Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
The Economics of the Global Environment—Catastrophic Risks in Theory and Practice Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Intergenerational Equity, Efficiency, and Constructibility

verfasst von : Luc Lauwers

Erschienen in: The Economics of the Global Environment

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

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.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Vorheriges Kapitel Sustainable Recursive Social Welfare Functions
Nächstes Kapitel Sustainable Exploitation of a Natural Resource: A Satisfying Use of Chichilnisky’s Criterion
Fußnoten
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
This conclusion extends to, for example, the widely used Dasgupta-Heal-Solow growth model.
 
3
Asheim (2010) provides an excellent survey.
 
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
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
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
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
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
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
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
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.
 
Literatur
Alvarez-Cuadrado, F., & Van Long, N. (2009). A mixed Bentham-Rawls criterion for intergenerational equity: Theory and implications. Journal of Environmental Economics and Management, 58, 154–168.CrossRef
Asheim, G. B. (2010). Intergenerational equity. Annual Review of Economics, 2, 197–222.CrossRef
Asheim, G. B., & Banerjee, K. (2010). Fixed-step anonymous overtaking and catching up. International Journal of Economic Theory, 6, 149–165.CrossRef
Asheim, G. B., & Mitra, T. (2010). Sustainability and discounted utilitarianism in models of economic growth. Mathematical Social Sciences, 59, 148–169.CrossRef
Ax, J. (1968). The elementary theory of finite fields. Annals of Mathematics, 88, 239–271.CrossRef
Banerjee, K. (2006). On the extension of the utilitarian and Suppes-Sen social welfare relations to infinite utility streams. Social Choice and Welfare, 27, 327–339.CrossRef
Chambers, C. P. (2009). Intergenerational equity: sup, inf, \(\limsup \), and \(\liminf \). Social Choice and Welfare, 32, 243–252.CrossRef
Chichilnisky, G. (1996). An axiomatic approach to sustainable development. Social Choice and Welfare, 13, 231–257.CrossRef
Chichilnisky, G. (2009a). The topology of fear. Journal of Mathematical Economics, 45, 807–816.
Chichilnisky, G. (2009b). Avoiding extinction: Equal treatment of the present and the future. The Open-Access, Open-Assessment E-Journal, 3, 2009–2032.
Chichilnisky, G. (2011). Sustainable markets with short sales. Economic Theory (reprinted in this volume).
Chipman, J. S., & Tian, G. (2011). Detrimental externalities, pollution rights, and the “Coase theorem”. Economic Theory (reprinted in this volume). doi:10.​1007/​s00199-011-0602-1.
Dianonescu, R. (1975). Axiom of choice and complementation. Proceedings of the American Mathematical Society, 51, 176–178.CrossRef
Dutta, P. K., & Radner, R. (2011). Capital growth in a global warming model: will China and India sign a climate treaty? Economic Theory (reprinted in this volume). doi:10.​1007/​s00199-010-0590-6.
Figuières, C., & Tidball, M. (2011). Sustainable exploitation of a natural resource: a satisfying use of Chichilnisky’s criterion. Economic Theory (reprinted in this volume). doi:10.​1007/​s00199-010-0579-1.
Fleurbaey, M., & Michel, P. (2003). Intertemporal equity and the extension of the Ramsey criterion. Journal of Mathematical Economics, 39, 777–802.CrossRef
Fraenkel, A. A., Bar-Hillel, Y., & Levy, A. (1973). Foundation of Set Theory. Amsterdam: North Holland.
Halbeisen, L., & Löwe, B. (2001). Ultrafilter spaces on the semilattice of partitions. Topology and its Applications, 115, 317–332.CrossRef
Hall, M, Jr. (1976). The theory of groups. New York: Chelsea Publishing Company.
Heal, G. M. (1998). Valuing the future: Economic theory and sustainability. New York: Columbia University Press.
Jech, T. J. (1973). The axiom of choice. Amsterdam: North-Holland.
Kamaga, K., & Kojima, T. (2009a). \({\cal{Q}}\)-anonymous social welfare relations on infinite utility streams. Social Choice and Welfare, 33, 405–413.CrossRef
Kamaga, K., & Kojima, T. (2009b). On the leximin and utilitarian criteria with extended anonymity. Tokyo, Japan: Waseda University.
Karp, L., & Zhang, J. (2011). Taxes versus quantities for a stock pollutant with endogenous abatement costs and asymmetric information. Economic Theory (reprinted in this volume). doi:10.​1007/​s00199-010-0561-y.
Lauwers, L. (1997). Infinite utility: Insisting on strong monotonicity. Australasian Journal of Philosophy, 75, 222–233.CrossRef
Lauwers., L. (2010a). Ordering infinite utility streams comes at the cost of a non-Ramsey set. Journal of Mathematical Economics, 46, 32–37.
Lauwers, L. (2010b). Purely finitely additive measures are non-constructible objects. K.U.Leuven: DPS 1010 Center for Economic Studies.
Lecocq, F., & Hourcade, J.-C. (2011). Unspoken ethical issues in the climate affair, insights from a theoretical analysis of negotiation mandates. Economic Theory (reprinted in this volume). doi:10.​1007/​s00199-010-0589-z.
Li, C.-Z., & Löfgren, K.-G. (2000). Renewable resources and economic sustainability: A dynamic analysis with heterogeneous time preferences. Journal of Environmental Economics and Management, 40, 236–250.CrossRef
Mathias, A. R. D. (1977). Happy families. Annals of Pure and Applied Logic, 12, 59–111.
Mitra, T., & Basu, K. (2007). On the existence of Paretian social welfare relations for infinite utility streams with extended anonymity. In J. Roemer & K. Suzumura (Eds.), Intergenerational equity and sustainability (pp. 85–99). London: Palgrave.CrossRef
Ostrom, E. (2011). Nested externalities and polycentric institutions: Must we wait for global solutions to climate change before taking actions at other scales? Economic Theory (reprinted in this volume). doi:10.​1007/​s00199-010-0558-6.
Rao, R. R. (1958). A note on finitely additive measures. Indian Journal of Statistics, 19, 27–28.
Yosida, K., & Hewitt, E. (1952). Finitely additive measures. Transactions of the American Mathematical Society, 72, 46–66.CrossRef
Zame, W. (2007). Can intergenerational equity be operationalized? Theoretical Economics, 2, 187–202.
Metadaten
Titel
Intergenerational Equity, Efficiency, and Constructibility
verfasst von
Luc Lauwers
Copyright-Jahr
2016
Buch
The Economics of the Global Environment

Print ISBN: 978-3-319-31941-4

Electronic ISBN: 978-3-319-31943-8

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-31943-8_10