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The Costate Variable in a Stochastic Renewable Resource Model


  • Kenneth Lyon
  • Saket Pande


In this paper we discuss the costate variable in a stochastic optimal control model of a renewable natural resource, which we call a fishery. The role of the costate variable in deterministic control models has been discussed extensively in the literature. See, for example, Lyon (1999), Clark (1990, pp. 102-107), and Arrow and Kurz (1970, pp. 35-37); however, there is little discussion of this variable for stochastic models, even though the costate variable has similar roles in the two models. In both models the costate variable is a shadow value of the associated state variable, and as such has the role of rationing the use of the state variable. In addition, as has been shown in Lyon (1999), in natural resource problems the costate variable can be partitioned into a scarcity effect and a cost effect. We show that this same partitioning can be done in the stochastic renewable resource problem. We discuss and contrast the similarities and differences in these concepts for deterministic and stochastic models. In addition, we present a numerical example help solidify the results.

Suggested Citation

  • Kenneth Lyon & Saket Pande, 2003. "The Costate Variable in a Stochastic Renewable Resource Model," Working Papers 2003-15, Utah State University, Department of Economics.
  • Handle: RePEc:usu:wpaper:2003-15

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    References listed on IDEAS

    1. Dickinson, David L. & Bailey, DeeVon, 2002. "Meat Traceability: Are U.S. Consumers Willing To Pay For It?," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 27(02), December.
    2. Liddell, Sterling & Bailey, DeeVon, 2001. "Market Opportunities And Threats To The U.S. Pork Industry Posed By Traceability Systems," International Food and Agribusiness Management Review, International Food and Agribusiness Management Association (IFAMA), vol. 4(03).
    3. Lusk, Jayson L. & Fox, John A., 2002. "Consumer Demand for Mandatory Labeling of Beef from Cattle Administered Growth Hormones or Fed Genetically Modified Corn," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 34(01), pages 27-38, April.
    4. Grannis, Jennifer L. & Hooker, Neal H. & Thilmany, Dawn D., 2000. "Consumer Preference For Specific Attributes In Natural Beef Products," 2000 Annual Meeting, June 29-July 1, 2000, Vancouver, British Columbia 36406, Western Agricultural Economics Association.
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