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The Economics of the Global Environment pp 191–206Cite as

Intergenerational Equity, Efficiency, and Constructibility

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Part of the book series: Studies in Economic Theory ((ECON.THEORY,volume 29))

Abstract

Global environmental issues—like biodiversity conservation or climate change—are in reality long term issues that are not properly taken into account with traditional models that incorporate the impatience axiom manifested in fixed discount factors and in the use of present discounted utility criteria. When both the short and the very long run are important, one can appeal to overtaking criteria and Chichilnisky criteria. Unfortunately, overtaking criteria are highly incomplete. In order to decrease this incompleteness, stronger anonymity (or equity) axioms were developed. I show that a maximal anonymity axiom compatible with Pareto is a non-constructible object; its existence relies on the Axiom of Choice. The Chichilnisky criterion is based upon two axioms: non dictatorship of the present and non dictatorship of the future. Here, the very long run is captured by a finitely additive measure. Such a measure is a non-constructible object and has therefore no explicit description.

I thank Norbert Brunner, Graciela Chichilnisky, Koen Decancq, Marc Fleurbaey, Johan Quaegebeur, and Luc Van Liedekerke for helpful conversations. I am grateful for the many constructive comments by the referee. A first version was presented at the workshop “Intergenerational equity in climate negotiations, overlapping generations and social welfare” organized by Claude d’Aspremont and Thierry Bréchet (CORE, April 27–28, 2006). This text presents research results of the Belgian Programme of Interuniversity Poles of Attraction initiated under the Science Policy Programmes of the Prime Minister’s Office, Belgium. The scientific responsibility is assumed by its authors.

Originally published in Economic Theory, Volume 49, Number 2, February 2012 DOI 10.1007/s00199-010-0573-7.

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Notes

  1. 1.

    An evaluation F of infinite utility streams is said to be normalized if \(F(r,r,\ldots ,r,\ldots ) = r\) for each r in \(\mathbb {R}\). Due to this normalization the discounted sum is premultiplied with \((1-\beta )\).

  2. 2.

    This conclusion extends to, for example, the widely used Dasgupta-Heal-Solow growth model.

  3. 3.

    Asheim (2010) provides an excellent survey.

  4. 4.

    Consider the streams \(w=(1,-1,-1,1;1,-1,-1,1;\ldots ;1,-1,-1,1;\ldots )\) and \(z=(0,0,\ldots ,0,\ldots )\). The overtaking criterion is unable to rank w and z. An utilitarian overtaking criterion that satisfies fixed step anonymity considers w and z equally good.

  5. 5.

    A welfare function displays ‘dictatorship of the present’ if it is insensitive for changes that affect the distinct future. A welfare function displays ‘dictatorship of the future’ if it is insensitive for changes that do not affect the limiting behavior criterion.

  6. 6.

    Burniaux and Martins (2011), Chipman and Tian (2011), Dutta and Radner (2011), Karp and Zhang (2011), and Ostrom (2011) tackle the question of how to implement policies that respect the interests of future generations and to assess their effectiveness in the context of global externalities with long-lasting effects. Lecocq and Hourcade (2011) argue that optimal policies may require estimates of future intragenerational distributions. Rezai et al. (2011) show that, in some cases, such policies may benefit all generations.

  7. 7.

    Purely finitely additive measures are typically obtained via non-constructive mathematics (Hahn-Banach’s theorem or ultrafilters, cf. Chichilnisky 2009a, 2011). This observation can be strengthened: it is impossible to create a purely finitely additive measure on \({\mathbb {N}_0}\) without recurse to non-constructive methods.

  8. 8.

    The map \(\liminf \) (see Sect. 2.1) is not additive: \(\liminf (1,0,1,0,\ldots )= \liminf (0,1,0,1,\ldots )=0\); while \(\liminf [(1,0,1,0,\ldots )+ (0,1,0,1,\ldots )]= \liminf (1,1,1,1,\ldots ) =1\).

  9. 9.

    AC is (i) consistent and (ii) independent: (i) AC can be added to the Zermelo-Fraenkel axioms of set theory (ZF) without yielding a contradiction, and (ii) AC is not a theorem of ZF (Fraenkel et al. 1973).

  10. 10.

    The law of the excluded middle states the truth of ‘P or not-P’ for each proposition P and can be used to claim the existence of certain objects without any hint to its construction. For example, the real number \(c={\scriptstyle \sqrt{2}}^{\,{\sqrt{2}}}\) either is rational (in which case one sets \(a=b=\sqrt{2}\,\)) or is not rational (in which case one sets \(a=c\) and \(b=\sqrt{2}\)). Conclude the existence of irrational numbers a and b for which \(a^b\) is rational.

  11. 11.

    In this example, \(\liminf (s_t)\) is the limit of the sequence 1 / 9, 11 / 99, \(111/999,\ldots \) and is equal to 1/9; \(\limsup (s_t)\) is the limit of the sequence 1, 11 / 19, \(111/199,\ldots \) and is equal to 5/9.

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Authors and Affiliations

  1. Center for Economic Studies, University of Leuven—KU Leuven, Naamsestraat 69—Bus 3565, 3000, Leuven, Belgium

    Luc Lauwers

  2. Departments of Economics, University of Leuven—KU Leuven, Naamsestraat 69—Bus 3565, 3000, Leuven, Belgium

    Luc Lauwers

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Editors and Affiliations

  1. Columbia University, New York, New York, USA

    Graciela Chichilnisky

  2. Department of Socio-Economics, Vienna University of Economics and Business, Vienna, Austria

    Armon Rezai

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Lauwers, L. (2016). Intergenerational Equity, Efficiency, and Constructibility. In: Chichilnisky, G., Rezai, A. (eds) The Economics of the Global Environment. Studies in Economic Theory, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-319-31943-8_10

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