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Norms and monetary fines as deterrents, and distributive effects

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Abstract

Both social norms and monetary fines can deter acts that are privately beneficial but socially undesirable. The number and the identities of those who commit the acts differ between with norms and with fines. Fines are more likely to make higher-income individuals better off than norms. As a society becomes more affluent, fines are more likely to increase the number of those who commit than norms, and norms become the better system of deterring socially undesirable acts.

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Notes

  1. Strategic default occurs when a homeowner-borrower walks away from a mortgage, and will be discussed in Sect. 6.

  2. The governor’s common sense on traffic tickets. The San Diego Union-Tribune, September 24, 2014, available at http://www.sandiegouniontribune.com/news/2014/sep/23/governor-jerry-brown-common-sense-traffic-tickets/ (accessed June 1, 2016).

  3. Unfair Traffic Tickets Put the Poor in a Hole; a Proposed Law Could Fix That. LA Weekly, April 9, 2015, available at http://www.laweekly.com/news/unfair-traffic-tickets-put-the-poor-in-a-hole-a-proposed-law-could-fix-that-5479631 (accessed June 2, 2016).

  4. Section 6 considers a more general case with the disutility of guilt dependent on income.

  5. There is a continuum of individuals who differ in their incomes and benefits from the act. However, for the sake of intuitive discussion, individuals are divided into the higher-income group and the lower-income group, and each income group is divided into three groups according to their benefits. The definitions of each group will be made precise in the subsequent sections.

  6. Since higher-income individuals are more likely to commit the act with fines than with norms, no higher-income individual switches from the commission with norms to the abstention with fines.

  7. Without this assumption, the result does not change qualitatively, but it is necessary to keep track of corner cases and interior cases.

  8. In the expression of \(\partial b_M(.)/\partial y\), \(U_y(y- m, b, n)\) should be \(U_{y-m}(y- m, b, n) \equiv \partial U(y-m, b, n)/\partial (y-m)\), but \(U_y(y- m, b, n)\) is kept for simplicity, as it appears to create no confusion.

  9. Their analysis concerns if the fine increases late pickups, as noted earlier, and has no bearing on this paper.

  10. Suppose the contrary, so that the curve \(b = b_N(y, n_N)\) and the curve \(b = b_M(y, m, p, n_M)\) do not intersect. For instance, suppose that \(b_N(y, n_N) > b_M(y, m, p, n_M)\) for all y in Fig. 1. Since those with \(b > b_N(.)\) commit the act with norms and those with \(b > b_M(.)\) commit the act with fines, more individuals commit the act for all y with fines than with norms, implying \(n_M > n_N\). The last inequality contradicts the assumption \(n_N = n_M\), and the two curves must intersect.

  11. In the figure, this first group of individuals are represented by the line segment between the horizontal axis and the curve \(b = b_M(y, m, p, n_M)\) on any vertical line to the right side of \(y^*.\) The second group below are represented by the line segment between the curve \(b = b_M(y, m, p, n_M)\) and the curve \(b = b_N(y, n_N)\) on any vertical line to the right side of \(y^*\), and the third group by the line segment between the curve \(b = b_N(y, n_N)\) and the horizontal line \(b = \overline{b}\) on any vertical line to the right side of \(y^*\).

  12. As noted above, the assumption of \(U_{yb}(.) \ge 0\) is consistent with case (i), \(\partial b_N(.)/\partial y \le 0\) and \(\partial b_M(.)/\partial y < 0.\) However, the assumption of \(U_{yb}(.) \le 0\) is consistent with \(\partial b_N(.)/\partial y > 0\) or \(\partial b_M(.)/\partial y > 0\) in the other two cases. Thus, for the sake of completeness, both assumptions are considered.

  13. At \(b = \hat{b}_1(y), \pi (y, \hat{b}_1(y)) = 0\) in (19) by the definition of \(\hat{b}_1(y)\), and total differentiation of \(\pi (y, \hat{b}_1(y)) = 0\) gives \(\partial \hat{b}_1(y)/\partial y = - [U_y(y-m, b, n) - U_y(y, b, n)]/[U_b(y-m, b, n) - U_b(y, b, n)] > 0\) due to the assumption of \(U_{yb}(y, b, n) > 0\) in the figure. The curve \(b = \hat{b}_1(y)\) is thus increasing in y.

  14. Googling ‘crackdown on dog fouling’ results in a large number of examples of cities and communities that have taken measures to deter the act, such as Moyle, Allerdale Borough, Winsford, Swansea, and Coventry.

  15. This case with \(n_M < n_N\) makes the example of the dog-fouling case more realistic, because stringent enforcement in the form of a high p by city councils would reduce \(n_M\) and it is more likely that \(n_M < n_N.\) Since this does not change Proposition 1 or Corollary 1, it is still true that the council of a city will support fines if \(F(y^*) < 1/2\) and \(U_{yb}(y, b, n) \le 0.\) However, Proposition 2 and Corollary 2 become ambiguous. Thus, as before, the council would not support fines if \(F(y^*) > 1/2\) and \(U_{yb}(y, b, n) \ge 0\). Alternatively, it may now support fines even if \(F(y^*) > 1/2\) and \(U_{yb}(y, b, n) \ge 0\).

  16. There are of course other situations. For example, even if \(\triangle n_M > 0\), it is possible that \(\triangle n_N < 0\), so the improvement makes all individuals better off with norms even if it makes all individuals worse off with fines.

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Correspondence to Kangoh Lee.

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I am grateful to the Editor and two anonymous referees for their helpful comments, which improved the paper significantly.

Appendix

Appendix

Proof of (14)

Observe that since U(ybn) is concave, \(U_y(y-m, b, n) > U_y(y, b, n)\) and

$$\begin{aligned} \frac{\partial b_M(.)}{\partial y}= & {} - \frac{1}{D_M}\left[ (1-p)U_y(y, b, n) + pU_y(y- m, b, n) - U_y(y, 0, n)\right] \\< & {} - \frac{1}{D_M}\left[ (1-p)U_y(y, b, n) + pU_y(y, b, n) - U_y(y, 0, n)\right] \\= & {} - \frac{1}{D_M}[U_y(y, b, n) - U_y(y, 0, n)]. \end{aligned}$$

Thus,

$$\begin{aligned} \frac{\partial b_N(.)}{\partial y} - \frac{\partial b_M(.)}{\partial y}> & {} - [U_y(y, b, n) - U_y(y, 0, n)] \left[ \frac{1}{D_N} - \frac{1}{D_M}\right] \nonumber \\= & {} \left[ U_y(y, 0, n) - U_y(y, b, n)\right] \frac{1}{D_N\;D_M} \left[ D_M - D_N\right] \nonumber \\= & {} \left[ U_y(y, 0, n) - U_y(y, b, n)\right] \nonumber \\&\times \frac{p}{D_N\;D_M} \left[ U_b(y-m, b, n) - U_b(y, b, n)\right] . \end{aligned}$$
(A1)

Since \(D_N > 0\) and \(D_M > 0\), the sign of (A1) depends on the signs of the expressions inside the two pairs of squared brackets, which in turn depend on the sign of \(U_{yb}(y, b, n).\) Suppose first that \(U_{yb}(y, b, n) \ge 0.\) The expression inside the first pair is negative, and so is that inside the second pair, making (A1) positive. If \(U_{yb}(y, b, n) < 0,\) the expressions inside both pairs are positive, making (A1) positive. This establishes (14).

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Lee, K. Norms and monetary fines as deterrents, and distributive effects. J Econ 121, 1–27 (2017). https://doi.org/10.1007/s00712-016-0517-1

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