Price discrimination: Teaching new results with simple exercises

Abstract

The authors of this article propose a simple exercise of monopoly pricing to illustrate complex theoretical results on the welfare effects of group pricing. By exposing students to this exercise, they aim to bridge a gap between the standard textbook analysis of group pricing and more general results in the literature and clarify some students’ misconceptions. They gear the exercise toward undergraduate students in principles and intermediate-level economics, microeconomics, and industrial organization courses.

Keywords:

• Market segmentation
• monopoly pricing
• third-degree price discrimination

JEL CODES:

• A2
• D42
• L12

Acknowledgments

The authors thank two anonymous referees and the associate editor for their helpful suggestions. They also thank Dirk Bergemann, Walter Cont, Daniel Levy, and the participants at the 2021 CTREE Conference.

Notes

1 This article is part of a more comprehensive project where we construct simple numerical exercises without using calculus or complicated algebraic expressions to discuss complex results on pricing under market power.

2 Pigou’s original typology distinguished ideal (perfect or first-degree), second-degree, and third-degree price discrimination. Belleflamme and Peitz (2010) proposed a more descriptive typology based on Shapiro and Varian (1999) and distinguished among personalized, menu, and group pricing.

3 See Bergemann, Brooks, and Morris (2015) for a literature review.

4 Instructors in advanced undergraduate courses may want to explore generalizations of this argument as applied to many buyers in Bergemann, Brooks, and Morris (2017) and an introduction to the role of information in Bergemann and Morris (2019).

5 The assumption of constant marginal cost is simply a normalization and does not affect the qualitative results. Instructors inclined to provide real-world examples of goods produced under zero marginal cost may refer to information goods.

6 This observation is discussed in Nahata, Ostaszewski, and Sahoo (1990).

7 None of the textbooks we reviewed for this article presents an example where prices in all segments are strictly below the uniform price.

8 Segmentations (5) to (10) in this exercise can be motivated with the same applications we motivated segmentations (2)–(4). Some results in (5)–(10) are different from those in (2)–(4) due to the number of high-, medium-, and low-valuation individuals in each group.

9 To construct a distribution of valuations that encompasses every segmentation described in this section, the instructor must start by choosing valuations in three categories: “high,” “medium,” and “low.” For instance, in our exercise, these values are $13, $7, and $5. With the uniform monopoly price and the desired prices in each segment in mind, assign individuals with these valuations (or with sufficiently similar valuations) to each segment, choosing the number of individuals to ensure it preserves the desired relationship between the optimal price in each segment and the uniform monopoly price. Instructors may contact us for additional examples.

10 While the qualitative results of group pricing for segmentations (2)–(10) in our exercise are comprehensive, readers are encouraged to contact us for additional examples or segmentations leading to specific results.

11 We thank the associate editor for suggesting the inclusion of this observation and the example that follows.