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On the Mitra–Wan forest management problem in continuous time

Author

Listed:
  • Giorgio Fabbri

    (UEVE - Université d'Évry-Val-d'Essonne)

  • Silvia Faggian

    (University of Ca’ Foscari [Venice, Italy])

  • Giuseppe Freni

    (Department of Business and Economics, Parthenope University of Naples)

Abstract

The paper provides a continuous-time version of the discrete-time Mitra–Wan model of optimal forest management, where trees are harvested to maximize the utility of timber flow over an infinite time horizon. The available trees and the other parameters of the problem vary continuously with respect to both time and age of the trees, so that the system is ruled by a partial differential equation. The behavior of optimal or maximal couples is classified in the cases of linear, concave or strictly concave utility, and positive or null discount rate. All sets of data share the common feature that optimal controls need to be more general than functions, i.e. positive measures. Formulas are provided for golden-rule configurations (uniform density functions with cutting at the ages that solve a Faustmann problem) and for Faustmann policies, and their optimality/maximality is discussed. The results do not always confirm the corresponding ones in discrete time.

Suggested Citation

  • Giorgio Fabbri & Silvia Faggian & Giuseppe Freni, 2015. "On the Mitra–Wan forest management problem in continuous time," Post-Print hal-01615431, HAL.
    • Handle: RePEc:hal:journl:hal-01615431
    DOI: 10.1016/j.jet.2015.03.004
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    Cited by:

    1. Giorgio Fabbri & Silvia Faggian & Giuseppe Freni, 2016. "Non-Existence of Optimal Programs in Continuous Time," AMSE Working Papers 1630, Aix-Marseille School of Economics, France.
    2. David Desmarchelier & Alexandre Mayol, 2022. "To seed, or not to seed? An endogenous labor supply approach in a simple overlapping generation economy," Bulletin of Economic Research, Wiley Blackwell, vol. 74(1), pages 25-38, January.
    3. Faggian, Silvia & Gozzi, Fausto & Kort, Peter M., 2021. "Optimal investment with vintage capital: Equilibrium distributions," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    4. Fabbri, Giorgio & Faggian, Silvia & Freni, Giuseppe, 2017. "Non-existence of optimal programs for undiscounted growth models in continuous time," Economics Letters, Elsevier, vol. 152(C), pages 57-61.
    5. Galo Nuno & Benjamin Moll, 2018. "Social Optima in Economies with Heterogeneous Agents," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 28, pages 150-180, April.
    6. Khan, M. Ali, 2016. "On a forest as a commodity and on commodification in the discipline of forestry," Forest Policy and Economics, Elsevier, vol. 72(C), pages 7-17.
    7. Silvia Faggian & Giuseppe Freni, 2015. "A Ricardian Model of Forestry," Working Papers 2015:12, Department of Economics, University of Venice "Ca' Foscari", revised 2015.

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    More about this item

    Keywords

    Optimal harvesting; Forest management; Measure-valued controls;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • Q23 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Forestry

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