Allais-anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth II: Pareto optimality and some economic interpretations

This paper studies the Pareto-optimality of the consensual optimum established in "Allais-anonymity as an alternative to the discounted-sum criterion I: consensual optimality" (Mabrouk 2006a). For that, a Pareto-optimality criterion is set up by the application of the generalized Karush, Kuhn and Tucker theorem and thanks to the decomposition of the space of geometrically-growing real sequences. That makes it possible to find sufficient conditions so that a bequest-rule path is Pareto-optimal. Through an example, it is then shown that the golden rule must be checked to achieve Allais-anonymous optimality. The introduction of an additive altruism makes it possible to highlight the intergenerational-preference rate compatible with Allais-anonymous optimality. In this approach, it is not any more the optimality which depends on the intergenerational-preference rate, but the optimal intergenerational-preference rate which rises from Allais-anonymous optimality.