Allais-anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth I: Consensual optimality

The objective of this work is to try to define and calculate the optimal growth path, in the presence of exogenous technical change, without resorting to the discounted-sum criterion. The solution suggested is to consider an optimality criterion expressing an Allais-anonymous intergenerational consensus. The partial characterization of consensual optimality was made possible thanks to the decomposition of the dual of the space of sub-geometric sequences of reason p. The main finding is a relation between the marginal rate of substitution between bequest and heritage, and the growth rate, relation which is a necessary condition for consensual optimality. The necessary study of the Pareto-optimality of the consensual optimum is the subject of a forthcoming paper "Allais-anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth II: Pareto optimality and some economic interpretations".Intergenerational anonymity; Intergenerational equity; Optimal growth; Technical change; Time-preference; Discounted-sum criterion; Consensual criterion; OG economy

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.Intergenerational anonymity; Allais-anonymity; Intergenerational equity; Optimal growth; Technical change; Time-preference; Discounted-sum criterion; Consensual criterion; Pareto-optimality; OG economy.

Intergenerational anonymity as an alternative to the discounted- sum criterion in the calculus of optimal growth I: Consensual optimality

The objective of this work is to try to define and calculate the optimal growth path, in the presence of exogenous technical change, without resorting to the discounted-sum criterion. The solution suggested is to consider an optimality criterion expressing an anonymous intergenerational consensus. The partial characterization of consensual optimality was made possible thanks to the decomposition of the dual of the space of sub-geometric sequences of reason p. The main finding is a relation between the marginal rate of substitution between bequest and heritage and the growth rate, relation which is a necessary condition for consensual optimality. The necessary study of the Pareto-optimality of the consensual optimum is the subject of a forthcoming paper « Intergenerational anonymity as an alternative to the discounted-sum criterion in the calculus of optimal growth II: Pareto-optimality and some economic interpretations »Intergenerational anonymity; Intergenerational equity; Optimal growth; Technical change; Time-preference; Discounted-sum criterion; Consensual criterion; OG economy

On the extension of a preorder under translation invariance

This paper proves the existence, for any preorder on a real vector space satisfying translation invariance, of a complete preorder extending the preorder and satisfying translation invariance. As application, the existence of a translation-invariant complete preorder on infinite utility streams satisfying strong Pareto and fixed-step anonymity, is established.Szpilrajn theorem; translation invariance

Translation invariance when utility streams are infinite and unbounded

The axiom translation invariance consists in asserting the invariance of the ranking of two utility streams if one applies the same translation to both. This axiom is significant in the characterization of utilitarian criteria in finite dimension. This characterization is achieved thanks to the "weak weighted utilitarianism theorem".The objective here is to propose a generalization of this theorem in a space of infinite and unbounded utility streams. A consequence of the suggested generalization is that, in the context of intergenerational choice, every maximal point with respect to a paretian utilitarian order granting comparable considerations to the present and the future, is also a maximal point with respect to some future-oriented criterion.Translation invariance; Infinite utility streams; Utilitarianism; Intergenerational equity

Optimal growth path in an OLG economy without time-preference assumptions : main results

The aim is to characterize optimal growth paths in an OLG economy where capital accumulation is achieved through bequests, without using the assumption of time preference theory on a social level, because such an assumption, that leads to use a discounted infinite horizon sum, introduce necessarily inequality between the different generations of the society. I investigated two optimality concepts: Pareto-optimality and consensual optimality. I considered the case without technical change. I found that all steady-state optimal growth paths converge necessarily to a level of capital where the marginal gain from a decrease of bequest is equal to the marginal loss from a similar decrease of heritage. With the use of an intergenerational altruistic utility, I showed that spontaneous equilibrium cannot be an optimal growth path unless generations feel (asymptotically) for their heirs as they feel for themselves.optimal growth, OLG economy, time-preference assumption, Pareto-optimality, egalitarianism, golden rule

Translation invariance when utility streams are infinite and unbounded

The axiom translation invariance consists in asserting the invariance of the ranking of two utility streams if one applies the same translation to both. This axiom is significant in the characterization of utilitarian criteria in finite dimension. This characterization is achieved thanks to the "weak weighted utilitarianism theorem".The objective here is to propose a generalization of this theorem in a space of infinite and unbounded utility streams. A consequence of the suggested generalization is that, in the context of intergenerational choice, every maximal point with respect to a paretian utilitarian order granting comparable considerations to the present and the future, is also a maximal point with respect to some future-oriented criterion.Translation invariance; Infinite utility streams; Utilitarianism; Intergenerational equity

On inversion and connection coefficients for basic hypergeometric polynomials

In this paper, we propose a general method to express explicitly the inversion and the connection coefficients between two basic hypergeometric polynomial sets. As application, we consider some $d$-orthogonal basic hypergeometric polynomials and we derive expansion formulae corresponding to all the families within the $q$-Askey scheme.Comment: 15 page