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Consumer-Optimal Segmentation in Multi-Product Markets

Dirk Bergemann, Tibor Heumann, Michael C. Wang

Abstract

We analyze how market segmentation affects consumer welfare when a monopolist can engage in both second-degree price discrimination (through product differentiation) and third-degree price discrimination (through market segmentation). We characterize the consumer-optimal market segmentation and show that it has several striking properties: (1) the market segmentation displays monotonicity$\unicode{x2014}$higher-value customers always receive higher quality product than lower-value regardless of their segment and across any segment; and (2) when aggregate demand elasticity exceeds a threshold determined by marginal costs, no segmentation maximizes consumer surplus. Our results demonstrate that strategic market segmentation can benefit consumers even when it enables price discrimination, but these benefits depend critically on demand elasticities and cost structures. The findings have implications for regulatory policy regarding price discrimination and market segmentation practices.

Consumer-Optimal Segmentation in Multi-Product Markets

Abstract

We analyze how market segmentation affects consumer welfare when a monopolist can engage in both second-degree price discrimination (through product differentiation) and third-degree price discrimination (through market segmentation). We characterize the consumer-optimal market segmentation and show that it has several striking properties: (1) the market segmentation displays monotonicityhigher-value customers always receive higher quality product than lower-value regardless of their segment and across any segment; and (2) when aggregate demand elasticity exceeds a threshold determined by marginal costs, no segmentation maximizes consumer surplus. Our results demonstrate that strategic market segmentation can benefit consumers even when it enables price discrimination, but these benefits depend critically on demand elasticities and cost structures. The findings have implications for regulatory policy regarding price discrimination and market segmentation practices.
Paper Structure (37 sections, 39 theorems, 240 equations, 10 figures)

This paper contains 37 sections, 39 theorems, 240 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Motivation and Results
  3. Related Literature
  4. Setup
  5. Payoffs and Pricing
  6. Markets
  7. Segmentations
  8. Notation
  9. The Binary Value Case
  10. Roadmap
  11. Optimal Screening and Consumer Surplus
  12. Distribution Over Inverse Hazard Rates
  13. Consumer Surplus and Local Informational Rents
  14. The Segmentation Problem as Bayesian Persuasion
  15. From Persuasion to Segmentations
  16. ...and 22 more sections

Key Result

Lemma 1

The consumer-optimal segmentation generates at most value eq:maxex. Furthermore, if a segmentation ${ \if@compatibility \mathchar"011B {} \mathchar"011B }$ maximizes consumer surplus if, for every $x\in \mathop{\mathrm{supp}}\nolimits({ \if@compatibility \mathchar"011B {} \mathchar"011B for a distribution ${ \if@compatibility \mathchar"0116 {} \mathchar"0116 } \in \Delta \mathbb

Figures (10)

  • Figure 1: Local information rent $u_{L}(h)$ as a function of the hazard rate $h$.
  • Figure 2: The local information rent $u_{L}(h)$ as a function of the cost elasticity ${ \if@compatibility \mathchar"010D {} \mathchar"010D }$.
  • Figure 3: $u_1$ and $\overline{u}_1$ for Example \ref{['ex:1']}.
  • Figure 4: $u_k$ and $\overline{u}_k$ for Example \ref{['ex:2']}.
  • Figure 5: Illustration of $O$ and regular markets with quadratic costs.
  • ...and 5 more figures

Theorems & Definitions (62)

  • Lemma 1: Segmentation as One-Dimensional Bayesian Persuasion
  • Proposition 2: Optimal Segmentation---Binary Values
  • Lemma 3: Supply in Regular Markets
  • Lemma 4: Consumer Surplus in Regular Markets
  • Lemma 5: Consumer Surplus in Irregular Markets
  • Theorem 6: Value of Segmentation
  • proof : Proof (Upper Bound)
  • Example 1: Within-Value Persuasion
  • Example 2: Between-Value Persuasion
  • Proposition 7: Properties of Consumption
  • ...and 52 more