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In the case of small pelagic fish, it seems reasonable to consider harvest functions depending nonlinearly on fishing effort and fish stock. Indeed, empirical evidence about these fish species suggests that marginal catch does not necessarily react in a linear way neither to changes in fishing effort nor in fish stock levels. This is in contradiction with traditional fishery economic models where catch-to-input marginal productivities are normally assumed to be constant. While allowing for nonlinearities in both catch-to-effort and catch-to-stock parameters, this paper extends the traditional single-stock harvesting economic model by focusing on the dependence of the stationary solutions upon the nonlinear catch-to-stock parameter. Thus, we analyze equilibrium responses to changes in this parameter, which in turn may be triggered either by climatic or technological change. Given the focus in this study on the case of small pelagic fish, the analysis considers positive but small values for the catch-to-stock parameter.
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Keywords: Cobb–Douglas production function; Small pelagic fisheries; maximum principle; optimal control

Document Type: Research Article

Affiliations: 1: Facultad de Economía y Negocios/ILADES, Universidad Alberto Hurtado, Erasmo Escala 1835, Santiago, Chile , Email: [email protected] 2: Departamento de Ingeniería Matemática, Centro de Modelamiento Matemático (CNRS UMI 2807), FCFM, Universidad de Chile, Avda. Blanco Encalada 2120, Santiago, Chile , Email: [email protected]

Publication date: 2011-05-01

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