IDEAS home Printed from https://ideas.repec.org/p/lec/leecon/11-42.html
   My bibliography  Save this paper

Hyperbolic Punishment Function

Author

Listed:
  • Sanjit Dhami
  • Ali al-Nowaihi

Abstract

All models in Law and Economics use punishment functions (PF) that incorporates 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

  • Sanjit Dhami & Ali al-Nowaihi, 2011. "Hyperbolic Punishment Function," Discussion Papers in Economics 11/42, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:11/42
    as

    Download full text from publisher

    File URL: https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp11-42.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Garoupa, Nuno, 2001. "Optimal magnitude and probability of fines," European Economic Review, Elsevier, vol. 45(9), pages 1765-1771, October.
    2. 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.
    3. 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.
    4. A. Mitchell Polinsky & Steven Shavell (ed.), 2007. "Handbook of Law and Economics," Handbook of Law and Economics, Elsevier, edition 1, volume 2, number 2.
    5. 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.
    6. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    7. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    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. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    10. 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.
    11. 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.
    12. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521748681.
    13. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015.
    14. 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.
    15. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    16. Kolm, Serge-Christophe, 1973. "A note on optimum tax evasion," Journal of Public Economics, Elsevier, vol. 2(3), pages 265-270, July.
    17. A. Mitchell Polinsky & Steven Shavell (ed.), 2007. "Handbook of Law and Economics," Handbook of Law and Economics, Elsevier, edition 1, volume 1, number 1.
    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. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Vjollca Sadiraj, 2014. "Probabilistic risk attitudes and local risk aversion: a paradox," Theory and Decision, Springer, vol. 77(4), pages 443-454, December.
    3. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2014. "An experimental test of prospect theory for predicting choice under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 1-17, February.
    4. Peter Brooks & Simon Peters & Horst Zank, 2014. "Risk behavior for gain, loss, and mixed prospects," Theory and Decision, Springer, vol. 77(2), pages 153-182, August.
    5. Simon Gächter & Eric J. Johnson & Andreas Herrmann, 2022. "Individual-level loss aversion in riskless and risky choices," Theory and Decision, Springer, vol. 92(3), pages 599-624, April.
    6. Kpegli, Yao Thibaut & Corgnet, Brice & Zylbersztejn, Adam, 2023. "All at once! A comprehensive and tractable semi-parametric method to elicit prospect theory components," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    7. Roee Sarel, 2022. "Crime and punishment in times of pandemics," European Journal of Law and Economics, Springer, vol. 54(2), pages 155-186, October.
    8. Laurent Denant-Boemont & Olivier L’Haridon, 2013. "La rationalité à l'épreuve de l'économie comportementale," Revue française d'économie, Presses de Sciences-Po, vol. 0(2), pages 35-89.
    9. Gwenola Trotin, 2012. "Solving the Yitzhaki Paradox," AMSE Working Papers 1238, Aix-Marseille School of Economics, France.
    10. Matthew D. Rablen, 2014. "Audit Probability versus Effectiveness: The Beckerian Approach Revisited," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(2), pages 322-342, April.
    11. Antonio Nicita & Matteo Rizzolli, 2014. "In Dubio Pro Reo. Behavioral Explanations of Pro-defendant Bias in Procedures," CESifo Economic Studies, CESifo Group, vol. 60(3), pages 554-580.
    12. Mohammed Abdellaoui & Olivier l’Haridon & Corina Paraschiv, 2013. "Individual vs. couple behavior: an experimental investigation of risk preferences," Theory and Decision, Springer, vol. 75(2), pages 175-191, August.
    13. Thomas Åstebro & José Mata & Luís Santos-Pinto, 2015. "Skewness seeking: risk loving, optimism or overweighting of small probabilities?," Theory and Decision, Springer, vol. 78(2), pages 189-208, February.
    14. Simon Gaechter & Eric Johnson & Andreas Herrmann, 2007. "Individual-Level Loss Aversion In Riskless And Risky Choices," Discussion Papers 2007-02, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    15. Gwenola Trotin, 2012. "Solving the Yitzhaki Paradox: Income Tax Evasion and Reference Dependence under Prospect Theory," Working Papers halshs-00793664, HAL.
    16. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    17. Robin Cubitt & Gijs van de Kuilen & Sujoy Mukerji, 2020. "Discriminating Between Models of Ambiguity Attitude: a Qualitative Test," Journal of the European Economic Association, European Economic Association, vol. 18(2), pages 708-749.
    18. Serge Blondel & Louis Lévy-garboua, 2011. "Can non-expected utility theories explain the paradox of not voting?," Economics Bulletin, AccessEcon, vol. 31(4), pages 3158-3168.
    19. Matteo Rizzolli & Luca Stanca, 2012. "Judicial Errors and Crime Deterrence: Theory and Experimental Evidence," Journal of Law and Economics, University of Chicago Press, vol. 55(2), pages 311-338.
    20. Erling Eide & Kristine von Simson & Steinar Strøm, 2011. "Rank-Dependent Utility, Tax Evasion, and Labor Supply," FinanzArchiv: Public Finance Analysis, Mohr Siebeck, Tübingen, vol. 67(3), pages 261-281, September.

    More about this item

    Keywords

    Punishment functions; Optimal punishment functions; Becker proposition; Law and economics; Behavioral models of crime and punishment.;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:lec:leecon:11/42. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Abbie Sleath (email available below). General contact details of provider: https://edirc.repec.org/data/deleiuk.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.