Hyperbolic Punishment Function

Sanjit Dhami and Ali al-Nowaihi ()

No 11/42, Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester

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.

Keywords: Punishment functions; Optimal punishment functions; Becker proposition; Law and economics; Behavioral models of crime and punishment. (search for similar items in EconPapers)
JEL-codes: D01 D8 K42 (search for similar items in EconPapers)
Date: 2011-08
New Economics Papers: this item is included in nep-cbe
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Citations: View citations in EconPapers (1)

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Journal Article: The Hyperbolic Punishment Function (2012)
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