An Oligopoly-Fringe Model with HARA Preferences

Gerard van der Meijden*, Cees Withagen, Hassan Benchekroun

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


Inspired by empirical evidence from the oil market, we build a model of an oligopoly facing a fringe as well as competition from renewable resources. We explore different subclasses of HARA utility functions (Cobb–Douglas, power and quadratic utility) to check the robustness of results found in the previous literature. For isoelastic demand, we characterize the equilibrium extraction rates of the fringe and the oligopolists. There always exists a phase of simultaneous supply of the oligopolists and the fringe, implying an inefficient order of use of resources since the oligopolists have smaller unit extraction costs and carbon emissions than the fringe. We calibrate our model to the oil market to quantify this sequence effect. In our benchmark calibration, we find for the three HARA subclasses that the sequence effect is responsible for almost all of the welfare loss compared to the first-best. It becomes smaller as market power decreases. Furthermore, we show that climate damage and Green Paradox effects depend non-monotonically on the degree of market power.

Original languageEnglish
Pages (from-to)954–976
Number of pages23
JournalDynamic Games and Applications
Issue number3
Early online date19 Mar 2022
Publication statusPublished - Sept 2022

Bibliographical note

Funding Information:
Hassan Benchekroun thanks the Fonds de recherche du Québec - Société et culture (FRQSC) and the Canadian Social Sciences and Humanities Research Council (SSHRC) for financial support. All data generated or analysed during this study are included in this published article and its supplementary information files.

Publisher Copyright:
© 2022, The Author(s).


  • Climate policy
  • HARA preferences
  • Herfindahl rule
  • Limit pricing
  • Non-renewable resource
  • Oligopoly
  • Oligopoly-fringe
  • Q31
  • Q42
  • Q54
  • Q58

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