Cyclical versus Non-Cyclical Harvesting Policies in Renewable Resource Management

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(1)Cyclical versus Non-Cyclical Harvesting Policies in Renewable Resource Management Katrin Erdlenbruch, Alain Jean-Marie, Michel Moreaux, Mabel Tidball. To cite this version: Katrin Erdlenbruch, Alain Jean-Marie, Michel Moreaux, Mabel Tidball. Cyclical versus Non-Cyclical Harvesting Policies in Renewable Resource Management. Monte Verità Conference on Sustainable Resource Use and Economic Dynamics - SURED 2008, Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology in Zürich [Zürich] (ETH Zürich). Zürich, CHE. Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology in Zürich [Zürich] (ETH Zürich), CHE., Jun 2008, Monte Verita, Switzerland. 34 p. �hal-02821646�. HAL Id: hal-02821646 https://hal.inrae.fr/hal-02821646 Submitted on 6 Jun 2020. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

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(474) . i) a ≥ b > c ≥ d . a. π(a, a − c) + π(b, b − d) =. . d. [p − c(x)] dx +. d. [p − c(x)] dx. c. = π(a, a − d) + π(b, b − c) . ii) ( , & ) * πxI + πII = 0 . iii) ( 1 8 ) ( (7* y ∗ (x0 ) y ∗(x0 ) = x∗ ) 4* 1 .

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(479) ' . . H(x, x ¯) = −p + c(x) + [p(¯ x − x) −. x ¯. −rτ. c(u)du] e x. ∂G (x, x¯) ∂x. > 0 . e−rτ r . F (x)(1 − e−rτ ) 1 − e−rτ. ! τ = τ (x, x ¯)G 1

(480) H(x, x¯). H(x, x ¯) =. H2 (x, x¯) x (p − c(x))(K − x) + α x g0 (K − x) + H3 (x, x¯) H1 (x, x¯) 4.

(481) . . . x¯(K − x) − 1 < 0, x(K − x¯) r x¯(K − x) g0 K < 0, H2 (x, x¯) = −α g0 x(K − x¯). H1 (x, x ¯) = α x g0 (K − x). . g rK 0. H3 (x, x ¯) = r p α(¯ x − x) + r b c (¯ x−α − x−α ).. ∂H3 (¯ x, x¯) = r α(−p + c(x)) x −p + ∂x c(x) < 0 H3 (x, x¯) > 0 ( &. H(x, x¯) > 0

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