Sustainability of an economy with an exhaustible resource: A viable control approach
In this article, the authors examine the conditions for the sustainability of a production–consumption system based on the use of an exhaustible natural resource. Instead of studying the environmental and economic interactions in terms of optimal control, they focus on the viability of the system, defined by a set of constraints combining guaranteed consumption and a stock of resources to be preserved at all times, which refers to a Rawlsian intergenerational equity perspective. Using the mathematical concept of viability kernel, which makes it possible to deal with the consistency between constraints and controlled dynamics, they exhibit the sustainable technological configurations and, whenever possible, the policy options and environmental economic states required to obtain a perennial system. They point out the flexibility of the sustainable ‘‘extraction–consumption’’ choices and they show how they are neither reduced to constant consumption paths nor to Hartwick’s rule. Numerical simulations illustrate the general results.
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