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Hyperbolic Punishment Function

  • Sanjit Dhami

    ()

  • Ali al-Nowaihi

    ()

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.

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Paper provided by Department of Economics, University of Leicester in its series Discussion Papers in Economics with number 11/42.

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Date of creation: Aug 2011
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Handle: RePEc:lec:leecon:11/42
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  1. 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.
  2. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  3. Matthew Rabin., 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Economics Working Papers E00-279, University of California at Berkeley.
  4. Nuno Garoupa, 2000. "Optimal magnitude and probability of fines," Economics Working Papers 454, Department of Economics and Business, Universitat Pompeu Fabra.
  5. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
  6. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  7. 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.
  8. 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.
  9. 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.
  10. Kolm, Serge-Christophe, 1973. "A note on optimum tax evasion," Journal of Public Economics, Elsevier, vol. 2(3), pages 265-270, July.
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