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Third-Degree Price Discrimination Versus Uniform Pricing

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Dirk Bergemann, Francisco Castro, Gabriel Weintraub

General Economics · Submitted 11 Dec 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our main result establishes that for a broad class of third-degree price discrimination problems with concave profit functions (in the price space) and common support, a uniform price is guaranteed to achieve one half of the optimal monopoly profits.

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arXiv ID1912.05164 (version 3)
Pith IDVO2UCJGT, Pith's permanent record of this paper and its review
CitationDirk Bergemann, Francisco Castro, Gabriel Weintraub. "Third-Degree Price Discrimination Versus Uniform Pricing." arXiv:1912.05164 (2019). https://pith.science/paper/VO2UCJGT
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,210 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.88 · human participants 0.02 · controlled comparison 0.76 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.93 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We compare the profit of the optimal third-degree price discrimination policy against a uniform pricing policy. A uniform pricing policy offers the same price to all segments of the market. Our main result establishes that for a broad class of third-degree price discrimination problems with concave profit functions (in the price space) and common support, a uniform price is guaranteed to achieve one half of the optimal monopoly profits. This profit bound holds for any number of segments and prices that the seller might use under third-degree price discrimination. We establish that these conditions are tight and that weakening either common support or concavity can lead to arbitrarily poor profit comparisons even for regular or monotone hazard rate distributions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We compare the profit of the optimal third-degree price discrimination policy against a uniform pricing policy. contribution 0.90 0.88 0.04 asserted 0.52
s1 A uniform pricing policy offers the same price to all segments of the market. background 1.00 0.06 0.01 asserted 1.00
s2 Our main result establishes that for a broad class of third-degree price discrimination problems with concave profit functions (in the price space) and common support, a uniform price is guaranteed to achieve one half of the optimal monopoly profits. result 1.00 0.95 0.98 asserted 1.00
s3 This profit bound holds for any number of segments and prices that the seller might use under third-degree price discrimination. result 0.89 0.83 0.12 asserted 0.99
s4 We establish that these conditions are tight and that weakening either common support or concavity can lead to arbitrarily poor profit comparisons even for regular or monotone hazard rate distributions. result 0.90 0.95 0.07 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We compare the profit of the optimal third-degree price discrimination policy against a uniform pricing policy. A uniform pricing policy offers the same price to all segments of the market. Our main result establishes that for a broad class of third-degree price discrimination problems with concave profit functions (in the price space) and common support, a uniform price is guaranteed to achieve one half of the optimal monopoly profits. This profit bound holds for any number of segments and prices that the seller might use under third-degree price discrimination. We establish that these conditions are tight and that weakening either common support or concavity can lead to arbitrarily poor profit comparisons even for regular or monotone hazard rate distributions.

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