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Revisited water-oriented relationships between a set of farmers and an aquifer: accounting for lag effect


  • Cyril Bourgeois
  • Pierre-Alain Jayet


Many environmental problems are due to damages caused by stock of pollutants which accumulate with time lag to their emission. In this paper, we focus on nitrates used in agriculture which can pollute groundwater years after their initial use. A dynamic optimal control problem with heterogeneous farmers is proposed. Usual structural parameters like the discount rate, the natural clearing rate, the lagged time interval between the soil-level pollution occurrence and the impact on groundwater are taken into account. We also examine pollution as caused by a continuous set of farms characterized by their individual performance index and by their individual marginal contribution to the pollution. The issue is further investigated by taking account of change in the information context, successively related to perfect information and to asymmetric information. As a result, when the delay between the spreading of N-fertilizer and the impact on the aquifer increases, i.e., the higher the lag, the steady state pollution stock and the steady state shadow price of the stock both increase. Moreover, asymmetric information leads to a higher stock of pollution. Given the U.S. EPA context or given the European Union context and their directives focusing on nitrate pollution and water quality, the qualitative results provided in this paper should help modellers and decision makers promote suitable environmental policies.

Suggested Citation

  • Cyril Bourgeois & Pierre-Alain Jayet, 2010. "Revisited water-oriented relationships between a set of farmers and an aquifer: accounting for lag effect," Working Papers 2010/06, INRA, Economie Publique.
  • Handle: RePEc:apu:wpaper:2010/06

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    References listed on IDEAS

    1. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
    2. Ulrich Brandt-Pollmann & Ralph Winkler & Sebastian Sager & Ulf Moslener & Johannes Schlöder, 2008. "Numerical Solution of Optimal Control Problems with Constant Control Delays," Computational Economics, Springer;Society for Computational Economics, vol. 31(2), pages 181-206, March.
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    4. Winkler, Ralph, 2011. "A Note On The Optimal Control Of Stocks Accumulating With A Delay," Macroeconomic Dynamics, Cambridge University Press, vol. 15(04), pages 565-578, September.
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    6. Xepapadeas, A. P., 1991. "Environmental policy under imperfect information: Incentives and moral hazard," Journal of Environmental Economics and Management, Elsevier, vol. 20(2), pages 113-126, March.
    7. Phoebe Koundouri, 2004. "Current Issues in the Economics of Groundwater Resource Management," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 703-740, December.
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    Cited by:

    1. Augeraud-Véron, Emmanuelle & Leandri, Marc, 2014. "Optimal pollution control with distributed delays," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 24-32.

    More about this item


    Non-point source pollution; Farming pollution; Aquifer; Nitrate; Time lag; Optimal control; Mechanism design;

    JEL classification:

    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design


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