Lecture 3 Optimal Law Enforcement

1. Anticorruption and the Design of Institutions 2009/10 Lecture 3 Optimal Law Enforcement Prof. Dr. Johann Graf Lambsdorff

2. Literature • Becker, G.S. (1968), “Crime and Punishment: An Economic Approach,” Journal of Political Economy, Vol. 76, 169–217. • Becker, G.S. and G.J. Stigler (1974), “Law enforcement, malfeasance, and compensation of enforcers,” Journal of Legal Studies, Vol. 3 (1), 1–18. • Polinsky, M. and S. Shavell (2001), “Corruption and optimal law enforcement,” Journal of Public Economics, Vol. 81: 1-24.

3. The Costs of Fighting Corruption Decision tree for a potentially corrupt businessperson - Penalty - Bribe (Corrupt service confiscated) r Pay bribe 1-r Corrupt service - Bribe Do not pay a bribe No corrupt service

4. The Costs of Fighting Corruption • Similarly, to the calculus of public servants (see lecture “The Economics of Corruption”), the following condition states whether a risk-neutral business person will pay a bribe: V  (rPd+B)/(1-r), • with V being the value of the corruptly provided service and r the probability of detection. B is the value of the bribe. Detection results in confiscation of the favor and a penalty on the side which demanded it, Pd. There might be transaction costs arising, which were disregarded here. • A high risk of detection, r, or severe penalties, Pd, induce businesspeople to abstain from paying bribes. • Another approach would be to make sure that public servants have little to distribute. If V is sufficiently small, the calculus would equally lead businesspeople to prefer legality.

5. The Costs of Fighting Corruption • But the government will also recognize the costs it must devote to detection. • At the same time, penalties are either costly (imprisonment) or if costless (fines) confronted with financial constraints of the convict. • If these costs become too large, a certain level of corruption becomes unavoidable. • This calculus can be graphically illustrated. • Assume that marginal costs of removing corruption are higher where there is little corruption. This might be due to increased difficulty of detection. • Marginal costs of corruption might have any slope, positive or negative.

6. Optimum social costs of corruption The Costs of Fighting Corruption Marginal social costs Marginal cost of corruption Additional social costs of eradicating corruption Marginal cost of removing corruption Optimum quantity of corruption Quantity of Corruption 0

7. Optimal Law Enforcement • Polinsky and Shavell (2001) provide a formal treatment of this problem. They investigate bribe-taking by public servants (called law enforcers in their study). We focus on their model subsequently. • A civilian considers acting illegally and thus harming society. If acting as an offender (a car driver who was speeding or a constructor who procures substandard quality) he faces detection by a public servant, for example an inspector, with probability p and imposition of the fine f.

8. Optimal Law Enforcement • Rather than paying the fine, the public servant may be bribed by the amount b=lf, with ldetermining the public servant’s bargaining power, 0<l<1. She is not confronted with penalties and risks of detection (but we will introduce these later). • The public servant may also falsify evidence and frame an innocent civilian, forcing him to pay the fine f. The same bribe x=b=lf, must then be paid to avoid the penalty. • The probability of being detected as an innocent civilian, qp with 0<q<1, is lower than for an offender, p, because it is difficult to falsify evidence. • The civilian now compares the gain from committing the harmful act, g, with the expected costs. He will prefer to offend ifg>pb-qpx=(1-q)lpf.

9. Optimal Law Enforcement • There results a critical value of the gain, , below which the civilian will abstain from offending. • Bribery lowers deterrence. In a world without bribery, the full penalty f rather than the reduced penalty lf applies. With the full penalty, f, a higher gain to the offender would be required for offending. • Also the size of the penalty is important. The higher the penalty, the higher the critical value of the gain, suggesting that an infraction is less frequent. • We can now determine social welfare. • We define s(g) as the density of gains among individuals, s(g) is positive on [0, ∞). We let h be the harm due to the infraction and c(p), c’(p)>0, be the costs for detecting offenders.

10. Optimal Law Enforcement • Social welfare can be expressed as: with • A first conclusion is that increasing f is always advantageous. Increasing fines does not increase costs for detection but raises the critical value, . • But there will be wealth constraints that limit the size of the fine. Let w0 be the wealth of the offender. This marks the upper limit of the fine. The optimal fine is then the maximal possible fine f*=w0. • The optimal probability of detection, p, is confronted with two countervailing effects. A higher p is costly, but it also increases , which reduces the harm from the infraction.

11. Optimal Law Enforcement • Corruption in the form of bribery or framing is harmful because it inhibits deterrence, (Becker and Stigler 1974: 5). This result is valid irrespective of the size of the harm, h. • Assuming h to be rather small results in optimal enforcement costs to be low and p small. Once introducing corruption, deterrence would be lower as compared to a situation without corruption. As a consequence, the optimum level of enforcement must increase. This increase in enforcement costs runs counter to public welfare and proves the adverse welfare effect of corruption. • We learn from the model, that any government will weigh the costs of enforcement, considering also the potential corruption of its own public servants, against the reduction of harmful acts.

12. Optimal Law Enforcement • Another approach to avoiding bribery and framing by public servants would be to confront this behavior, not just the civilian’s infraction, with penalties and the risk of detection. This has been suggested by Becker and Stigler (1974) and implemented in the model by Polinsky and Shavell (2001). • Assume that the bribe is detected with probability q resulting in the bribe transaction being undone and the fine fB being imposed on the offender and the public servant each. The fine f is not collected. For the sake of simplicity fB is equal for both actors. The public servant is assumed to be endowed with the same level of wealth, enabling her to pay the same fine. We now drop the public servant’s option to frame the civilian.

13. Optimal Law Enforcement • Now, an offender who is caught will prefer to pay a bribe only if (1-q)b+qfB<f. • The public servant will accept a bribe if (1-q)b-qfB>0. • A bribe is feasible only ifqfB/(1-q)<b<(f-qfB)/(1-q) • A bribe will be paid if qfB<(f-qfB)  2qfB<f, which we assume subsequently. • The public servant can now achieve the fraction l of the total surplus, f-2qfB.

14. Optimal Law Enforcement • The bribe must now compensate for the public servant’s expected penalty q(fB+b)and provide her with the fraction l of the total surplus f-2qfB. We thus obtain b = l(f-2qfB)+q(fB+b)  b = [l(f-2qfB)+qfB]/(1-q). • A civilian will now offend if the probability of detection multiplied by the costs of the bribe strategy are lower than his gain. The costs of the bribe strategy are (1-q)b in case of non-detection and qfB in case of detection. g>p(b(1-q)+qfB)=p[l(f-2qfB)+qfB]+pqfB=p[lf+2(1-l)qfB] • An increase in fBincreases the critical value of . The optimum penalty is thus the maximum penalty, fB=f=w0.

15. Optimal Law Enforcement • Social welfare can be expressed as: with • The optimal probability of detection, q, is confronted with two countervailing effects. A higher q is costly, but it also increases , which reduces the harm from the infraction. • The government has two instruments for deterring the infraction. It can employ more public servants so as to increase p, or it can employ more prosecutors so as to increase q.

16. Appendix Discussion1) Disregarding ethics, how would businesspeople and public officials determine whether to engage in bribery?

17. Appendix Exercise1) Let the harm h be 1.5 and the distribution function be s(g)=0.5 for all g with 0≤g ≤2. Determine and solve the integral. 2) Let the harm h be 1 and the distribution function be s(g)=1-g/2 for all g with 0≤g ≤2. a) Determine and solve the integral.b) Let =pf due an absence of bribery and c(p)=p2. How can you determine the optimal p?

18. Appendix 3) Let the harm h be € 1500; the gain g that individuals obtain from committing the harmful act be distributed uniformly between € 0 and € 2000; the enforcement expenditure c required to detect violators with probability p be € 10 000p2. The wealth of offenders w is € 10 000. a) Determine the first-best outcome when disregarding enforcement costs!b) Determine the maximum social welfare considering enforcement costs if corruption is absent!c) Determine the maximum social welfare with corruption (bribery and framing). Let the bargaining power of the public servant l be 0.7 and the ratio of the probability that an innocent individual could be framed to the probability that an offender is detected, q, be 0.3.d) The government can now detect bribery with the probability q and enforcement costs 5000q2. Let l = 0.49 and q = 0. The probability p can be shown to remain as in question c). Determine the optimal q!