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A Resource Extraction Model with Technology Adoption under Time Inconsistent Preferences

Author

Listed:
  • Carles Mañó-Cabello

    (Departament Matemàtica Econòmica, Financera i Actuarial and BEAT, Universitat de Barcelona, 08034 Barcelona, Spain
    These authors contributed equally to this work.)

  • Jesús Marín-Solano

    (Departament Matemàtica Econòmica, Financera i Actuarial and BEAT, Universitat de Barcelona, 08034 Barcelona, Spain
    These authors contributed equally to this work.)

  • Jorge Navas

    (Departament Matemàtica Econòmica, Financera i Actuarial and BEAT, Universitat de Barcelona, 08034 Barcelona, Spain
    These authors contributed equally to this work.)

Abstract

A two-stage non-standard optimal control problem with time inconsistent preferences is studied. In an infinite horizon setting, a time consistent (sophisticated) decision maker chooses the time of switching between two consecutive regimes. The second regime corresponds to the implementation of a new technology, and a cost must be paid at the switching time. Although the problem is formulated for a general discount function, special attention is devoted to models with nonconstant discounting and heterogeneous discounting. The problem is solved by transforming it into a problem in a finite horizon and free terminal time. The corresponding dynamic programming equations are presented, and conditions for the derivation of the switching time by decision makers with different degrees of sophistication are studied. A resource extraction model with technology adoption is solved in detail. Effects of the adoption of different discount functions are illustrated numerically.

Suggested Citation

  • Carles Mañó-Cabello & Jesús Marín-Solano & Jorge Navas, 2021. "A Resource Extraction Model with Technology Adoption under Time Inconsistent Preferences," Mathematics, MDPI, vol. 9(18), pages 1-24, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2205-:d:631711
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    References listed on IDEAS

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