Mabrouk, Mohamed (2006): Allaisanonymity as an alternative to the discountedsum criterion in the calculus of optimal growth I: Consensual optimality.

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Abstract
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 discountedsum criterion. The solution suggested is to consider an optimality criterion expressing an Allaisanonymous intergenerational consensus. The partial characterization of consensual optimality was made possible thanks to the decomposition of the dual of the space of subgeometric 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 Paretooptimality of the consensual optimum is the subject of a forthcoming paper "Allaisanonymity as an alternative to the discountedsum criterion in the calculus of optimal growth II: Pareto optimality and some economic interpretations".
Item Type:  MPRA Paper 

Original Title:  Allaisanonymity as an alternative to the discountedsum criterion in the calculus of optimal growth I: Consensual optimality 
Language:  English 
Keywords:  Intergenerational anonymity; Intergenerational equity; Optimal growth; Technical change; Timepreference; Discountedsum criterion; Consensual criterion; OG economy 
Subjects:  O  Economic Development, Technological Change, and Growth > O4  Economic Growth and Aggregate Productivity > O41  One, Two, and Multisector Growth Models D  Microeconomics > D7  Analysis of Collective DecisionMaking > D71  Social Choice; Clubs; Committees; Associations D  Microeconomics > D6  Welfare Economics > D63  Equity, Justice, Inequality, and Other Normative Criteria and Measurement O  Economic Development, Technological Change, and Growth > O3  Technological Change; Research and Development; Intellectual Property Rights > O30  General D  Microeconomics > D9  Intertemporal Choice and Growth > D90  General C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis 
Item ID:  10512 
Depositing User:  Mohamed ben Ridha Mabrouk 
Date Deposited:  21. Nov 2008 04:58 
Last Modified:  17. Feb 2013 22:55 
References:  M. Allais, Economie et intérêt, Clément Juglar(2ieme edition), Paris, 1998. K. Arrow, Intergenerational equity and the rate of discount in longterm social investment, IEA World Congress, December 1995. G.B. Asheim, Unjust intergenerational allocations, Journal of economic theory 54(1991)350371. G.B. Asheim, W. Buchholz, B. Tungodden, Justifying sustainability, Journal of environmental economics and management 41(2001)252268. G.B. Asheim, T. Mitra, B. Tungodden, Sustainable recursive social welfare functions, working paper, University of Oslo, Cornell University, Norwegian School of Economics and Business Administration, March 2006. G.B. Asheim, W. Buchholz, The malleability of undiscounted utilitarianism as a criterion of intergenerational justice, Economica 70, 405422, 2003. Y. Balasko, K. Shell, The OLG model, I: the case of pure exchange without money, Journal of Economic Theory 23(1980)281306. K. Basu, T. Mitra, Aggregating infinite utility streams with intergenerational equity: the impossibility of being paretian, Econometrica vol71, n°5, September 2003, 15571563 S. Bayer, D. Cansier, Intergenerational discounting: a new approach, Tübinger Diskussionsbeitrag Nr145, September 1998. A. Beltratti, G. Chichilnisky, G. Heal, The environment and the long run: a comparison of different criteria, Ricerche Economiche (1994) 48,319340. C. Blackorby, W. Bossert, D. Donaldson, Intertemporal social evaluation, Département des sciences économiques, Université de Montréal, CIREQ 062005, January 2005. W. Bosser, Y. Sprumont, K. Suzumura, The possibility of ordering infinite utility streams, Working paper July 2004, Université de Montréal. J.H. Boyd, Recursive utility and the Ramsey problem, Journal of Economic Theory 50(1990)326345. D. Cass, On the existence of weakly maximal programmes in a multisector economy, Review of Economic Studies 37, 275280. D. Cass, On capital overaccumulation in the aggregative, neoclassical model of economic growth: a complete characterization, Journal of Economic Theory 4(1972)200223. G. Chichilnisky, An axiomatic approach to sustainable development, Social Choice and Welfare 14(1996)231257. T. Cowen, D. Parfit, Against the social discount rate, in Justice between age groups and generations, P. Laslett and J. Fishkin eds, Yale University press (1992), New Haven, 162168. P.A. Diamond, The evaluation of infinite utility streams, Econometrica, vol.33, n°1(January, 1965) R.E.A. Farmer, A. Lahiri, Recursive preferences and balanced growth, Journal of Economic Theory (in press). J. Ferejohn, T. Page, On the foundations of intertemporal choice, American Journal of Agricultural Economics 60(1978)269275. M. Fleurbaey, P. Michel, Intertemporal equity and the extension of the Ramsey criterion, Journal of Mathematical Economics 39(2003)777802. M. Fleurbaey, K. Suzumura, K. Tadenuma, Arrovian aggregation in economic environments: how much should we know about indifference surfaces? Journal of Economic Theory 124(2005)2244. S. Frederick, G. Loewenstein, T. O'Donoghue, Time discounting and time preference: a critical review, Journal of Economic Literature 40(2002)351401. C. Gollier, Maximizing the expected net future value as an alternative strategy to gamma discounting, Finance research letters 1(2)(2004)8589. C. Gollier, Time horizon and the discount rate, Journal of economic theory 107(2)(2002) 463473. C. Groth, Course of advanced macroeconomics 2003, Institute of Economics, University of Copenhagen, www.econ.ku.dk. R. Guesnerie, Calcul économique et développement durable, DELTA wp n°20042 C. Hara, T. Shinotsuka, K. Suzumura, Y. Xu, On the possibility of continuous paretian and egalitarian evaluation of infinite utility streams, Working paper, Institute of economic Research, Hitotsubashi University 26/5/2005. Optimality or sustainability?, G. Heal, paper prepared for presentation at the EAERE 2001 Conference, Southampton June 2001. B. Heijdra, R. van der Poeg, Foundations of modern macroeconomics, Oxford, 2002. T.C. Koopmans, Stationnary ordinal utility and impatience, Econometrica 28(1960)287309. T. C. Koopmans, P.A. Diamond, R.E Williamson, Stationnary utility and time perspective, Econometrica, vol32,n°1,(1964)82100. L. Lauwers, Intertemporal objective functions: Strong Pareto versus anonymity, Mathematical Social Sciences 35(1998)3755. L. Lauwers, Topological social choice, Mathematical social sciences 40(2000)139. C. LeVan, Y Vailakis, Recursive utility and optimal growth with bounded or unbounded returns, Journal of Economic Theory (in press). C. Le Van, H.C. Saglam, Optimal growth models and the Lagrange multiplier, Journal of Mathematical Economics 40(2004)393410. D. Luenberger, Optimization by vector spaces, WileyInterscience, New Ed edition 1997. M. Mabrouk, Optimal growth path in an OLG economy without timepreference assumptions, Annales Maghrébines de l'Ingénieur ENITTunis (in press), available at http://econwpa.wustl.edu/eps /ge/papers/0510/0510006.pdf G.N. Mankiw, Macroéconomie (French translation), De Boeck Université, Bruxelles, 2001. P. Michel, Criticism of the social timepreference hypothesis in optimal growth, CORE discussion paper 9039, LouvainlaNeuve. H. R. Mihara, Arrow's theorem, countably many agents, and more visible invisible dictators, Journal of Mathematical Economics 32(1999)267287. T. Mitra, K. Basu, On the existence of paretian welfare relations for infinite utility streams with extended anonymity, CAE workingpaper ♯0506, Cornell University, May 2005. M.A. Naimark, Normed rings, WoltersNoordhoff, Groningen, 1970. T.Rasmussen, Modeling the economics of greenhouse gas abatement: infinite horizon or overlapping generations?, Discussion papers n°20012, Center for Economic and Business Research, Copenhagen, March 2001. J. Rawls, A theory of justice, Harvard University Press, 1971 T. Sakai, An axiomatic approach to intergenerational equity, Social Choice and Welfare, vol20, issue1(2003)167176. T. Sakai, Intergenerational preferences and the sensitivity to the present, Economics Bulletin, vol4, n°26(2003)15. P.A. Samuelson, An exact consumptionloan model of interest with or without the social contrivance of money, Journal of Political Economics. 66(1958)467482. T.C. Schelling, Intergenerational discounting, Energy policy, 23(4/5)(1995)395401. H. Sidgwick, The methods of Ethics, Macmillan, London. R. Solow, A contribution to the theory of optimal growth, Quarterly Journal of Economics 70(1956) 6594. R. Solow, Intergenerational equity and exhaustible resources, discussion paper n°103, M.I.T. L.G. Svensson, Equity among generations, Econometrica 48(1980)12511256. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/10512 