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

• ##### Mohamed Mabrouk
University Library of Munich, Germany, MPRA Paper 01/2006;
Source: RePEc

ABSTRACT 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.

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##### Article: Discounting and altruism to future decision-makers
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ABSTRACT: Is discounting of future decision-makers’ consumption utilities consistent with "pure" altruism toward those decision-makers, that is, a concern that they are better off according to their own, likewise forward-looking, preferences? It turns out that the answer is positive for many but not all discount functions used in the economics literature. In particular, "hyperbolic" discounting of the form used by Phelps and Pollak (1968) and Laibson (1997) is consistent with exponential altruism towards all future generations. More generally, we establish a one-to-one relationship between discount functions and altruism weight systems, and provide sufficient, as well as necessary, conditions for discount functions to be consistent with pure altruism.
01/2005;