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Research Note—Quantity Discounts in Differentiated Consumer Product Markets

School of Business, University of Kansas, Lawrence, Kansas 66045
Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
srama{at}ku.edu
esther{at}katz.pitt.edu

In this paper, we extend the standard Hotelling model of product differentiation to incorporate a second dimension of consumer heterogeneity that relates to the quantity of the product consumers wish to buy. This extension allows us to derive optimal nonlinear pricing rules chosen by competing sellers when offering differentiated products in the marketplace. It also permits us to assess whether sellers find it optimal to offer quantity discounts in such a setting, and the implications of such discounts on their profitability. We find that offering quantity discounts corresponds, indeed, to equilibrium behavior. The extent of discounting declines the less differentiated the products. Surprisingly, when sellers offer to consumers a choice between two different-sized packages, their profits are, at most, as high as when such a choice is unavailable. Moreover, when utilizing nonlinear pricing rules is not feasible, the profits of the sellers actually decline when they offer consumers a choice between different-sized packages. A limited empirical investigation supports the comparative statics we derive in our theoretical model.

Key Words: price discrimination; game theory; nonlinear pricing; pricing research; competition
History: Received: April 3, 2007; accepted: December 13, 2007.