E. ANN STANLEY
AND HÉLÈNE CLÉMENT-PITIOT
(1)Laboratoire de Physique Statistique
de l'Ecole Normale Supérieure
24 rue Lhomond, F 75231 Paris Cedex 5, France.
(2) Mathematics department
Iowa State University
Ames, IA 50011, USA.
(3) The SantaFe Institute
1399 Hyde Park Road
Santa FE, NM 87501, USA
(4) CIRAD - GREEN,
42, rue Scheffer, 75116 Paris, France
(5) MODEM, Université de Paris X - Nanterre,
200 Avenue de la République,
92 001 Nanterre Cedex, France.
A simple differential equation system describes the dynamics of a renewable resource coupled by a Cobb-Douglas production function to the capital invested in resource harvesting. Capital dynamics is driven by very simple and myopic mechanisms, precluding rational expectations of investors or central planing authorities. This system can model fisheries which operate under open access. Significant resource depletion is shown to follow capital overshoot. We study the influence of biological and economic mechanisms such as the existence of a carrying capacity for the resource, the role of prices and the possibility of a minimum consumption for the labour force on the amplitude of resource depletion. We define a concept of fragility that relates resource depletion to the initial distance of the dynamic variables from equilibrium. An analytic expression of fragility, applicable to differential models of bio-economic systems is derived in this paper. The influence of some institutional interventions is also assessed.
This html manuscript is a long version of a working paper of Santa Fe series 94-04-018.