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The Costate Variable in a Stochastic Renewable Resource Model

Kenneth Lyon () and Saket Pande

No 2003-15, Working Papers from Utah State University, Department of Economics

Abstract: 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.

Keywords: costate variable; stochastic dynamic programming; deterministic dynamic programming; renewable resource model; simulation (search for similar items in EconPapers)
Pages: 20 pages
Date: 2003-12
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