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Price, scarcity rent, and a modified r per cent rule for non‐renewable resources

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  • John Livernois
  • Patrick Martin

Abstract

Since Hotelling's seminal paper on the optimal depletion of exhaustible resources, much has been published; yet confusion remains about whether scarcity rent and price increase or decrease as a resource is depleted when costs tend to rise with depletion. We show that Hotelling's fundamental results of rising scarcity rent and price paths are sustained and that the path of scarcity rent converges on the r per cent rule, provided the objective function is concave. Predictions of non‐monotonic or declining scarcity rent paths are due to implicit assumptions that lead to a non‐concave objective function. We identify the sources of these non‐concavities. JEL Classification: Q30, D90, C60 Prix, rente de rareté et une règle modifiée du r‐pourcent pour les ressources non renouvelables. Malgré la volumineuse littérature spécialisée qui a fleuri depuis qu'Hotelling a écrit son mémoire fondateur sur l'épuisement optimal des ressources renouvelables, une grande confusion règne toujours quand il faut établir si la rente de rareté et le prix augmentent ou chutent à proportion que la ressource s'épuise quand les coûts tendent à croître avec l'épuisement. Ce mémoire montre que les résultats fondamentaux obtenus par Hotelling quant aux sentiers de croissance de la rente de rareté et du prix tiennent toujours, et que le sentier de croissance de la rente de rareté converge vers la règle du r‐pourcent pourvu que la fonction objective soit concave. Les prédictions de sentiers de croissance non monotone ou de déclin de la rente de rareté présentées dans la littérature spécialisée sont attribuables à des postulats implicites qui engendrent une fonction objective non concave. Les auteurs identifient les sources de ces non‐concavités.

Suggested Citation

  • John Livernois & Patrick Martin, 2001. "Price, scarcity rent, and a modified r per cent rule for non‐renewable resources," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 34(3), pages 827-845, August.
  • Handle: RePEc:wly:canjec:v:34:y:2001:i:3:p:827-845
    DOI: 10.1111/0008-4085.00101
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    Cited by:

    1. Voss, Achim & Schopf, Mark, 2021. "Lobbying over exhaustible-resource extraction," European Economic Review, Elsevier, vol. 135(C).
    2. repec:elg:eechap:14605_1 is not listed on IDEAS
    3. Roel van Veldhuizen & Joep Sonnemans, 2018. "Nonrenewable Resources, Strategic Behavior and the Hotelling Rule: An Experiment," Journal of Industrial Economics, Wiley Blackwell, vol. 66(2), pages 481-516, June.

    More about this item

    JEL classification:

    • Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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