Résumé en anglais

This paper presents an example of the advantages of using mathematical viability theory concepts and tools to study sustainable development issues. Instead of seeking optimal solutions according to a predefined value function, viability theory follows a inverse approach and does not postulate any a priori behaviours. Its methods and tools concern the set of all evolutions from a given situation that remain within a given set of constraints. An evolution is called viable (sustainable) if constraints are permanently satisfied. These constraints may be physical and as such imperative, or normative and consequently possibly modifiable. The aim of the paper is to show that the viability approach does not only encompass constraint satisfaction but also helps solve intertemporal optimisation problems. By applying a macroeconomic model generally used as a benchmark model to study theoretical issues of sustainable development we propose a new approach to assessing intergenerational equity. We describe two viability approaches to tackle the intergenerational equity issue: the first, proposed earlier by previous authors, concerns a minimal set of guaranteed rights for all generations; the second aims to minimize inequalities between generations while respecting resources and production constraints. Numerical computations have been performed to graphically display the solutions.