Nonlinear Pricing Published in association

What do phone rates, frequent flyer programs, and railroad tariffs all have in common? They are all examples of nonlinear pricing. Pricing is nonlinear when it is not strictly proportional to the quantity purchased. The Electric Power Research Institute has commissioned Robert Wilson to review the various facets of nonlinear pricing. The work starts with a general non-mathematical discussion, followed by a more technical presentation intended for readers with a fairly advanced background. Thorough and detailed, this study has ample examples of case studies from a variety of industries.

1. Introduction

3

(24)

1.1 Motivations for Nonlinear Pricing

5

(2)

1.2 Practical Uses for Nonlinear Pricing

7

(3)

1.3 Feasibility of Nonlinear Pricing

10

(5)

1.4 Illustration: The Electric Power Industry

15

(2)

1.5 Overview of the Chapters

17

(6)

1.6 Summary

23

(4)

I: FUNDAMENTALS OF NONLINEAR PRICING

27

(98)

2. Illustrations of Nonlinear Pricing

27

(19)

2.1 Time and Newsweek's Advertising Rates

28

(2)

2.2 EDF's Tariffs for Electric Power

30

(6)

2.3 PG&E's Curtailable Service

36

(3)

2.4 MCI's and AT&T's Telephone Tariffs

39

(2)

2.5 Federal Express' Mail Rates

41

(1)

2.6 Delta Airlines' Frequent Flyer Rebates

41

(3)

2.7 Summary

44

(2)

3. Models and Data Sources

46

(27)

3.1 Descriptions of Demand Behavior

49

(8)

3.2 Estimation of the Demand Profile

57

(5)

3.3 Welfare Considerations

62

(4)

3.4 Cautions and Caveats

66

(1)

3.5 Standard Assumptions(*)

67

(4)

3.6 Summary

71

(2)

4. Tariff Design

73

(25)

4.1 The Price Schedule of a Monopolist

73

(8)

4.2 Extensions and Qualifications

81

(7)

4.3 The Bundling Interpretation

88

(1)

4.4 Fixed Costs and Fixed Fees

89

(2)

4.5 Multipart Tariffs

91

(5)

4.6 Summary

96

(2)

5. Ramsey Pricing

98

(27)

5.1 The Price Schedule of a Regulated Firm

99

(9)

5.2 Pareto-Improving Tariffs

108

(10)

5.3 Long-Distance Telephone Tariffs

118

(3)

5.4 Summary

121

(3)

II: DISAGGREGATED DEMAND MODELS

125

(86)

6. Single-Parameter Disaggregated Models

125

(39)

6.1 A Model with Discrete Types

126

(6)

6.2 Models with One-Dimensional Types

132

(4)

6.3 Two-Part Tariffs

136

(5)

6.4 Multipart Tariffs

141

(9)

6.5 Nonlinear Tariffs

150

(3)

6.6 Some Examples

153

(5)

6.7 Fixed Costs and Fixed Fees

158

(5)

6.8 Summary

163

(1)

7. Income Effects

164

(13)

7.1 Construction of the Demand Profile

164

(1)

7.2 Characterization of the Optimal Tariff

165

(1)

7.3 Examples

166

(7)

7.4 Fixed Fees

173

(2)

7.5 Summary

175

(2)

8. Technical Amendments

177

(34)

8.1 Technical Considerations

177

(8)

8.2 Derivations of the Optimal Tariff

185

(5)

8.3 Approximate Optimality of Multipart Tariffs

190

(4)

8.4 Multiple Dimensions of Customers' Types

194

(6)

8.5 A General Demand-Profile Formulation

200

(6)

8.6 Summary

206

(5)

III: MULTIDIMENSIONAL TARIFFS

211

(70)

9. Multidimensional Pricing

211

(25)

9.1 A Multidimensional Formulation

212

(7)

9.2 Design of Multidimensional Tariffs

219

(4)

9.3 Examples

223

(5)

9.4 An Item-Assignment Formulation

228

(7)

9.5 Summary

235

(1)

10. Priority Pricing

236

(23)

10.1 Capacity-Constrained Tariffs: Priority Pricing

237

(7)

10.2 Ramsey Pricing of Priority Service

244

(9)

10.3 Nonlinear Pricing in a Priority Queuing System

253

(4)

10.4 Summary

257

(2)

11. Capacity Pricing

259

(22)

11.1 Background

259

(2)

11.2 Cost Recovery of Load-Duration Demands

261

(5)

11.3 Pricing Load-Duration Demands

266

(10)

11.4 Summary

276

(5)

IV: MULTIPRODUCT TARIFFS

281

(94)

12. Multiple Products and Competitive Tariffs

281

(52)

12.1 Separable Multiproduct Tariffs

282

(19)

12.2 Monopolistic Competition

301

(2)

12.3 Oligopoly

303

(6)

12.4 Nonlinear Supply Schedules

309

(2)

12.5 Summary

311

(2)

13. Multiproduct Pricing

313

(37)

13.1 Special Features of Multiproduct Tariffs

314

(3)

13.2 Formulation

317

(8)

13.3 A Reprise of Priority Service

325

(2)

13.4 Single Type Parameters

327

(5)

13.5 Multiple Type Parameters

332

(12)

13.6 Construction of Multiproduct Prices

344

(4)

13.7 Summary

348

(2)

14. Multiproduct Tariffs

350

(25)

14.1 Formulation

351

(3)

14.2 The Optimal Multiproduct Tariff

354

(5)

14.3 Numerical Examples

359

(4)

14.4 Illustration: Load-Factor Tariffs

363

(5)

14.5 An Alternative Formulation*

368

(3)

14.6 Summary

371

(4)

SUPPLEMENT

375

(36)

15. Other Applications of Nonlinear Pricing

375

(26)

15.1 Product Pricing Applications

375

(7)

15.2 Incentives in Markets with Private Information

382

(8)

15.3 Incentives in Labor Contracting

390

(5)

15.4 Taxation and Regulatory Policies

395

(3)

15.5 Summary

398

(3)

16. Bibliography

401

(10)

16.1 A Short History

401

(5)

16.2 Chapter References

406

(5)

References

411

(12)

Index

423

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Nonlinear Pricing Published in association with the Electric Power Research Institute

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Nonlinear Pricing Published in association with the Electric Power Research Institute

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