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Hyperbolic Punishment Function

Author

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  • 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
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    References listed on IDEAS

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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

    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

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