The Optimal Use of Fines and Imprisonment If Governments Do Not Maximize Welfare

We consider a stylized model of crime and punishment in which the prosecution policy is defined by three variables: the size of punishment, the type of punishment, and the detection probability. We derive the optimal type of punishment under the assumption that the detection probability is chosen by a government whose objective function places a higher weight on the government's budget than the social welfare function does. We show that for serious crimes exclusive imprisonment is welfare maximizing. If costs of imprisonment are taken into account, the optimal punishment is a prison term with an additional fine that is smaller or equal to the costs of the prison term. For less serious crimes, fines without imprisonment are welfare maximizing. Therefore, this paper demonstrates that the standard result of the literature that fines should be used whenever feasible need not hold in the presence of a rent‐seeking government. Moreover, it offers a new explanation for the widespread use of mandatory imprisonment for serious crimes.     

The optimal use of fines and imprisonment when wealth is unobservable

This article studies the optimal use of fines and imprisonment when an offender's level of wealth cannot be observed by the enforcement authority. I employ a model in which there are two types of offenders—a low-wealth type and a high-wealth type. The consequence of the unobservability of wealth depends on whether the enforcement authority would employ fines alone, or would also impose imprisonment sentences, if wealth were observable. In the former case, the inability to observe wealth lowers social welfare. But in the latter case, the unobservability of wealth does not lower social welfare. In both cases, offering offenders a choice of sanctions can induce high-wealth offenders to pay higher fines even though their wealth is unobservable. Specifically, a relatively high imprisonment sentence must accompany the payment of a low fine, so that high-wealth offenders will prefer to pay a higher fine and bear a lower (possibly no) imprisonment sentence.     

Accident Law: Efficiency May Require an Inefficient Standard

In a world with risk-neutral agents in which accidents occur with a positive probability, liability rules will only induce efficient behaviour if these rules impose the full (marginal) costs of an action on the parties. However, institutional restrictions or bilateral activity choices can prevent the full internalization of costs. A mechanism is proposed which guarantees an efficient outcome: monetary fines which are not related to the occurrence of an accident. Such a mechanism requires individuals to violate the standard of care in order to trigger the fine payments. Hence, efficiency requires an excessive standard.     

Direct Versus Indirect Taxation: The Design of the Tax Structure Revisited

This article studies the optimal direct/indirect tax mix problem when individuals differ in several unobservable characteristics (productivity and endowments). It presents general expressions for the optimal commodity tax rates and proves that contrary to Atkinson and Stiglitz's (1976) result, differential commodity taxation remains a useful instrument of tax policy even if preferences are separable between labor and produced goods. When cross substitution effects are zero, the expressions resemble traditional many households Ramsey rules. In a Cobb–Douglas illustration, where endowments differ only in good 1 (interpreted as “wealth”), the tax on good 2 provides an indirect way to tax the unobservable wealth.     

Wealth, Enterprise and Credit Policy

Empirical evidence suggests that capital-market constraints prevent low-wealth individuals from setting up in business. This paper shows this finding to be consistent with socially excessive lending and an interest-rate tax being welfare-improving. One feature of the model, banks' inability to identify entrepreneurial quality, leads to excessive bank lending and investment in low-return projects. The reduction in the probability of bankruptcy lowers the cost of borrowing and eliminates deadweight costs and hence promotes entry. If the incentive effects are sufficiently large, wealth and the volume of entrepreneurial activity move together. A key result of the paper is to show that a market equilibrium in which there is a positive relationship between entry and the level of wealth is consistent with either subsidies to inactivity or taxes on interest raising welfare.     

Penalty lottery*

To control sequential public bad productions under imperfect monitoring, this paper proposes a penalty lottery: a violator passes the responsibility of the fine to the next potential violator with some probability and pays all the accumulated fines with the complementary probability. The penalty lottery does not merely impose extreme fines because an absorbing state is practically unreachable. It self-selects people more willing to produce public bads and endogenously imposes the larger expected fines on them. It has advantages over the day-fine system in which the fine depends on the offender's daily income. Experimental evidence is consistent with the proposed theoretical predictions.     

TIME, MONEY, AND OPTIMAL CRIMINAL PENALTIES

The economic approach to optimal criminal penalties measures the welfare effects of crime and punishment in dollar terms, ignoring differences in the marginal utility of money among people. This paper alternatively proposes using time as the unit of measure in determining optimal criminal penalties, measuring the costs and benefits of crime in hours or days instead of dollars. The policy implications differ substantially from those in the existing economic literature. Equal prison terms impose similar time costs on all individuals rather than being more costly for those with higher foregone earnings. Equal fines impose the same cost on all individuals in the dollar-based economic models but in a time-denominated system are costlier to those who require more time to earn the money to pay the fines. In principle, one can use either money or time in setting penalties. However, time-based penalties are more consistent with the fundamental and widely held principles of justice on which the U.S. legal system rests.     

Optimal taxes on wealth and consumption in the presence of tax evasion

This article incorporates tax evasion into an optimum taxation framework with individuals differing in earning abilities and initial wealth. We find that despite the possibility of its evasion a tax on initial wealth should supplement the optimal nonlinear income tax, given a positive correlation between initial wealth and earning abilities. Further, even if income and initial wealth are taxed optimally, it is still desirable to levy a tax on commodities, though it can be evaded as well. Thus, our result provides a rationale for a comprehensive tax system. Optimal tax rates on commodities differ in general, however for the special case of a uniform evasion technology equal rates are optimal if preferences are homothetic and weakly separable.     

Legal Principles in Antitrust Enforcement

We study antitrust enforcement that aims to channel price‐fixing incentives of cartels through setting fine schedules and detection levels. Fines obey legal principles, such as the punishment should fit the crime, proportionality, bankruptcy considerations, and minimum fines. Bankruptcy considerations limit maximum fines, ensure abnormal cartel profits, and impose a challenge for optimal antitrust enforcement. We derive the fine schedule and detection level that are constrained‐optimal under legal principles and sustainability of cartel prices. This fine schedule lies below the maximum fine, makes collusion on lower prices more attractive than on higher prices, and, hence, relates to the body of literature on marginal deterrence.     

ASSET FORFEITURE AS A LAW ENFORCEMENT TOOL

This article examines the impact on deterrence of laws that allow the seizure of assets used in the commission of a crime but owned by someone other than the offender. The results suggest that forfeiture can be used effectively, in combination with more standard tools (criminal fines or imprisonment), as a deterrent under certain conditions, but the risk of overuse is real. In particular, complete forfeiture (seizure of the entire value of the asset) is not generally socially optimal, but when enforcers are rent‐seekers who care primarily about the revenue generated by forfeiture, they will use the tool to the maximum extent allowed by law. (JEL H11, K14, K41)     

Why Do Some Households Save So Little? A Rational Explanation

This paper offers an explanation for the puzzle of low wealth holdings among a significant fraction of the elderly. Instead of invoking irrational, nonrational, or nonoptimal behavior to resolve the puzzle, it is shown that widespread low wealth holdings are consistent with a rational life-cycle model of saving with uncertain lifetime and borrowing constraint. When there is uncertainty about the length of life, it is optimal for some individuals to save little and exhaust their wealth early. The characteristics of these individuals are derived. The simulation results support that the model can account for low wealth holdings as well as early terminal wealth depletion. The analysis also rejects the common perception that uncertain lifetime reduces dissaving. Journal of Economic Literature Classification Numbers: D11, D91, E21, I12, J14.     

Optimal Fines under Announced and Surprise Inspections

This paper examines optimal fines in a regulatory framework where the regulator can choose either surprise or announced inspections to monitor a firm for compliance. The firm can invest in detection avoidance, but it receives a fine if the regulator discovers that it is noncompliant. In the welfare maximization problem, we focus on the trade‐off between the frequency of inspections and the magnitude of the fine. We find that when inspections are unannounced, the optimal fine is maximal, but when they are announced, the optimal fine may be less than maximal.     

Private disclosure: Is honesty enough?

If disclosure is costless a truthful monopolist selling to identical rational consumers will never withhold socially valuable information. But it preferences differ between individuals and are non-hierarchical, then too little information may be revealed.     

Pollution standards, technology investment and fines for non-compliance

In this paper, we analyze whether it is socially desirable that fines for exceeding pollution standards depend not only on the degree of non-compliance but also on technology investment efforts by the polluting firms. For that purpose, we consider a partial equilibrium framework where a representative firm chooses the investment effort and the pollution level in response to an environmental policy composed of a pollution standard, an inspection probability and a fine for non-compliance. We find that the fine should strictly decrease with the investment effort when (i) there are administrative costs of sanctioning; (ii) the optimal policy induces non-compliance; and (iii) either the fine is sufficiently convex in the degree of non-compliance or the investment effort decreases marginal abatement costs significantly.     

Occupational choice, incentives and wealth distribution

We consider a model of occupational choice in large economies where individuals differ in their wealth endowment. Individuals can remain self-employed or engage in productive matches with another individual, i.e., form firms. Matches are subject to a moral hazard problem with limited liability. The division of the gains from such matches is determined by competitive forces. When the incentive problem is asymmetric, matches are typically wealth-heterogeneous, with richer individuals choosing the occupation for which incentives are more important. The utilities attained within a match depend on the wealth distribution and changes in the latter give rise to ‘trickle down’ effects.     

Growth Optimal Investment Strategy: The Impact of Reallocation Frequency and Heavy Tails

The strategy to maximize the long‐term growth rate of final wealth (maximum expected log strategy, maximum geometric mean strategy, Kelly criterion) is based on probability theoretic underpinnings and has asymptotic optimality properties. This article reviews the allocation of wealth in a two‐asset economy with one risky asset and a risk‐free asset. It is also shown that the optimal fraction to be invested in the risky asset (i) depends on the length of the basic return period and (ii) is lower for heavy‐tailed log returns than for light‐tailed log returns.     

The Impact of Industry Structure and Penalty Policies on Incentives for Compliance and Regulatory Enforcement

This paper examines the optimal fine for violations of environmental regulations, taking into account financial constraints facing regulated firms and the hierarchical structure of regulatory enforcement. Contrary to the existing literature, which suggests that maximal fines are sub-optimal, we find that the optimal fine is either the maximum amount the firm can afford to pay or zero (i.e., no regulation). The impact of a change in industry structure on the optimal fine, firm compliance and regulatory resource strategies is considered. We identify conditions under which the equilibrium level of regulatory resources decreases with an increase in the number of firms in the industry.     

Does It Matter if You Are Observed by Others? Evidence from Donations in the Field*

We investigate whether people's donations in the field are affected by the presence of others. In the analysis, we distinguish between individuals who arrived at a national park alone and those who arrived as members of a group. We also investigated the effect of donations being made in the presence of a third party made in the presence of a third party. We find that donations are significantly more frequent for individuals who are members of a group. When a third party is present, we find that the total donations by individuals who are a part of a group are significantly higher than those of lone travelers, mainly because of the increased probability of donating.     

A simple explanation of the relative performance evaluation puzzle

We study a simple moral hazard model in which two risk-neutral owners establish incentives for their risk-averse managers to exert effort. Because the probability distributions over output realizations depend on a common aggregate shock, optimal contracts make the compensation of each manager contingent on own performance but also on a performance benchmark—the performance of the other firm. If the marginal return of effort depends on the aggregate state, optimal contracts are not monotonically decreasing in the performance benchmark. This provides a simple explanation of the Relative Performance Evaluation (RPE) Puzzle—the documented lack of a negative relationship between CEO compensation and comparative performance measures, such as industry or market performance. Our simple model can also explain one-sided RPE—the documented tendency to insulate a CEO's rewards from bad luck, but not from good luck. We clarify that our results are robust in several dimensions and we discuss other applications of our findings.     

Task scheduling and moral hazard

We study a two-period moral hazard problem with risk-neutral and wealth-constrained agents and three identical tasks. We show that the allocation of tasks over time is important if there is a capacity constraint on the number of tasks that can be performed in one period. We characterize the optimal schedule of tasks over time and the optimal assignment of tasks to agents conditional on the outcomes of previous tasks. In particular, we show that delaying tasks is optimal if and only if the effect of an agent’s effort on the probability of success is relatively low. We have benefitted from helpful discussions with A. Roider, L. Samuelson, and U. Schweizer. The paper has been substantially improved due to the detailed and very valuable comments of an Associate Editor. Financial support by Deutsche Forschungsgemeinschaft, SFB/TR15, is gratefully acknowledged.