The optimal extinction of a renewable natural resource (original) (raw)

A note on the extinction of renewable resources

Journal of Environmental Economics and Management, 1988

This paper presents two sets of conditions under which a sole owner of a renewable resource stock who maximize s a nonlinear benefit function would find it more profitable to harvest the stock to extinction than follow a continuous harvesting strategy. When the minimum viable resource stock is positive, extinction is optimal as long as the initial resource stock is sufficiently small, regardless of the discount rate. When the minimum viable resource stock is zero and the discount rate exceeds the growth potential of the species extinction is optimal for sufficiently small initial stocks. 0 1988 AC&IICC PXSS, IIIC. 'In writing this paper I have benefitted from discussions with Tracy Lewis and William R. Porter. 'The growth potential of the species is defined to be the rate of change in net births as the resource stock approaches the minimum viable population.

Renewable resource management and extinction

Journal of Environmental Economics and Management, 1978

Several authors have noted that extinction of a biological resource could be consistent with a policy of maximizing the discounted present value of economic rent. However, the arguments put forward in support of this assertion have hitherto been based on autonomous models. In this note we discuss the nonautonomous case, which turns out to be considerably more difficult to analyze.

FROM HARVESTING TO NONHARVESTING UTILITY: AN OPTIMAL CONTROL APPROACH TO SPECIES CONSERVATION

The purpose of this paper is to retrace the evolution of mathematical models focused on relation and interaction between economic growth, sustainable development, and natural environment conservation. First, generic defensive expenditures are introduced into a common-property harvesting model in order to favor the species growth. Second, a transition model comprising both harvesting and nonharvesting values of wildlife biological species emerges. The latter gives rise to a group of purely nonharvesting models where anthropic activities and economic growth may have positive or negative impact on the natural evolution of wildlife species. Several scholars have proved that optimal strategies that are relatively good for harvesting purposes are not simply " transferrable " to the context of conservation of wildlife biological species with no harvesting value. In addition, the existence of optimal policies for long-term conservation of all biological species (with or without harvesting value) cannot be guaranteed without having relatively large species populations at the initial time. Therefore, all such strategies are incapable of enhancing the scarce populations of endangered species and, therefore, cannot save these species from eventual (local) extinction. As an alternative, policymakers may soon be compelled to design and implement short-term defensive actions aimed at recovery and enhancement of endangered wildlife species.

Optimal management of renewable resources with Darwinian selection induced by harvesting

Journal of Environmental Economics and Management, 2008

We present a bioeconomic analysis of the optimal long-term management of a genetic resource in the presence of selective harvesting. It is assumed that individuals possessing a particular gene have a lower natural mortality rate and are more valuable to capture. Highly selective harvesting may cause such a gene to lose its fitness advantage, and hence change the evolutionary path of the species. Results indicate that in a zero-cost harvesting regime, the decision to preserve the valuable gene depends on the natural rate of selection against less valuable individuals and the interest rate. On the other hand, the decision to let the less valuable gene become a significant fraction of the genes depends only on biological parameters. If marginal costs are positive, it is never optimal to let a valuable gene become extinct. Further, for some parameter values, the system exhibits multiple equilibriums. Therefore, optimal regulation may depend on initial conditions.

The optimal depletion of exhaustible resources: A complete characterization

Resource and Energy Economics, 2011

Le Centre interuniversitaire de recherche en économie quantitative (CIREQ) regroupe des chercheurs dans les domaines de l'économétrie, la théorie de la décision, la macroéconomie et les marchés financiers, la microéconomie appliquée et l'économie expérimentale ainsi que l'économie de l'environnement et des ressources naturelles. Ils proviennent principalement des universités de Montréal, McGill et Concordia. Le CIREQ offre un milieu dynamique de recherche en économie quantitative grâce au grand nombre d'activités qu'il organise (séminaires, ateliers, colloques) et de collaborateurs qu'il reçoit chaque année.

From population dynamics to resource exploitation: an introduction

Academia Letters, 2021

The topic was suggested by a note on Hubbert's curve for predicting decay of resource exploitation [1]. Suggestion came also from interpretation of Hubbert's curve in terms of the Lotka-Volterra (LV) equations by Bardi and Lavacchi [2]. Link with population dynamics was obvious since logistic and LV equations were proposed within the demography science field. The note provides an overview of fundamental models and application results. Details can be found in [3]. Mathematical population dynamics has a history of about two centuries. The first model can be regarded the exponential law [4] of Malthus [1766-1834]. The population volume x is written as an increasing exponential x(t)=exp(bt)x0 where x0 denotes initial population, t denotes time and b growth rate. The exponential is the free response of a first-order unstable differential equation dx/dt=b x(t), just describing short-term evolution. In order to better describe long-term evolutions, Malthusian model was refined in XIX century [5] to include mortality rate by Gompertz [1779-1865]. Population volume, written as x(t)=exp(ln(xmax/x0)(1-exp(-bt))), asymptotically attains the finite value xmax. The differential equation includes the stabilizing factor ln(xmax/x0) which is the asymptotic limit of f(x,n)=(1-(x/xmax)n)/n. By inserting f(x,n) as a factor in the exponential equation, that is dx/dt=bxf(x,n), one obtains the generalized logistic equation ([6], 1959, also known as Richards' equation). The standard logistic equation, for n=1, is the following: Standard logistic equation: dx/dt=b(1-x(t)/xmax) x(t), x(0)=x0. Figure 1 shows three profiles of the normalized logistic rate (dx/dt)/xmax with tmax=10 time units, the time when the rate attains the maximum value, and b=1/(time unit). The unitary

Optimal depletion of an exhaustible resource

Applied Mathematical Modelling, 1979

This paper considers an optimal control problem for the dynamics of an exhaustible natural resource model, the optimal control being the price over time to maximize the total present value of a parameterized social welfare function under the assumption that a substitute become available at a high enough price. Thus, the problem can be reinterpreted as one of the optimal phasing-in of an expensive substitute. Furthermore, the problem is constrained in the sense that the total consumption of the natural resource implied by a price trajectory ...