×

zbMATH — the first resource for mathematics

Intertemporal equity and the extension of the Ramsey criterion. (English) Zbl 1046.91104
Summary: We examine social orderings applied to infinite intergenerational consumption paths. Fundamental dilemmas between several reasonable axioms lead to a taxonomy and characterization of different kinds of relations, some of which are well known extensions of the Ramsey criterion. We show how filters and ultrafilters can be used to understand the general structure of these extensions and to construct orderings which meet as many axioms as possible.

MSC:
91D20 Mathematical geography and demography
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Asheim, G.B., Unjust intergenerational allocations, Journal of economic theory, 54, 350-371, (1991) · Zbl 0733.90007
[2] Blackorby, C.; Donaldson, D., Social criteria for evaluating population change, Journal of public economics, 25, 13-33, (1984)
[3] Blackorby, C.; Bossert, W.; Donaldson, D., Intertemporal population ethics, critical-level Utilitarian principles, Econometrica, 63, 1303-1320, (1995) · Zbl 0836.90008
[4] Bourbaki, N., 1961. Topologie Générale. Hermann, Paris.
[5] Brock, W.A., On existence of weakly maximal programmes in a multisector economy, Review of economic studies, 37, 275-280, (1970) · Zbl 0212.23901
[6] Broome, J., 1993. The welfare economics of population. Discussion Paper 93/360, University of Bristol.
[7] Campbell, D., Impossibility theorems and infinite horizon planning, Social choice and welfare, 2, 283-293, (1985) · Zbl 0578.90001
[8] Cass, D., On capital accumulation in the aggregative, neoclassical model of economic growth, a complete characterization, Journal of economic theory, 4, 200-223, (1972)
[9] Diamond, P.A., The evaluation of infinite utility streams, Econometrica, 33, 170-177, (1965) · Zbl 0127.36602
[10] Dutta, P.K., What do discounted optima converge to? A theory of discount rate asymptotics in economic models, Journal of economic theory, 55, 64-94, (1991) · Zbl 0743.90024
[11] Ferejohn, J.; Page, T., On the foundations of intertemporal choice, American journal of agricultural economics, 60, 269-275, (1978)
[12] Fleurbaey, M.; Michel, P., Transfer principles and inequality aversion, with an application to optimal growth, Mathematical social sciences, 42, 1-11, (2001) · Zbl 0980.91060
[13] Gale, D., On optimal development in a multi-sector economy, Review of economic studies, 34, 1-18, (1967)
[14] Gorman, W.M., The structure of utility functions, Review of economic studies, 35, 369-390, (1968) · Zbl 0217.26801
[15] Kirman, A.P.; Sondermann, D., Arrow’s theorem, many agents, and invisible dictators, Journal of economic theory, 5, 267-277, (1972)
[16] Koopmans, T.C., On the concept of optimal economic growth. in: the econometric approach to development planning, Pontificiae academiae scientiarum scripta varia, 28, 225-287, (1965)
[17] Lauwers, L., 1993. Equity among infinitely many generations. KUL Mimeo.
[18] Lauwers, L., Time-neutrality and linearity, Journal of mathematical economics, 24, 347-351, (1995) · Zbl 0826.90009
[19] Lauwers, L., Intertemporal objective functions. strong Pareto versus anonymity, Mathematical social sciences, 35, 37-55, (1998) · Zbl 0926.91015
[20] Lauwers, L.; Van Liedekerke, L., Ultraproducts and aggregation, Journal of mathematical economics, 24, 217-237, (1995) · Zbl 0829.90005
[21] Michel, P., Some clarifications on the transversality condition, Econometrica, 58, 705-723, (1990) · Zbl 0731.90022
[22] Michel, P., 1991. Economic growth from a normative point of view, historical background and new considerations. Mimeo.
[23] Monjardet, B., 1983. On the use of ultrafilters in social choice theory. In: Pattanaik, P.K., Salles, M. (Eds.), Social Choice and Welfare. North-Holland, Amsterdam. · Zbl 0523.90014
[24] Ramsey, F.P., A mathematical theory of savings, Economic journal, 38, 543-559, (1928)
[25] Sen, A.K., 1970. Collective Choice and Social Welfare. Oliver, London. · Zbl 0227.90011
[26] Shinotsuka, T., Equity, continuity, and myopia, a generalization of diamond’s impossibility theorem, Social choice and welfare, 15, 21-30, (1998) · Zbl 0894.90010
[27] Svensson, L.G., Equity among generations, Econometrica, 48, 1251-1256, (1980) · Zbl 0436.90029
[28] Szpilrajn, E., Sur l’extension de l’ordre partiel, Fundamenta mathematicae, 16, 386-389, (1930) · JFM 56.0843.02
[29] Von Weizsäcker, C.C., Existence of optimal programs of accumulation for an infinite time horizon, Review of economic studies, 32, 85-104, (1965)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.