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The Hyperbolic Punishment Function

Author

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  • al-Nowaihi Ali M.

    (University of Leicester, England)

  • Dhami Sanjit

    (University of Leicester, England)

Abstract

All models in Law and Economics use punishment functions (hereafter, PF) that incorporate a trade-off between probability of detection, p, and punishment, F. Suppose society wishes to minimize the total costs of enforcement and damages from crime, T( p,F). For a given p, an optimal punishment function (OPF) determines an F that minimizes T( p,F). A popular and tractable PF is the hyperbolic punishment function (HPF). We show that the HPF is an OPF for a large class of total cost functions. Furthermore, the HPF is an upper (lower ) bound for an even larger class of punishment functions. If the HPF cannot (can) deter crime, then none (all ) of the PF’s for which the HPF is an upper (lower ) bound can deter crime. Thus, if one can demonstrate that a particular policy is ineffective (effective) under the HPF, there is no need to even compute the OPF. Our results should underpin an even greater use of the HPF. We give illustrations from mainstream and behavioral economics.

Suggested Citation

  • al-Nowaihi Ali M. & Dhami Sanjit, 2012. "The Hyperbolic Punishment Function," Review of Law & Economics, De Gruyter, vol. 8(3), pages 759-787, December.
    • Handle: RePEc:bpj:rlecon:v:8:y:2012:i:3:p:759-787:n:5
    DOI: 10.1515/1555-5879.1570
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    1. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    2. A. Mitchell Polinsky & Steven Shavell (ed.), 2007. "Handbook of Law and Economics," Handbook of Law and Economics, Elsevier, edition 1, volume 2, number 2.
    3. Polinsky, A. Mitchell & Shavell, Steven, 2007. "The Theory of Public Enforcement of Law," Handbook of Law and Economics, in: A. Mitchell Polinsky & Steven Shavell (ed.), Handbook of Law and Economics, edition 1, volume 1, chapter 6, pages 403-454, Elsevier.
    4. Gary S. Becker, 1974. "Crime and Punishment: An Economic Approach," NBER Chapters, in: Essays in the Economics of Crime and Punishment, pages 1-54, National Bureau of Economic Research, Inc.
    5. Dhami, Sanjit & al-Nowaihi, Ali, 2007. "Why do people pay taxes? Prospect theory versus expected utility theory," Journal of Economic Behavior & Organization, Elsevier, vol. 64(1), pages 171-192, September.
    6. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, January.
    7. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    8. Steven Shavell & A. Mitchell Polinsky, 2000. "The Economic Theory of Public Enforcement of Law," Journal of Economic Literature, American Economic Association, vol. 38(1), pages 45-76, March.
    9. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    10. Allingham, Michael G. & Sandmo, Agnar, 1972. "Income tax evasion: a theoretical analysis," Journal of Public Economics, Elsevier, vol. 1(3-4), pages 323-338, November.
    11. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    12. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    13. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    14. Kolm, Serge-Christophe, 1973. "A note on optimum tax evasion," Journal of Public Economics, Elsevier, vol. 2(3), pages 265-270, July.
    15. A. Mitchell Polinsky & Steven Shavell (ed.), 2007. "Handbook of Law and Economics," Handbook of Law and Economics, Elsevier, edition 1, volume 1, number 1.
    16. Garoupa, Nuno, 2001. "Optimal magnitude and probability of fines," European Economic Review, Elsevier, vol. 45(9), pages 1765-1771, October.
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    Cited by:

    1. Dhami, Sanjit & al-Nowaihi, Ali, 2013. "An extension of the Becker proposition to non-expected utility theory," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 10-20.

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    More about this item

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • K42 - Law and Economics - - Legal Procedure, the Legal System, and Illegal Behavior - - - Illegal Behavior and the Enforcement of Law

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