The Economics of Scams

Stan Miles; Derek Pyne

doi:10.1515/rle-2015-0035

Article

The Economics of Scams

Stan Miles and Derek Pyne

Published/Copyright: February 4, 2017

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From the journal Review of Law & Economics Volume 13 Issue 1

Abstract

This paper offers one of the first economic analyses of scams. Its major finding is that, unlike other crimes, imperfect enforcement may increase victimization by deterring only low-ability scammers whose failed attempts would otherwise alert potential victims before encounters with high-ability scammers. High-ability scammers may actually benefit from partial enforcement, which reduces their competition. These results may be reinforced when failed attempts are punished.

Keywords: scams; deterrence; crime; enforcement

JEL Classification: K42

Acknowledgments

This paper benefited from the comments of Cliff Henson, Georgia Martin, Katarina Mayer, Murat Mungan, Lijun Zhang, two anonymous referees and participants at the 48^th Canadian Economic Association Conference.

Appendix

Proof of Lemma 1, part (b):

With the substitutions R=nL+nHR=nL+nH and x=1−aTx=1−aT, eq. [2] can be rewritten as oA=TaR(1−xR)oA=TaR(1−xR). Thus

[17]∂oA∂R=Ta{1R[−(xR )ln(x)]+(1−xR )(−1R2)} =Ta{xR[1−Rln(x)]−1R2}

Since TaR2>0TaR2>0, it suffices to show that xR[1−Rln(x)]−1<0xR[1−Rln(x)]−1<0.

Define the function g(u)=u(1−lnu)−1g(u)=u(1−lnu)−1 on the set of all real numbers u such that 0<u≤10<u≤1. Then g′(u)=u(−1/u)+(1−lnu)(1)=−1+1−lnu=−lnug′(u)=u(−1/u)+(1−lnu)(1)=−1+1−lnu=−lnu for all u in the domain of g. Note that g′(u)>0g′(u)>0 for all u in the open interval (0, 1), which implies that g is strictly increasing on that interval. Also, g(1)=0g(1)=0. Since g is continuous on the half-open interval (0, 1], this implies that g(u)<0g(u)<0 for all u in the open interval (0, 1).

Setting u to xRxR and using the fact that Rlnx=ln(xR)Rlnx=ln(xR), we obtain xR[1−Rln(x)]−1<0xR[1−Rln(x)]−1<0.

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Published Online: 2017-2-4

Published in Print: 2017-3-1

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https://doi.org/10.1515/rle-2015-0035

Keywords for this article

scams; deterrence; crime; enforcement