My bibliography  Save this paper

# A Never-decisive and Anonymous Criterion for Optimal Growth Models

## Author

Listed:
• Alain Ayong Le Kama

() (EconomiX - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique)

• Thai Ha-Huy
• Cuong Le Van
• Katheline Schubert

## Abstract

We address in this paper the question of the existence of a Social Welfare Function that would be sustainable and would allow us to obtain solutions to optimal growth models. We define sustainability by two new axioms called Never-decisiveness of the present and Never-decisiveness of the future. We first show that a SWF which has Never-decisiveness properties cannot be defined on a ball of $$l_{\infty }^{+}$$ l ∞ + . We must (i) restrict to the set of utility streams for which the value of the SWF is finite and (ii) introduce additional assumptions in order to obtain the Never-decisiveness properties. Our main result in this paper is therefore to show that the undiscounted utilitarian criterion is an anonymous and never-decisive criterion for optimal growth models. We consider the set of utilities of consumptions which are generated by a specific technology, namely a technology with decreasing returns for high levels of capital, and restrict ourselves to good programs, i.e., any program for which intertemporal utility is well defined. Copyright Springer-Verlag Berlin Heidelberg 2014
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)

## Suggested Citation

• Alain Ayong Le Kama & Thai Ha-Huy & Cuong Le Van & Katheline Schubert, 2014. "A Never-decisive and Anonymous Criterion for Optimal Growth Models," Post-Print hal-01385926, HAL.
• Handle: RePEc:hal:journl:hal-01385926
Note: View the original document on HAL open archive server: https://hal-univ-paris10.archives-ouvertes.fr/hal-01385926
as

To our knowledge, this item is not available for download. To find whether it is available, there are three options:
1. Check below whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.

## References listed on IDEAS

as
1. Alvarez-Cuadrado, Francisco & Van Long, Ngo, 2009. "A mixed Bentham-Rawls criterion for intergenerational equity: Theory and implications," Journal of Environmental Economics and Management, Elsevier, vol. 58(2), pages 154-168, September.
2. Asheim, Geir B. & Mitra, Tapan, 2010. "Sustainability and discounted utilitarianism in models of economic growth," Mathematical Social Sciences, Elsevier, vol. 59(2), pages 148-169, March.
3. Asheim, Geir B. & d'Aspremont, Claude & Banerjee, Kuntal, 2010. "Generalized time-invariant overtaking," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 519-533, July.
4. Ayong Le Kama, Alain D., 2001. "Sustainable growth, renewable resources and pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1911-1918, December.
5. Le Van, Cuong & Schubert, Katheline & Nguyen, Tu Anh, 2010. "With exhaustible resources, can a developing country escape from the poverty trap?," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2435-2447, November.
6. Geir Asheim & Tapan Mitra & Bertil Tungodden, 2012. "Sustainable recursive social welfare functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(2), pages 267-292, February.
7. repec:dau:papers:123456789/13605 is not listed on IDEAS
8. Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
9. Kaushik Basu & Tapan Mitra, 2003. "Aggregating Infinite Utility Streams with InterGenerational Equity: The Impossibility of Being Paretian," Econometrica, Econometric Society, vol. 71(5), pages 1557-1563, September.
10. Fleurbaey, Marc & Michel, Philippe, 2003. "Intertemporal equity and the extension of the Ramsey criterion," Journal of Mathematical Economics, Elsevier, vol. 39(7), pages 777-802, September.
11. R. M. Solow, 1974. "Intergenerational Equity and Exhaustible Resources," Review of Economic Studies, Oxford University Press, vol. 41(5), pages 29-45.
12. Basu, Kaushik & Mitra, Tapan, 2007. "Utilitarianism for infinite utility streams: A new welfare criterion and its axiomatic characterization," Journal of Economic Theory, Elsevier, vol. 133(1), pages 350-373, March.
13. Heal, G., 1998. "Valuing the Future: Economic Theory and Sustainability," Papers 98-10, Columbia - Graduate School of Business.
14. Cuong Le Van & Katheline Schubert & Tu-Anh Nguyen, 2007. "With exhaustible resources, can a developing country escape from the poverty trap?," Post-Print halshs-00203180, HAL.
15. David Gale, 1967. "On Optimal Development in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 34(1), pages 1-18.
16. Brock, William A, 1970. "An Axiomatic Basis for the Ramsey- Weizsacker Overtaking Criterion," Econometrica, Econometric Society, vol. 38(6), pages 927-929, November.
17. Graciela Chichilnisky, 1996. "An axiomatic approach to sustainable development," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(2), pages 231-257, April.
18. Graciela Chichilnisky, 1997. "What Is Sustainable Development?," Land Economics, University of Wisconsin Press, vol. 73(4), pages 467-491.
19. Charles Figuières & Mabel Tidball, 2012. "Sustainable exploitation of a natural resource: a satisfying use of Chichilnisky’s criterion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(2), pages 243-265, February.
20. Cuong Le Van & Rose-Anne Dana, 2003. "Dynamic Programming in Economics," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00119098, HAL.
21. repec:dau:papers:123456789/416 is not listed on IDEAS
22. Luc Lauwers, 2012. "Intergenerational equity, efficiency, and constructibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(2), pages 227-242, February.
23. W. A. Brock, 1970. "On Existence of Weakly Maximal Programmes in a Multi-Sector Economy," Review of Economic Studies, Oxford University Press, vol. 37(2), pages 275-280.
24. repec:hal:journl:halshs-00470655 is not listed on IDEAS
Full references (including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as

Cited by:

1. Kirill Borissov & Mikhail Pakhnin, 2018. "Economic growth and property rights on natural resources," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 423-482, March.
2. Geir B. Asheim & Ivar Ekeland, 2016. "Resource conservation across generations in a Ramsey–Chichilnisky model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(4), pages 611-639, April.

### JEL classification:

• D60 - Microeconomics - - Welfare Economics - - - General
• D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
• D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
• Q0 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - General

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-01385926. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.