《法学相关资料合集》（英文版） Steven shavells.pdf_大学文库

Economic Analysis of Public law enforcement and criminal law (part of Foundations of Economic Analysis of Law Steven shavell C2003. Steven Shavell. All Rights Reserved Chapter 20 Deterrence with Monetary Sanctions The topic addressed here is the control of undesirable acts by the state through the use, or threatened use, of monetary sanctions. That is, the general subject is the deterrence of undesirable behavior through the use of monetary sanctions In the first part of the chapter, I assume for simplicity that monetary sanctions will apply with certainty--that all parties to whom a rule should apply will be brought before social authorities and bear the intended sanctions. Then, in the second part, I assume that sanctions apply only with a probability. There I examine the use of sanctions assuming that the public must incur enforcement expense to locate and/or to convict and ultimately to penalize parties who should bear sanctions. The principal problems for society that are studied are the choice of the level of enforcement effort- which determines the probability of penalizing parties-and the choice of the magnitude of sanctions so as to maximize social welfare For convenience, I focus on the case in which parties are risk-neutral, so that parties will commit an act if the benefit to them from so doing exceeds the expected sanction. However, I also examine the case in which parties are risk-averse. In the risk-neutral case, social welfare is assumed to equal the gains parties obtain from acts, less the harm done by acts, less the costs of enforcement; in the risk-averse case the measure of social welfare also incorporates the disutility of risk-bearing. By the costs of enforcement, I mean the expenses of apprehending and convicting violators, but I assume that there is no resource cost associated with the actual imposition of monetary sanctions. This assumption is made to capture the important point that the payment of a fine is, in itself, only a transfer of purchasing pov d to expenditure of real resources. (In contrast, the imposition of the nonmonetary sanction of imprisonment involves substantial direct costs. In the next chapter, the significance of this difference will be emphasized. Of course, in fact the imposition of monetary sanctions does involve social costs, such as those involved in locating a person s assets and collecting a fine; this issue will be discussed in section 3 of chapter 22

Chapter 20 – Page 1 Economic Analysis of Public Law Enforcement and Criminal Law (part of Foundations of Economic Analysis of Law) Steven Shavell ©2003. Steven Shavell. All Rights Reserved. Chapter 20 Deterrence with Monetary Sanctions The topic addressed here is the control of undesirable acts by the state through the use, or threatened use, of monetary sanctions. That is, the general subject is the deterrence of undesirable behavior through the use of monetary sanctions. In the first part of the chapter, I assume for simplicity that monetary sanctions will apply with certainty -- that all parties to whom a rule should apply will be brought before social authorities and bear the intended sanctions. Then, in the second part, I assume that sanctions apply only with a probability. There I examine the use of sanctions assuming that the public must incur enforcement expense to locate and/or to convict and ultimately to penalize parties who should bear sanctions. The principal problems for society that are studied are the choice of the level of enforcement effort – which determines the probability of penalizing parties -- and the choice of the magnitude of sanctions, so as to maximize social welfare. For convenience, I focus on the case in which parties are risk-neutral, so that parties will commit an act if the benefit to them from so doing exceeds the expected sanction. However, I also examine the case in which parties are risk-averse. In the risk-neutral case, social welfare is assumed to equal the gains parties obtain from acts, less the harm done by acts, less the costs of enforcement; in the risk-averse case the measure of social welfare also incorporates the disutility of risk-bearing. By the costs of enforcement, I mean the expenses of apprehending and convicting violators, but I assume that there is no resource cost associated with the actual imposition of monetary sanctions. This assumption is made to capture the important point that the payment of a fine is, in itself, only a transfer of purchasing power, as opposed to an expenditure of real resources.1 (In contrast, the imposition of the nonmonetary sanction of imprisonment involves substantial direct costs. In the next chapter, the significance of this difference will be emphasized.) 1 Of course, in fact the imposition of monetary sanctions does involve social costs, such as those involved in locating a person=s assets and collecting a fine; this issue will be discussed in section 3 of chapter 22

1. Certain Enforcement: Basic Theory of liability 1.1 Introduction. Here, as just stated, I examine the theory of enforcement assuming that it occurs with certainty. I consider first the two basic forms of harm-based liability: strict liability; and fault-based liability, that is, liability for a harmful act that is judged to be an undesirable act. Then I consider analogous act-based rules. (This discussion will be in substantial respects a restatement of the discussion of strict liability and of negligence rules in chapter 8 1. 2 Strict liability for harm. Under this rule, because a party always pays for the harm an act causes, the party s expected sanction equals the expected harm. Hence, he will commit an act if and only if his expected benefit exceeds the expected harm. That is, he will commit an act if and only if the act is socially desirable; the optimal outcome will result. Note that, in general if the sanction is less than harm, parties will sometimes act in ways that create greater harm than benefits. And if the sanction is greater than harm, there will be a chilling effect on desirable acts parties will be discouraged from acts that create greater benefits than harm Comments. (a) The only information required by the social authority in order to apply the strict liability rule is the level of harm b)The assets of a party must be sufficient to pay for the harm; otherwise, the party will not generally be induced to act optimally and may engage excessively in harmful acts Risk-averse case. If parties are risk averse, they will tend to bear risk because they may find themselves in circumstances where the benefits from a harmful act are high enough to make committing it desirable, meaning that they will bear sanctions. In order to reduce the magnitude of this risk, it may be socially beneficial for the sanction to be less than harm. Moreover, if the sanction is less than harm. overdeterrence that is the discouragement of desirable acts tends to be avoided. (These statements presume that parties are not insured against sanctions; on such Let g be the gain, h the harm, and g the probability of harm(this notation will also be used in subsequent notes) E8otetut(suppose that a firm discharges a potentially harmful pollutant into a river in order to save the costs of hauling here are two natural cases to examine: where g is enjoyed only when harm comes about(suppose a person throws a rock at a window and is trying to break it), and where g is enjoyed when the act is committed, regardless of whether harm its waste to a dump site -here it saves the costs for sure, regardless of whether the pollutant causes harm). In either ca o liability equal to harm will lead to optimal behavior. In the first case, it is optimal for the act to be committed if and only if gg>gh, and because the sanction equals harm, the person will commit the act if and only if that is true. In the second case, it is optimal for the act to be committed if and only if g>gh, and again, if the sanction equals harm, the person will it will be clear that the conclusions to be noted hold for both cases, as I will sometimes explicitly note d convenience, and commit the act if and only if g>gh In the text, I will not usually distinguish these cases for expositional STo be more precise, let me specify the state's problem of maximizing social welfare in a simple model where parties are risk averse. Suppose that UC) is the utility function from income y of members of a population of risk averse individuals with identical initial incomes, and among whom the gain g from committing the act(for concreteness, consider here and in many later notes the case where g is enjoyed with certainty; see note 2)is distributed according to the density fg). Then, if s is the sanction for harm, an individual will commit the act if and only if(1/q)u+g)+qUo+g/ s)$ UC). Thus individuals will commit the act when $g*(, s), where the critical g* can be shown to be decreasing in y and ncreasing in s. It is presumed that the income y of each individual is income net of taxes, where taxes are set in order to over the states expenses. The state collects fine revenue and, for simplicity, is assumed to suffer harms done. Therefore, f, for(1/ F(g*)is the fraction of individuals who commit the act, gh is the expected harm caused by a person Hho on of y==/(1/ F(g ")(gh/ gs ), where is the initial income of each person and F is the cumulative distribution funct commits the act, and gs is the expected revenue collected from such a person. The social problem is then to choose s to maximize social welfare W, the sum of expected utilities, that is W=F(g°(y,s)U0y)+l[(!q)(y+g)+qUU+g!s)gdg

Chapter 20 – Page 2 1. Certain Enforcement: Basic Theory of Liability 1.1 Introduction. Here, as just stated, I examine the theory of enforcement assuming that it occurs with certainty. I consider first the two basic forms of harm-based liability: strict liability; and fault-based liability, that is, liability for a harmful act that is judged to be an undesirable act. Then I consider analogous act-based rules. (This discussion will be in substantial respects a restatement of the discussion of strict liability and of negligence rules in chapter 8.) 1.2 Strict liability for harm. Under this rule, because a party always pays for the harm an act causes, the party=s expected sanction equals the expected harm. Hence, he will commit an act if and only if his expected benefit exceeds the expected harm. That is, he will commit an act if and only if the act is socially desirable; the optimal outcome will result.2 Note that, in general, if the sanction is less than harm, parties will sometimes act in ways that create greater harm than benefits. And if the sanction is greater than harm, there will be a chilling effect on desirable acts; parties will be discouraged from acts that create greater benefits than harm. Comments. (a) The only information required by the social authority in order to apply the strict liability rule is the level of harm. (b) The assets of a party must be sufficient to pay for the harm; otherwise, the party will not generally be induced to act optimally and may engage excessively in harmful acts. Risk-averse case. If parties are risk averse, they will tend to bear risk because they may find themselves in circumstances where the benefits from a harmful act are high enough to make committing it desirable, meaning that they will bear sanctions. In order to reduce the magnitude of this risk, it may be socially beneficial for the sanction to be less than harm. Moreover, if the sanction is less than harm, overdeterrence, that is, the discouragement of desirable acts, tends to be avoided.3 (These statements presume that parties are not insured against sanctions; on such 2 Let g be the gain, h the harm, and q the probability of harm (this notation will also be used in subsequent notes). There are two natural cases to examine: where g is enjoyed only when harm comes about (suppose a person throws a rock at a window and is trying to break it), and where g is enjoyed when the act is committed, regardless of whether harm comes about (suppose that a firm discharges a potentially harmful pollutant into a river in order to save the costs of hauling its waste to a dump site -- here it saves the costs for sure, regardless of whether the pollutant causes harm). In either case, liability equal to harm will lead to optimal behavior. In the first case, it is optimal for the act to be committed if and only if qg > qh, and because the sanction equals harm, the person will commit the act if and only if that is true. In the second case, it is optimal for the act to be committed if and only if g > qh, and again, if the sanction equals harm, the person will commit the act if and only if g > qh. In the text, I will not usually distinguish these cases for expositional convenience, and it will be clear that the conclusions to be noted hold for both cases, as I will sometimes explicitly note below. 3 To be more precise, let me specify the state’s problem of maximizing social welfare in a simple model where parties are risk averse. Suppose that U(y) is the utility function from income y of members of a population of risk averse individuals with identical initial incomes, and among whom the gain g from committing the act (for concreteness, consider here and in many later notes the case where g is enjoyed with certainty; see note 2) is distributed according to the density f(g). Then, if s is the sanction for harm, an individual will commit the act if and only if (1 ! q)U(y + g) + qU(y + g ! s) $ U(y). Thus individuals will commit the act when g $ g*(y, s), where the critical g* can be shown to be decreasing in y and increasing in s. It is presumed that the income y of each individual is income net of taxes, where taxes are set in order to cover the state’s expenses. The state collects fine revenue and, for simplicity, is assumed to suffer harms done. Therefore, y = z ! (1 ! F(g*))(qh ! qs), where z is the initial income of each person and F is the cumulative distribution function of f; for (1 ! F(g*)) is the fraction of individuals who commit the act, qh is the expected harm caused by a person who commits the act, and qs is the expected revenue collected from such a person. The social problem is then to choose s to maximize social welfare W, the sum of expected utilities, that is 4 W = F(g*(y, s))U(y) + I[(1 ! q)U(y + g) + qU(y + g ! s)]f(g)dg

insurance, see section 6 of chapter 22) 1.3 Fault-based liability for harm. Under this rule a party who causes harm is liable and bears a sanction equal to harm only if his act was undesirable, that is, only if the social authority finds that the expected harm exceeded his expected benefits. If, for example, the expected harm is $100 and the gain $60, the act would be found undesirable, so there would be liability for harm. a party would, however, not engage in such an undesirable act, for his expected sanction would equal the expected harm and thus exceed his benefit (his expected liability would equal $100 and exceed $60). If an act is desirable, however, a party will clearly commit it, for then he will not bear liability for any harm that comes about as a result Note again that if the sanction for an undesirable act is less than harm, then parties may sometimes commit such acts because their gain may exceed their expected sanction. If, however the sanction for an undesirable act exceeds harm there will not be an chilling effect on desirable acts, for these acts are not subject to sanctions under fault-based liability; hence, sanctions for undesirable acts that exceed harm will still lead to optimal outcomes Comments.(a) The information needed by the social authority to apply the fault-based liability rule is not only the level of harm, but also its likelihood and the benefit from the act, for to determine whether an act is desirable or not, the authority must compare the benefit to the expected harm (b)Again, the level of assets must in general be sufficient to pay for the harm, in order that the party be induced not to commit undesirable acts Risk-averse case. Parties will bear no risk under fault-based liability if fault is found without error; this is an advantage of the fault-based form of liability over strict liability(again assuming that insurance against sanctions is not sold ). Parties will, however, bear some risk of sanctions in the presence of uncertainty concerning findings of fault-- generated by errors in the determination of fault or by parties'imperfect ability to control their behavior. Thus, if parties to the extent that the parties bear risk due to uncertainty in findings of fault. Notably, aaai t are risk averse, the observations made in the case of strict liability carry over to the present rule, exceeding harm may well have a chilling effect on desirable acts g*(,s) It can be shown under fairly general conditions that the optimal s is less than h, the intuition being as stated in text. Of note that by lowering s from h, there is a gain in social welfare due to a reduction in risk-bearing by those who commit the act and might be sanctioned. This is so as long as the wealth of those who are sanctioned, y+g-S, tends to be lower than that of individuals in general (who have to pay higher taxes if s is lowered), for then the marginal utility of those who are sanctioned is higher than average marginal utility Finally, it should be observed that the expression for social welfare W reduces in the risk-neutral case to W==+ gfg)dg /(1/ F(gs))gh that is, a constant plus total gains minus total harms For in the risk-neutral case, we can take U()=y, so that g*U, s) reduces to qs, and substitution in the previous expression for w yields this expression To amplify, under fault-based liability, a party who commits an act and causes harm will be held liable if and nly if the act was undesirable, that is, if and only if g gh; otherwise he will not beheld liable If the sanction s= h, then party for whom g gh will face expected liability if he commits the act equal to gh, so will not commit the act; others will face no liability. Hence, if s= h, all undesirable acts will be deterred and all desirable acts will be committed

Chapter 20 – Page 3 insurance, see section 6 of chapter 22.) 1.3 Fault-based liability for harm. Under this rule a party who causes harm is liable and bears a sanction equal to harm only if his act was undesirable, that is, only if the social authority finds that the expected harm exceeded his expected benefits. If, for example, the expected harm is $100 and the gain $60, the act would be found undesirable, so there would be liability for harm. A party would, however, not engage in such an undesirable act, for his expected sanction would equal the expected harm and thus exceed his benefit (his expected liability would equal $100 and exceed $60). If an act is desirable, however, a party will clearly commit it, for then he will not bear liability for any harm that comes about as a result.4 Note again that if the sanction for an undesirable act is less than harm, then parties may sometimes commit such acts because their gain may exceed their expected sanction. If, however, the sanction for an undesirable act exceeds harm, there will not be an chilling effect on desirable acts, for these acts are not subject to sanctions under fault-based liability; hence, sanctions for undesirable acts that exceed harm will still lead to optimal outcomes. Comments. (a) The information needed by the social authority to apply the fault-based liability rule is not only the level of harm, but also its likelihood and the benefit from the act, for to determine whether an act is desirable or not, the authority must compare the benefit to the expected harm. (b) Again, the level of assets must in general be sufficient to pay for the harm, in order that the party be induced not to commit undesirable acts. Risk-averse case. Parties will bear no risk under fault-based liability if fault is found without error; this is an advantage of the fault-based form of liability over strict liability (again assuming that insurance against sanctions is not sold). Parties will, however, bear some risk of sanctions in the presence of uncertainty concerning findings of fault -- generated by errors in the determination of fault or by parties= imperfect ability to control their behavior. Thus, if parties are risk averse, the observations made in the case of strict liability carry over to the present rule, to the extent that the parties bear risk due to uncertainty in findings of fault. Notably, liability exceeding harm may well have a chilling effect on desirable acts. g*(y, s) It can be shown under fairly general conditions that the optimal s is less than h, the intuition being as stated in text. Of note is that by lowering s from h, there is a gain in social welfare due to a reduction in risk-bearing by those who commit the act and might be sanctioned. This is so as long as the wealth of those who are sanctioned, y + g – s, tends to be lower than that of individuals in general (who have to pay higher taxes if s is lowered), for then the marginal utility of those who are sanctioned is higher than average marginal utility. Finally, it should be observed that the expression for social welfare W reduces in the risk-neutral case to 4 W = z + Igf(g)dg ! (1 ! F(qs))qh, qs that is, a constant plus total gains minus total harms. For in the risk-neutral case, we can take U(y) = y, so that g*(y, s) reduces to qs, and substitution in the previous expression for W yields this expression. 4 To amplify, under fault-based liability, a party who commits an act and causes harm will be held liable if and only if the act was undesirable, that is, if and only if g < qh; otherwise he will not beheld liable. If the sanction s = h, then any party for whom g < qh will face expected liability if he commits the act equal to qh, so will not commit the act; others will face no liability. Hence, if s = h, all undesirable acts will be deterred and all desirable acts will be committed

Sanction equal to wrongdoer's gains. A version of fault-based liability that is of interest is that under which a party who commits a harmful undesirable act bears a sanction equal to hi gains. This sanction is sometimes thought to be a natural one for purposes of deterring acts, as it removes a wrongdoer's gains. But al though a sanction equal to gains will discourage undesirable behavior, it will, in principle, only barely do so, as parties lose no more than their gains. Consequently, the rule of sanctions equal to gains is peculiarly vulnerable to judicial error in assessment of gains, and for that reason tends to be inferior to fault-based liability with sanctions equal to harm. Specifically, under the rule with sanctions equal to gains, if the gain is underestimated even by a small amount, parties will have an incentive to engage in an act, no matter how much harm it causes. Suppose, for example, that an act creates a gain of $1,000 and harm of $1,000,000. If the gain is estimated to be $950, a party would have an incentive to engage in it, because he would profit by $50. In contrast, if liability is equal to harm, parties will be strongly discouraged from committing the act, even if there is substantial judicial error in estimating the harm 1. 4 Act-based liability. Both strict and fault-based liability for harm have act-based counterparts. The act-based analogue to strict liability for harm is the rule under which a party is liable for the expected harm due to an act, regardless of whether harm actually occurs or not Thus, if a party commits an act that will cause harm of $1, 000 with probability 10 percent, he will be liable for $100 for having committed the act. It is apparent that under this rule, the party will behave just as under strict liability for harm; he will commit an act if and only if the benefit obtained exceeds the expected harm. Similarly, the act -based analogue to fault-based liabil ity for harm is liability equal to the expected harm for undesirable acts, and it is clear that under this rule, parties will be induced not to commit undesirable acts Comments. (a) The social authority needs to know more in order to apply act-based rules than harm-based rules. To apply act-based strict liability, the authority needs to know not only the harm--which it does not observe if harm does not come about- but also the probability of harm. By contrast, to apply harm-based strict liability, it needs only to know the harm that has occurred. With regard to act-based fault liability, the social authority also faces the disadvantage that it does not observe harm(but it needs to know the probability of harm and the benefits from the act under either harm-based or act-based fault liability) (b) The level of assets that a party needs to have in order to be motivated to act appropriately is lower under act-based liability than under harm-based liability. Under act-based liability, to be properly motivated, a party needs assets equal only to the expected harm rather han the actual harm (in the example, assets of $100 rather than $1,000) 'I do not consider the analogue to this rule under strict liability, namely, liability equal to gains for desirable acts as well as undesirable acts. Such a rule would obviously be perverse, as it would remove any incentive to engage in desirable acts More precisely, under the rule in consideration, if a party obtains his gain g only if he does harm(see note 2), the sanction imposed on the party equals g. However, in the case where the party obtains g for sure when he acts, the sanction under the rule in consideration is interpreted to be g/q, so that the expected sanction equals g On the advantage under discussion of sanctions equal to harm rather than the wrongdoers gains, see Polinsky and Shavell 1994

Chapter 20 – Page 4 Sanction equal to wrongdoer’s gains.5 A version of fault-based liability that is of interest is that under which a party who commits a harmful undesirable act bears a sanction equal to his gains.6 This sanction is sometimes thought to be a natural one for purposes of deterring acts, as it removes a wrongdoer=s gains. But although a sanction equal to gains will discourage undesirable behavior, it will, in principle, only barely do so, as parties lose no more than their gains. Consequently, the rule of sanctions equal to gains is peculiarly vulnerable to judicial error in assessment of gains, and for that reason tends to be inferior to fault-based liability with sanctions equal to harm. Specifically, under the rule with sanctions equal to gains, if the gain is underestimated even by a small amount, parties will have an incentive to engage in an act, no matter how much harm it causes. Suppose, for example, that an act creates a gain of $1,000 and harm of $1,000,000. If the gain is estimated to be $950, a party would have an incentive to engage in it, because he would profit by $50. In contrast, if liability is equal to harm, parties will be strongly discouraged from committing the act, even if there is substantial judicial error in estimating the harm.7 1.4 Act-based liability. Both strict and fault-based liability for harm have act-based counterparts. The act-based analogue to strict liability for harm is the rule under which a party is liable for the expected harm due to an act, regardless of whether harm actually occurs or not. Thus, if a party commits an act that will cause harm of $1,000 with probability 10 percent, he will be liable for $100 for having committed the act. It is apparent that under this rule, the party will behave just as under strict liability for harm; he will commit an act if and only if the benefit obtained exceeds the expected harm. Similarly, the act-based analogue to fault-based liability for harm is liability equal to the expected harm for undesirable acts, and it is clear that under this rule, parties will be induced not to commit undesirable acts. Comments. (a) The social authority needs to know more in order to apply act-based rules than harm-based rules. To apply act-based strict liability, the authority needs to know not only the harm -- which it does not observe if harm does not come about -- but also the probability of harm. By contrast, to apply harm-based strict liability, it needs only to know the harm that has occurred. With regard to act-based fault liability, the social authority also faces the disadvantage that it does not observe harm (but it needs to know the probability of harm and the benefits from the act under either harm-based or act-based fault liability). (b) The level of assets that a party needs to have in order to be motivated to act appropriately is lower under act-based liability than under harm-based liability. Under act-based liability, to be properly motivated, a party needs assets equal only to the expected harm rather than the actual harm (in the example, assets of $100 rather than $1,000). 5 I do not consider the analogue to this rule under strict liability, namely, liability equal to gains for desirable acts as well as undesirable acts. Such a rule would obviously be perverse, as it would remove any incentive to engage in desirable acts. 6 More precisely, under the rule in consideration, if a party obtains his gain g only if he does harm (see note 2), the sanction imposed on the party equals g. However, in the case where the party obtains g for sure when he acts, the sanction under the rule in consideration is interpreted to be g/q, so that the expected sanction equals g. 7 On the advantage under discussion of sanctions equal to harm rather than the wrongdoer=s gains, see Polinsky and Shavell 1994

Risk-averse case. Risk-averse parties bear less risk under act-based liability beca sanctions equal the expected harm rather than the realized harm 1.5 Actual use of rules. In fact. we often observe use of harm-based sanctions both on a strict basis and according to fault. Penalties may be imposed by the state for spills of toxic materials, for failure to pay proper taxes, and for many other harmful events. Perhaps more often however, we see that public law enforcement involves act-based sanctions. This is typically the case with violation of safety, environmental, and many financial regulations, where sanctioned behavior is that which creates a positive expected harm but need not do actual harm 2. Law Enforcement with a probability: The optimal probability and magnitude of Sanctions 2.1 Introduction. Here it will be assumed that it is costly to identify and penalize liabl parties, so that society has to choose a level of enforcement effort, which will determine the probability of applying sanctions, as well as the magnitude of sanctions In determining the social-welfare-maximizing choice of the probability and magnitude of sanctions, I will for simplicity assume that liability is strict and based on harm, for the major points to be made do not depend on the nature of the rule of liability(except as remarked in section 2.6 on fault-based liability) 2.2 Behavior given the probability and magnitude of sanctions. How will a person behave who will face a sanction only with a probability if he commits an act? If the person is risk neutral, he will evaluate the sanction in terms of its expected value. Hence, the person will commit an act if and only if his benefit exceeds the expected sanction Risk-averse case. If the individual is risk averse, he will commit an act if and only if his expected utility is raised by so doing, and in general he will not be equally deterred by different combinations of sanction and probability with the same expected value, he will be more deterred the higher the magnitude of the potential sanction in the combination, the expected sanction held constant. For example, a risk-averse person will be more deterred by a sanction of $1,000 borne with probability 20 percent than by a sanction of $500 borne with probability 40 percent even though their expected values, $200, are equal. The reason is that, for a risk-averse party, the disutility of sanctions rises more than in proportion to their size, when the sanction rises from $500 to $1,000, its disutility more than doubles. Comments.(a) Probability versus magnitude of sanction. It is sometimes asked whether an increase in the probability or an increase in the magnitude of sanctions would make a greater difference in deterrence. But this question is incomplete as stated, for it is not explicit about the degree of change of these two factors. Obviously, if the magnitude of the sanction rises by much more than the probability, an increase in the magnitude would exert a greater effect on More generally, if U is the utility of income function of a risk-averse person, y is income, g is the gain from the act, p is the probability of a sanction, and s is the magnitude of the sanction(this notation will be used in many later note as well), the person' s expected utility if he commits the act will be eU=(l! p)U +g)+pUC +g! s). If p falls to kp where k0 because UMs decreasing. Hence, the lower is k, the lower is expected utility, and therefore the greater

Chapter 20 – Page 5 Risk-averse case. Risk-averse parties bear less risk under act-based liability because sanctions equal the expected harm rather than the realized harm. 1.5 Actual use of rules. In fact, we often observe use of harm-based sanctions, both on a strict basis and according to fault. Penalties may be imposed by the state for spills of toxic materials, for failure to pay proper taxes, and for many other harmful events. Perhaps more often, however, we see that public law enforcement involves act-based sanctions. This is typically the case with violation of safety, environmental, and many financial regulations, where sanctioned behavior is that which creates a positive expected harm but need not do actual harm. 2. Law Enforcement with a Probability: The Optimal Probability and Magnitude of Sanctions 2.1 Introduction. Here it will be assumed that it is costly to identify and penalize liable parties, so that society has to choose a level of enforcement effort, which will determine the probability of applying sanctions, as well as the magnitude of sanctions. In determining the social-welfare-maximizing choice of the probability and magnitude of sanctions, I will for simplicity assume that liability is strict and based on harm, for the major points to be made do not depend on the nature of the rule of liability (except as remarked in section 2.6 on fault-based liability). 2.2 Behavior given the probability and magnitude of sanctions. How will a person behave who will face a sanction only with a probability if he commits an act? If the person is risk neutral, he will evaluate the sanction in terms of its expected value. Hence, the person will commit an act if and only if his benefit exceeds the expected sanction. Risk-averse case. If the individual is risk averse, he will commit an act if and only if his expected utility is raised by so doing, and in general he will not be equally deterred by different combinations of sanction and probability with the same expected value; he will be more deterred the higher the magnitude of the potential sanction in the combination, the expected sanction held constant. For example, a risk-averse person will be more deterred by a sanction of $1,000 borne with probability 20 percent than by a sanction of $500 borne with probability 40 percent even though their expected values, $200, are equal. The reason is that, for a risk-averse party, the disutility of sanctions rises more than in proportion to their size; when the sanction rises from $500 to $1,000, its disutility more than doubles.8 Comments. (a) Probability versus magnitude of sanction. It is sometimes asked whether an increase in the probability or an increase in the magnitude of sanctions would make a greater difference in deterrence. But this question is incomplete as stated, for it is not explicit about the degree of change of these two factors. Obviously, if the magnitude of the sanction rises by much more than the probability, an increase in the magnitude would exert a greater effect on 8 More generally, if U is the utility of income function of a risk-averse person, y is income, g is the gain from the act, p is the probability of a sanction, and s is the magnitude of the sanction (this notation will be used in many later notes as well), the person’s expected utility if he commits the act will be EU = (1 ! p)U(y + g) + pU(y + g ! s). If p falls to kp, where k 0 because UN is decreasing. Hence, the lower is k, the lower is expected utility, and therefore the greater is deterrence

deterrence than would an increase in the probability, and conversely A natural and well-posed question, however, is how a given percentage increase in the probability of sanctions compares in importance to the same percentage increase in the magnitude of sanctions If parties are risk neutral, any named percentage increase in the probability of sanctions has an identical effect to an equal percentage increase in the magnitude of sanctions--for a given percentage increase in either the probability or the magnitude of sanction will raise the expected sanction by exactly that percentage. If there is a 20 percent probability of imposition of a sanction of $500 and the probability doubles to 40 percent, the expected sanction will double, from $100 to $200; and likewise if the sanction doubles to $1,000 (and the probability remains at 20 percent), the expected sanction will double to $200. Thus, a risk-neutral party will be affected in the same way by either type of change If parties are risk averse, however, they will be more affected by a percentage increase ir the magnitude of sanctions than by an equal increase in the probability of sanctions. a risk-averse party will be more deterred by the sanction of $1,000 with probability 20 percent than by the sanction of $500 with probability 40 percent. The reason is, as was just noted, that risk-averse parties suffer disutility more than in proportion to increases in the magnitude of sanctions Still, one often encounters the notion that the probability of sanctions(or, as it is frequently expressed, the certainty of sanctions )matters more than their magnitude. Although this disagrees with our conclusions for both risk-neutral and risk-averse individuals, it could be the case that probability matters more due to the ineffectiveness of large sanctions, notably, the fact that people may be unable to pay large amounts (b) Perception of the probability of sanctions. Information that individuals have about publish data on the likelihood of punishment. Moreover, the probability of sanctions (o not the probability of sanctions will often be imperfect. Enforcement authorities generally frequently variable, depending on the circumstances of the violation, so that even if enforcement authorities were forthcoming, there would inevitably be substantial imperfection of knowle about the probability. In addition, individuals often experience difficulty in assessing and interpreting probabilities, especially small ones, sometimes failing to discriminate among them sometimes inflating their importance and sometimes essentially ignoring them. These observations suggest the need for caution in applying what would appear to be the effect of the probability of sanctions on behavior. 10 (c) Perception of the magnitude of sanctions. Information about the magnitude of sanctions may also be imperfect. This is most likely to be true when the sanction is decided upon by a court or other tribunal that enjoys discretion over sanctions, so that there is no set specifically, let us assume as in the previous note that expected utility Eu=(1 I p)U+g)+ pU+g! s) We want to show that the(negative of) the elasticity of EU with respect to p is less than that with respect to s. The elasticity of EU with respect to p is [p/EUdEUldp]=plU+g! s)! U(+ g)EU, and the elasticity of EU with respect to s is (S/EUldEUlds]=! psU(+g! sEU. We therefore need to show that sU(+g! s)>[U0+g)! Uv+ g! s)l, but this holds because U is decreasin See Bebchuk and Kaplow 1992, Garoupa 1999, and Sah 1991 on perceptions of the likelihood of sanctions and learning about them. For empirical evidence on knowledge of expected sanctions, see, for example, Wilson and herrnstein 1985

Chapter 20 – Page 6 deterrence than would an increase in the probability, and conversely. A natural and well-posed question, however, is how a given percentage increase in the probability of sanctions compares in importance to the same percentage increase in the magnitude of sanctions. If parties are risk neutral, any named percentage increase in the probability of sanctions has an identical effect to an equal percentage increase in the magnitude of sanctions -- for a given percentage increase in either the probability or the magnitude of sanction will raise the expected sanction by exactly that percentage. If there is a 20 percent probability of imposition of a sanction of $500 and the probability doubles to 40 percent, the expected sanction will double, from $100 to $200; and likewise if the sanction doubles to $1,000 (and the probability remains at 20 percent), the expected sanction will double to $200. Thus, a risk-neutral party will be affected in the same way by either type of change. If parties are risk averse, however, they will be more affected by a percentage increase in the magnitude of sanctions than by an equal increase in the probability of sanctions. A risk-averse party will be more deterred by the sanction of $1,000 with probability 20 percent than by the sanction of $500 with probability 40 percent. The reason is, as was just noted, that risk-averse parties suffer disutility more than in proportion to increases in the magnitude of sanctions.9 Still, one often encounters the notion that the probability of sanctions (or, as it is frequently expressed, the certainty of sanctions) matters more than their magnitude. Although this disagrees with our conclusions for both risk-neutral and risk-averse individuals, it could be the case that probability matters more due to the ineffectiveness of large sanctions, notably, the fact that people may be unable to pay large amounts. (b) Perception of the probability of sanctions. Information that individuals have about the probability of sanctions will often be imperfect. Enforcement authorities generally do not publish data on the likelihood of punishment. Moreover, the probability of sanctions is frequently variable, depending on the circumstances of the violation, so that even if enforcement authorities were forthcoming, there would inevitably be substantial imperfection of knowledge about the probability. In addition, individuals often experience difficulty in assessing and interpreting probabilities, especially small ones, sometimes failing to discriminate among them, sometimes inflating their importance, and sometimes essentially ignoring them. These observations suggest the need for caution in applying what would appear to be the effect of the probability of sanctions on behavior.10 (c) Perception of the magnitude of sanctions. Information about the magnitude of sanctions may also be imperfect. This is most likely to be true when the sanction is decided upon by a court or other tribunal that enjoys discretion over sanctions, so that there is no set 9 Specifically, let us assume as in the previous note that expected utility EU = (1 ! p)U(y + g) + pU(y + g ! s). We want to show that the (negative of) the elasticity of EU with respect to p is less than that with respect to s. The elasticity of EU with respect to p is [p/EU][dEU/dp] = p[U(y + g ! s) ! U(y + g)]/EU, and the elasticity of EU with respect to s is [s/EU][dEU/ds] = !psU=(y + g ! s)/EU. We therefore need to show that sU=(y + g ! s) > [U(y + g) ! U(y + g ! s)], but this holds because U= is decreasing. 10See Bebchuk and Kaplow 1992, Garoupa 1999, and Sah 1991 on perceptions of the likelihood of sanctions and learning about them. For empirical evidence on knowledge of expected sanctions, see, for example, Wilson and Herrnstein 1985