On the attainment of the maximum sustainable yield in the Verhulst–Lotka–Volterra model. (December 2019)

• Record Type: Journal Article
• Authors: Lambertini, Luca; Leitmann, George
• Is Part Of: Automatica. Volume 110(2019)
• Publication Date: 2019-12
• Subjects: Tragedy of commons -- Sustainability -- Resource extraction -- Differential games -- Open-loop controls; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.108555
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: We reformulate the Verhulst–Lotka–Volterra model of natural resource extraction under the alternative assumptions of Cournot behaviour and perfect competition, to revisit the tragedy of commons vs the possibility of sustainable harvesting. After a brief layout of the open-loop solution including the Ramsey rule, we rely on the state-redundancy property and the consequent strong time consistency of the static equilibrium output to investigate the different impact of demand elasticity on the regulator's possibility of driving industry harvest to the maximum sustainable yield in the two settings. The presence of a flat demand function offers the authority a fully effective regulatory tool in the form of the exogenous price faced by perfectly competitive firms, to drive their collective harvest rate to the maximum sustainable yield. The same cannot happen under Cournot competition, as in this case the price is endogenous and the regulator's policy is confined to limiting access to the common pool.