Scholar 

  • Mazzeo, M. (2002). Product choice and oligopoly market structure. RAND Journal of Economics, 33, 221–242.

    Article  Google Scholar 

  • Nevo, A. (2000). Mergers with differentiated products: The case of the ready-to-eat cereal industry. RAND Journal of Economics, 31(3), 395–421.

    Article  Google Scholar 

  • Nevo, A. (2001). Measuring market power in the ready-to-eat cereal industry. Econometrica, 69(2), 307–342.

    Article  Google Scholar 

  • Orhun, Y. (2006). Spatial differentiation in the supermarket industry. Working Paper, GSB Chicago.

  • Reiss, P. C., & Spiller, P. T. (1989). Competition and entry in small airline markets. Journal of Law & Economics, 32(2), S179–202.

    Article  Google Scholar 

  • Rust, J. (1994). Estimation of dynamic structural models, problems and prospects: Discrete decision processes. In C. Sims (Ed.), Advances in econometrics: Sixth world congress (Vol. 2). Cambridge: Cambridge University Press.

    Google Scholar 

  • Seim, K. (2006). An empirical model of firm entry with endogenous product-type choices. RAND Journal of Economics, 37(3), 619–642.

    Article  Google Scholar 

  • Shankar, V., & Bolton, R. (2004). An empirical analysis of determinants of retailer pricing strategy. Marketing Science, 23(1), 28–49.

    Article  Google Scholar 

  • Thomadsen, R. (2007). Product positioning and competition: The role of location in the fast food industry. Marketing Science, 26(6),792–804.

    Article  Google Scholar 

  • Zhu, T., & Singh, V. (2006). Spatial competition and endogenous location choices: An application to discount retailing. Quantitive Marketing and Economics, Forthcoming.

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Correspondence to Michaela Draganska.

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The authors thank MSI for financial support and Noriko Kakihara for excellent research assistance. This paper has greatly benefited from comments from Ulrich Doraszelski, Brett Gordon, Ken Wilbur and seminar audiences at University of Chicago, Duke, UNC, USC, and the Summer Institute for Competitive Strategy at Berkeley.

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Draganska, M., Mazzeo, M. & Seim, K. Beyond plain vanilla: Modeling joint product assortment and pricing decisions. Quant Mark Econ 7, 105–146 (2009).

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  • Product assortment decisions
  • Multi-product firms
  • Discrete games

JEL Classification

  • L0
  • L1
  • L2
  • L8
  • M3