Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-27T09:37:18.740Z Has data issue: false hasContentIssue false

From the St. Petersburg paradox to the dismal theorem

Published online by Cambridge University Press:  08 May 2020

Susumu Cato*
Affiliation:
Institute of Social Science, The University of Tokyo, Tokyo, Japan
*
*Corresponding author. E-mail: [email protected]

Abstract

This paper aims to consider the meaning of the dismal theorem, as presented by Martin Weitzman [(2009) On modeling and interpreting the economics of catastrophic climate change. Review of Economics and Statistics91, 1–19]. The theorem states that a standard cost–benefit analysis breaks down if there is a possibility of catastrophes occurring. This result has a significant influence on debates regarding the economics of climate change. In this study, we present an intuitive similarity between the dismal theorem and the St. Petersburg paradox using a simple discrete probability distribution.

Type
Research Article
Copyright
Copyright © The Author(s) 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arrow, KJ (1974) The use of unbounded utility functions in expected-utility maximization: response. Quarterly Journal of Economics 88, 136138.10.2307/1881800CrossRefGoogle Scholar
Arrow, KJ and Priebsch, M (2014) Bliss, catastrophe, and rational policy. Environmental and Resource Economics 58, 491509.10.1007/s10640-014-9788-6CrossRefGoogle Scholar
Bernoulli, D (1954) Exposition of a new theory on the measurement of risk. Econometrica 22, 2336.10.2307/1909829CrossRefGoogle Scholar
Cato, S (2019) Inutsu-na-kikitaiou [Dismal countermeasures against crisis]. In Genda, Y and Iida, T (eds), Kikitaiou-no-Shakaikagaku. Tokyo: University of Tokyo Press, pp. 229250 (in Japanese).Google Scholar
Geweke, J (2001) A note on some limitations of CRRA utility. Economics Letters 71, 341345.10.1016/S0165-1765(01)00391-3CrossRefGoogle Scholar
Horowitz, J and Lange, A (2014) Cost-benefit analysis under uncertainty – a note on Weitzman's dismal theorem. Energy Economics 42, 201203.10.1016/j.eneco.2013.12.013CrossRefGoogle Scholar
Menger, K (1934) Das Unsicherheitsmoment in der Wertlehre. Zeitschrift fur Nationalokonomie 5, 459485 (in German).10.1007/BF01311578CrossRefGoogle Scholar
Millner, A (2013) On welfare frameworks and catastrophic climate risks. Journal of Environmental Economics and Management 65, 310325.10.1016/j.jeem.2012.09.006CrossRefGoogle Scholar
Nordhaus, WD (2009) An analysis of the dismal theorem. Cowles Foundation Discussion Paper No. 1686, New Haven, CT.Google Scholar
Peters, O (2011) The time resolution of the St Petersburg paradox. Philosophical Transactions of the Royal Society 369, 49134931.10.1098/rsta.2011.0065CrossRefGoogle ScholarPubMed
Pindyck, RS (2011) Fat tails, thin tails, and climate change policy. Review of Environmental Economics and Policy 5, 258274.10.1093/reep/rer005CrossRefGoogle Scholar
Samuelson, PA (1977) St. Petersburg paradoxes: defanged, dissected, and historically described. Journal of Economic Literature 15, 2455.Google Scholar
Seidl, C (2013) The St. Petersburg Paradox at 300. Journal of Risk and Uncertainty 46, 247264.10.1007/s11166-013-9165-9CrossRefGoogle Scholar
Wagner, G and Weitzman, ML (2016) Climate Shock: The Economic Consequences of a Hotter Planet. Princeton, NJ: Princeton University Press.Google Scholar
Weitzman, ML (2009) On modeling and interpreting the economics of catastrophic climate change. Review of Economics and Statistics 91, 119.10.1162/rest.91.1.1CrossRefGoogle Scholar
Weitzman, ML (2014) Fat tails and the social cost of carbon. American Economic Review 104, 544546.10.1257/aer.104.5.544CrossRefGoogle Scholar