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The Hyperbolic Punishment Function

Author

Listed:
  • 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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    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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