privately induced behavior will also be socially desirable. In such a setting, the behavior of the polluter is like that of a person who purchases a good on a market(where, note, the payment for the good is made with certainty) 2.6. Fault-based liability. The conclusions about the optimal probability and magnitude of sanctions under fault-based liability are similar to those I have discussed above for strict liability, but with some differences Optimal sanctions given the probability of their imposition. In this case, as under strict liability, it is optimal for the sanction to equal the harm multiplied by the inverse of the probability of its imposition, for that will result in an expected sanction equal to harm, and thus induce individuals not to act with fault. However, unlike the outcome under strict liability, any higher sanction will also lead to desirable behavior, assuming that the fault system is error free Higher sanctions only reinforce the incentive not to act with fault, but do not discoura desirable yet possibly harmful behavior-- for such behavior is not sanctioned. Also, unlike the outcome under strict liability, risk aversion does not reduce the optimal sanction, assuming again that the fault system is error free, as parties do not bear risk, parties who do harm will be those whose acts are not faulty and thus will not be sanctioned, and others will be discouraged from committing harmful acts Yet if the fault system is not error free, the optimal magnitude of sanction could, in general, be different from the harm multiplied by the inverse of the probability; the optimal sanction could be higher or lower depending on circumstances. The presence of error also means that risk aversion becomes relevant under the fault system and thus lowers the sanction from what would otherwise be its optimal level Optimal sanctions and the optimal probability of their imposition. Here, as under strict liability, the optimal policy involves the maximal sanction and a low probability of its imposition if parties are risk neutral, for this policy conserves enforcement resources. If parties are risk averse, there is a lesser need to employ moderate sanctions than under strict liability because many of the parties who do harm are those who act without fault and thus do not bear risk However, some risk will tend to be borne by parties if there is error in the fault determination Also, it will often be the case that some parties will bear risk because of the general optimality of permitting underdeterrence in order to save enforcement costs 3. Synopsis The basic rules of liability to the state and optimal sanctions were first considered here under the assumption of certain enforcement. The main conclusions about liability rules were that both strict liability and the fault rule give rise to correct behavior, but strict liability requires less equaloe oThis will be so provided that the polluters can pay the tax. Polluters are more likely to be able to pay a tax harm than the higher sanction that would be necessary to create an expected sanction equal to harm when sanctions are applied only with a probability. For example, the firm mentioned in the paragraph above would be able to pay a tax equal to the pollution harm of $25,000, as its assets are $100,000, but the firm would not able to pay $500,000, which is the sanction necessary to create an expected sanction of $25,000 when the probability of sanctions is 5 percent 2 Under the fault system a person is liable if and only if g< h. Thus, if s=h/p, then because expected liability for fault is h. no one will act with fault
Chapter 20 – Page 12 privately induced behavior will also be socially desirable.20 In such a setting, the behavior of the polluter is like that of a person who purchases a good on a market (where, note, the payment for the good is made with certainty). 2.6. Fault-based liability. The conclusions about the optimal probability and magnitude of sanctions under fault-based liability are similar to those I have discussed above for strict liability, but with some differences. Optimal sanctions given the probability of their imposition. In this case, as under strict liability, it is optimal for the sanction to equal the harm multiplied by the inverse of the probability of its imposition, for that will result in an expected sanction equal to harm, and thus induce individuals not to act with fault.21 However, unlike the outcome under strict liability, any higher sanction will also lead to desirable behavior, assuming that the fault system is error free. Higher sanctions only reinforce the incentive not to act with fault, but do not discourage desirable yet possibly harmful behavior -- for such behavior is not sanctioned. Also, unlike the outcome under strict liability, risk aversion does not reduce the optimal sanction, assuming again that the fault system is error free, as parties do not bear risk; parties who do harm will be those whose acts are not faulty and thus will not be sanctioned, and others will be discouraged from committing harmful acts. Yet if the fault system is not error free, the optimal magnitude of sanction could, in general, be different from the harm multiplied by the inverse of the probability; the optimal sanction could be higher or lower depending on circumstances. The presence of error also means that risk aversion becomes relevant under the fault system, and thus lowers the sanction from what would otherwise be its optimal level. Optimal sanctions and the optimal probability of their imposition. Here, as under strict liability, the optimal policy involves the maximal sanction and a low probability of its imposition if parties are risk neutral, for this policy conserves enforcement resources. If parties are risk averse, there is a lesser need to employ moderate sanctions than under strict liability because many of the parties who do harm are those who act without fault and thus do not bear risk. However, some risk will tend to be borne by parties if there is error in the fault determination. Also, it will often be the case that some parties will bear risk because of the general optimality of permitting underdeterrence in order to save enforcement costs. 3. Synopsis The basic rules of liability to the state and optimal sanctions were first considered here under the assumption of certain enforcement. The main conclusions about liability rules were that both strict liability and the fault rule give rise to correct behavior, but strict liability requires less 20This will be so provided that the polluters can pay the tax. Polluters are more likely to be able to pay a tax equal to harm than the higher sanction that would be necessary to create an expected sanction equal to harm when sanctions are applied only with a probability. For example, the firm mentioned in the paragraph above would be able to pay a tax equal to the pollution harm of $25,000, as its assets are $100,000, but the firm would not able to pay $500,000, which is the sanction necessary to create an expected sanction of $25,000 when the probability of sanctions is 5 percent. 21Under the fault system a person is liable if and only if g < h. Thus, if s = h/p, then because expected liability for fault is h, no one will act with fault
knowledge on the part of the state(only knowledge of harm). It was also noted that harm-based sanctions require the state to possess less information than act-based sanctions, but that act-based sanctions have the advantage that parties' assets need not be as high for liability rules to function well. The optimal magnitude of sanctions equals harm if parties are risk neutral, and is less than harm if parties are risk averse(and uninsured against sanctions Then it was assumed that parties face sanctions only with a probability, but the probability was regarded as fixed (which is sometimes realistic). The main point here was that the magnitude of sanctions should be raised to offset the probability of escaping sanctions. In particular, the optimal sanction equals the harm multiplied by the inverse of the probability of sanctions if parties are risk neutral, and is less than this if parties are risk averse Last, it was assumed that parties face sanctions with a probability that is optimally hosen. Here a crucial point was that there is a social advantage associated with a low probability-high sanction enforcement strategy: The low probability means that the state conserves enforcement resources, and the high magnitude of sanctions prevents dilution of desired deterrence. The optimal strategy involves maximal sanctions if parties are risk neutral, but lesser sanctions if parties are risk averse A second point of stress about optimal law enforcement is that it will tend to involve underdeterrence, for the costliness of enforcement effort will make it desirable to spend less than what would be needed to achieve perfect deterrence. Therefore, the fact that an individual chooses to commit an act and suffer the consequences does not imply that the act was desirable to commit-the analogy to sanctions as prices that lead to socially desirable choices is misleading Note on the literature The basic point that sanctions should be inflated to offset the probability of escaping liability, and in particular multiplied by the inverse of the probability of escaping liability, was emphasized by Bentham([1789]1973)in his treatment of law enforcement. Becker(1968)first considered the question of the optimal social choice of the probability of enforcement and stressed the advantage of the low probability-high sanction enforcement policy. Polinsky and Shavell (1979)initially considered risk aversion in enforcement policy and showed that it implied that optimal sanctions are not maximal S, For surveys of economic literature on enforcement, see Garoupa 1997, Mookherjee 1997, and Polinsky and
Chapter 20 – Page 13 knowledge on the part of the state (only knowledge of harm). It was also noted that harm-based sanctions require the state to possess less information than act-based sanctions, but that act-based sanctions have the advantage that parties= assets need not be as high for liability rules to function well. The optimal magnitude of sanctions equals harm if parties are risk neutral, and is less than harm if parties are risk averse (and uninsured against sanctions). Then it was assumed that parties face sanctions only with a probability, but the probability was regarded as fixed (which is sometimes realistic). The main point here was that the magnitude of sanctions should be raised to offset the probability of escaping sanctions. In particular, the optimal sanction equals the harm multiplied by the inverse of the probability of sanctions if parties are risk neutral, and is less than this if parties are risk averse. Last, it was assumed that parties face sanctions with a probability that is optimally chosen. Here a crucial point was that there is a social advantage associated with a low probability-high sanction enforcement strategy: The low probability means that the state conserves enforcement resources, and the high magnitude of sanctions prevents dilution of desired deterrence. The optimal strategy involves maximal sanctions if parties are risk neutral, but lesser sanctions if parties are risk averse. A second point of stress about optimal law enforcement is that it will tend to involve underdeterrence, for the costliness of enforcement effort will make it desirable to spend less than what would be needed to achieve perfect deterrence. Therefore, the fact that an individual chooses to commit an act and suffer the consequences does not imply that the act was desirable to commit -- the analogy to sanctions as prices that lead to socially desirable choices is misleading. Note on the literature. The basic point that sanctions should be inflated to offset the probability of escaping liability, and in particular multiplied by the inverse of the probability of escaping liability, was emphasized by Bentham ([1789] 1973) in his treatment of law enforcement. Becker (1968) first considered the question of the optimal social choice of the probability of enforcement and stressed the advantage of the low probability-high sanction enforcement policy. Polinsky and Shavell (1979) initially considered risk aversion in enforcement policy and showed that it implied that optimal sanctions are not maximal.22 22For surveys of economic literature on enforcement, see Garoupa 1997, Mookherjee 1997, and Polinsky and Shavell 2000a
Chapter 21 Deterrence with nonmonetary sanctions In this chapter, I consider the deterrence of undesirable behavior by the state when the form of sanctions is nonmonetary. The important assumption that will be made about nonmonetary sanctions is that they are socially costly to impose, and the primary form of nonmonetary sanction that will be borne in mind is imprisonment. Imprisonment is clearly socially costly to employ: Prisons must be built and operated, production of individuals is forgone during their mprisonment, and individuals suffer disutility during imprisonment In the first section of the chapter, I consider enforcement assuming that nonmonetary sanctions are imposed with certainty, and in the second section, that they are imposed only with a probability determined by the enforcement effort of the state. Then, in sections three and four, I examine the question of when it is socially desirable to employ nonmonetary sanctions, rather han only monetary sanctions. In the last section, I consider types of nonmonetary sanctions apart from imprisonment The assumptions about individual behavior and social welfare that i make are similar to those of the last chapter. For simplicity, I focus on the assumption that individuals are risk neutral with respect to sanctions, but I will note other possibilities. Social welfare is assumed to equal the benefits that parties obtain from their acts, less the harm done by the acts, less the costs of enforcement, and less the costs associated with the imposition of sanctions l. Certain Enforcement with Nonmonetary Sanctions: Basic Theory of liability 1.1 Introduction. Here I initially consider strict liability and explain why it is generally disadvantageous form of liability compared to fault-based liability when sanctions are nonmonetary. (This is in fundamental contrast to the conclusions reached when sanctions are monetary, as discussed in chapter 20. )I then discuss the optimal use of fault liability 1.2 Strict liability for harm. Suppose that individuals are held strictly liable for causing harm. Then the sanction can generally be chosen so as to induce ideal behavior. If, for instance, an act causes harm of 1, 000 and there exists an imprisonment sanction creating disutility equal to 1,000, then individuals will commit the act if and only if they obtain benefits exceeding 1,000, which constitutes ideal behavior under our assumptions Although optimal behavior can therefore be induced, this socially desirable behavior will be accompanied by the imposition of socially costly sanctions on those who commit harmful acts. 2The points made in this section are developed in Shavell 1985b, 1987a 2The only reason that ideal behavior would not be achievable is that there may not exist a sanction high enough to offset the benefits to an individual. This possibility will be discussed below, but is not important to the argument to be nade in this section on strict liability, so it will not be mentioned again here forms 1 will speak of nonmonetary sanctions as imprisonment until section 5 below, where l explicitly consider other
Chapter 21 – Page 1 Chapter 21 Deterrence with Nonmonetary Sanctions In this chapter, I consider the deterrence of undesirable behavior by the state when the form of sanctions is nonmonetary. The important assumption that will be made about nonmonetary sanctions is that they are socially costly to impose, and the primary form of nonmonetary sanction that will be borne in mind is imprisonment. Imprisonment is clearly socially costly to employ: Prisons must be built and operated, production of individuals is forgone during their imprisonment, and individuals suffer disutility during imprisonment. In the first section of the chapter, I consider enforcement assuming that nonmonetary sanctions are imposed with certainty, and in the second section, that they are imposed only with a probability determined by the enforcement effort of the state. Then, in sections three and four, I examine the question of when it is socially desirable to employ nonmonetary sanctions, rather than only monetary sanctions. In the last section, I consider types of nonmonetary sanctions apart from imprisonment. The assumptions about individual behavior and social welfare that I make are similar to those of the last chapter. For simplicity, I focus on the assumption that individuals are risk neutral with respect to sanctions, but I will note other possibilities. Social welfare is assumed to equal the benefits that parties obtain from their acts, less the harm done by the acts, less the costs of enforcement, and less the costs associated with the imposition of sanctions. 1. Certain Enforcement with Nonmonetary Sanctions: Basic Theory of Liability23 1.1 Introduction. Here I initially consider strict liability and explain why it is generally a disadvantageous form of liability compared to fault-based liability when sanctions are nonmonetary. (This is in fundamental contrast to the conclusions reached when sanctions are monetary, as discussed in chapter 20.) I then discuss the optimal use of fault liability. 1.2 Strict liability for harm. Suppose that individuals are held strictly liable for causing harm. Then the sanction can generally be chosen so as to induce ideal behavior.24 If, for instance, an act causes harm of 1,000 and there exists an imprisonment sanction25 creating disutility equal to 1,000, then individuals will commit the act if and only if they obtain benefits exceeding 1,000, which constitutes ideal behavior under our assumptions. Although optimal behavior can therefore be induced, this socially desirable behavior will be accompanied by the imposition of socially costly sanctions on those who commit harmful acts. 23The points made in this section are developed in Shavell 1985b, 1987a. 24The only reason that ideal behavior would not be achievable is that there may not exist a sanction high enough to offset the benefits to an individual. This possibility will be discussed below, but is not important to the argument to be made in this section on strict liability, so it will not be mentioned again here. 25I will speak of nonmonetary sanctions as imprisonment until section 5 below, where I explicitly consider other forms of nonmonetary sanctions
If the social cost of imposing the sanction that creates disutility of 1, 000 is, for instance, 1, 500 (composed of the disutility of 1, 000 suffered by a person who is sanctioned and the costs of operating the prisons), then each time a person commits the act(because the person obtains high benefits from so doing), social costs of 1, 500 as well as the harm of 1,000 are generated. This makes strict liability a socially expensive way to induce behavior that would otherwise be desirable 2 Note too that because under strict liability social costs of imposing sanctions are incurre magnitude that leads to ideal behavior; it will be such as to reduce the social costs of imposi lg a whenever individuals commit harmful acts, the optimal magnitude of the sanction will not be the sanctions assume Comment: comparison to the case under monetary sanctions. When sanctions are ed to be monetary and costless to impose, as in the last chapter, optimal behavor can be induced at no social cost by setting the sanction equal to the harm. Here, when sanctions are nonmonetary, the situation is altogether different, due to the cost of actually imposing the sanction. For example, consider a harmful act such as polluting. If sanctions are monetary, then strict liability induces optimal behavior at no social cost, for whenever an individual pollutes (because the benefits from doing so are higher than harm), he merely pays for harm, which causes no social cost, as his payment represents merely a transfer of command over resources But if an individual is jailed for having polluted when the disutility of jail equals the harm from pollution, then although his polluting behavior is desirable(by assumption his benefits from so doing are higher than the harm generated), this form of sanction absorbs social resources harm if his act was undesirable, but is not held liable if his act was desirable. hence, if the or 1.3 Fault-based liability for harm. Under this rule, a person is subject to liability for desirable behavior will not be discouraged because it will not result in punishment. Ao ereas sanction for causing harm is sufficiently high, undesirable behavior will be deterred, whe individual who would obtain a benefit of less than 1.000 from an act that causes harm of 1.000 To amplify, let g be the gain from committing an act that causes certain harm of h, let fg)be the probability density of g in the population, let s be the sanction, let d(s) be the disutility of s to individuals, and let ks be the additional social cost of imposing the sanction s, where k>0. Under strict liability, ideal behavior--commission of the act if an only if g is at least h-can be induced if s=h. If so, social welfare equals W=l(g!h!仂h+h)g)kg where m is the maximum gain from committing the act. The ideal level of social welfare is not achieved because of the term /(h+ kh), which are the total costs associated with imposition of punishment. Using the notation of the previous note, the optimal magnitude of the sanction is the s that maximizes w =I(g/h/(s+ks))f(gdg ng the derivative of w with respect to s equal to 0 gives the first-order condition for the optimum, (h+ks)f(s)=(1 D)(1+k), where F is the cumulative distribution off. The interpretation of this condition is that the marginal net benefit from deterrence equals the marginal cost. From this condition, it is apparent that the optimal s could be above h(reflecting the fact that the harmful act involves social costs of not only h, but also s+ ks, so exceeding h) or below h(reflecting the fact that social costs of punishment can be reduced by lowering s). The solution to this problem is discussed in Polinsky and Shavell 1984 and Kaplow 1990
Chapter 21 – Page 2 If the social cost of imposing the sanction that creates disutility of 1,000 is, for instance, 1,500 (composed of the disutility of 1,000 suffered by a person who is sanctioned and the costs of operating the prisons), then each time a person commits the act (because the person obtains high benefits from so doing), social costs of 1,500 as well as the harm of 1,000 are generated. This makes strict liability a socially expensive way to induce behavior that would otherwise be desirable.26 Note too that because under strict liability social costs of imposing sanctions are incurred whenever individuals commit harmful acts, the optimal magnitude of the sanction will not be the magnitude that leads to ideal behavior; it will be such as to reduce the social costs of imposing sanctions.27 Comment: comparison to the case under monetary sanctions. When sanctions are assumed to be monetary and costless to impose, as in the last chapter, optimal behavor can be induced at no social cost by setting the sanction equal to the harm. Here, when sanctions are nonmonetary, the situation is altogether different, due to the cost of actually imposing the sanction. For example, consider a harmful act such as polluting. If sanctions are monetary, then strict liability induces optimal behavior at no social cost, for whenever an individual pollutes (because the benefits from doing so are higher than harm), he merely pays for harm, which causes no social cost, as his payment represents merely a transfer of command over resources. But if an individual is jailed for having polluted when the disutility of jail equals the harm from pollution, then although his polluting behavior is desirable (by assumption his benefits from so doing are higher than the harm generated), this form of sanction absorbs social resources. 1.3 Fault-based liability for harm. Under this rule, a person is subject to liability for harm if his act was undesirable, but is not held liable if his act was desirable. Hence, if the sanction for causing harm is sufficiently high, undesirable behavior will be deterred, whereas desirable behavior will not be discouraged because it will not result in punishment. An individual who would obtain a benefit of less than 1,000 from an act that causes harm of 1,000 -- 26To amplify, let g be the gain from committing an act that causes certain harm of h, let f(g) be the probability density of g in the population, let s be the sanction, let d(s) be the disutility of s to individuals, and let ks be the additional social cost of imposing the sanction s, where k > 0. Under strict liability, ideal behavior -- commission of the act if and only if g is at least h -- can be induced if s = h. If so, social welfare equals m W = I(g ! h! (h + kh)f(g)dg, h where m is the maximum gain from committing the act. The ideal level of social welfare is not achieved because of the term !(h + kh), which are the total costs associated with imposition of punishment. 27Using the notation of the previous note, the optimal magnitude of the sanction is the s that maximizes m W = I(g ! h ! (s + ks))f(g)dg. s Setting the derivative of W with respect to s equal to 0 gives the first-order condition for the optimum, (h + ks)f(s) = (1 ! F(s))(1 + k), where F is the cumulative distribution of f. The interpretation of this condition is that the marginal net benefit from deterrence equals the marginal cost. From this condition, it is apparent that the optimal s could be above h (reflecting the fact that the harmful act involves social costs of not only h, but also s + ks, so exceeding h) or below h (reflecting the fact that social costs of punishment can be reduced by lowering s). The solution to this problem is discussed in Polinsky and Shavell 1984 and Kaplow 1990
and thus for whom the act would be socially undesirable -- will not commit the act if the sanction is sufficiently high; but an individual who would obtain a benefit exceeding 1,000 from the act and thus for whom the act would be socially desirable - would commit the act because he would not be held at fault and punished for so doing. Thus, ideal behavior is achieved under fault-based liability without the actual imposition of socially costly punishment a corollary point is that the optimal magnitude of the sanction for a socially undesirable cannot be deterred from committing an undesirable act because his benefit exceeds even the 5 a act is any sanction sufficient to deter. It does not matter how high the sanction is, for because the threat of sanctions deters, sanctions are never applied, and hence higher sanctions do not result i higl An important factor should be added: There is sometimes a possibility that an individu maximal sanction(such as life imprisonment). In this situation, it is optimal not to impose any sanction on the individual even though his act is socially undesirable. For by hypothesis, all that imposing a sanction would create is a social cost; it would not accomplish deterrence of the individual, for that is by hypothesis impossible. For instance, suppose that the highest sanction that can be imposed on a person is 100(because, say, imprisonment would not create such great harm of 1,000. Then, although his act is undesirable, it is optimal not to punish him. 28 Q\sing disutility for him), and that he would obtain a benefit of 200 from committing the act The conclusion is that, under optimal fault-based liability, sanctions are never imposed They are not imposed if individuals act desirably, and their use is threatened when and only when that threat will successfully deter undesirable behavior. In sum, ideal behavior is achieved except when deterrence is impossible, and it is achieved without the bearing of costs of actually imposing sanctions o This conclusion about optimally applied fault-based liability will be important to bear in mind in what follows. It should be emphasized that the point that sanctions are never imposed depends on the implicit presumption that the information of the social authority is perfect. In particular, the social authority has to know the benefits that individuals obtain not only to be able to determine which acts are desirable and which not but also to be able to forecast when imposition of a sanction would deter and when not In the previous chapter on monetary sanctions, I did not emphasize the point analogous to the one here-that deterrence of undesirable acts might be impossible because the assets of a person might be limited. However, in the case of monetary sanctions, there is no advantage of relieving an impossible-to-deter person of liability, for the assumption is that imposing a monetary sanction does not involve a social cost. That is why the situation where individuals cannot be deterred was not a focus of discussion where sanctions are monetary, but it is significant here Let me be precise about fault-based liability as discussed in this section. Under such liability, any act that is desirable--such thatg Sh--is not sanctioned, and hence individuals commit such acts and are not punished. If an act is undesirable-- such that g h-then, if there is an s exceeding g for the individual, he will be sanctioned for committing the act with such an s, and thus will be deterred But if there does not exist an s for the person such that s >g, then he cannot be deterred, so that it is optimal to set s =0 for that person(otherwise he will commit the act and social costs will be h+ ks rather than just h). In sum, the formula for the optimal sanction under the fault rule, is as follows. Let g, h, and m harm, and maximal sanction that can be imposed on an individual. Then the optimal sanction s= s(g, h, m) parent: if g Sh, then s=0; if g h and m <g, then S=0; if g h and m sg, then s Sg. Therefore, all individuals whose acts would be desirable commit them all those who can be deterred from committing undesirable acts are deterred. and no one actually suffers punishment
Chapter 21 – Page 3 and thus for whom the act would be socially undesirable -- will not commit the act if the sanction is sufficiently high; but an individual who would obtain a benefit exceeding 1,000 from the act -- and thus for whom the act would be socially desirable -- would commit the act because he would not be held at fault and punished for so doing. Thus, ideal behavior is achieved under fault-based liability without the actual imposition of socially costly punishment. A corollary point is that the optimal magnitude of the sanction for a socially undesirable act is any sanction sufficient to deter. It does not matter how high the sanction is, for because the threat of sanctions deters, sanctions are never applied, and hence higher sanctions do not result in higher social costs. An important factor should be added: There is sometimes a possibility that an individual cannot be deterred from committing an undesirable act because his benefit exceeds even the maximal sanction (such as life imprisonment). In this situation, it is optimal not to impose any sanction on the individual even though his act is socially undesirable. For by hypothesis, all that imposing a sanction would create is a social cost; it would not accomplish deterrence of the individual, for that is by hypothesis impossible. For instance, suppose that the highest sanction that can be imposed on a person is 100 (because, say, imprisonment would not create such great disutility for him), and that he would obtain a benefit of 200 from committing the act causing harm of 1,000. Then, although his act is undesirable, it is optimal not to punish him.28 The conclusion is that, under optimal fault-based liability, sanctions are never imposed. They are not imposed if individuals act desirably, and their use is threatened when and only when that threat will successfully deter undesirable behavior. In sum, ideal behavior is achieved, except when deterrence is impossible, and it is achieved without the bearing of costs of actually imposing sanctions.29 This conclusion about optimally applied fault-based liability will be important to bear in mind in what follows. It should be emphasized that the point that sanctions are never imposed depends on the implicit presumption that the information of the social authority is perfect. In particular, the social authority has to know the benefits that individuals obtain not only to be able to determine which acts are desirable and which not, but also to be able to forecast when imposition of a sanction would deter and when not. 28In the previous chapter on monetary sanctions, I did not emphasize the point analogous to the one here -- that deterrence of undesirable acts might be impossible because the assets of a person might be limited. However, in the case of monetary sanctions, there is no advantage of relieving an impossible-to-deter person of liability, for the assumption is that imposing a monetary sanction does not involve a social cost. That is why the situation where individuals cannot be deterred was not a focus of discussion where sanctions are monetary, but it is significant here. 29Let me be precise about fault-based liability as discussed in this section. Under such liability, any act that is desirable -- such that g $ h -- is not sanctioned, and hence individuals commit such acts and are not punished. If an act is undesirable -- such that g < h -- then, if there is an s exceeding g for the individual, he will be sanctioned for committing the act with such an s, and thus will be deterred. But if there does not exist an s for the person such that s > g, then he cannot be deterred, so that it is optimal to set s = 0 for that person (otherwise he will commit the act and social costs will be h + ks rather than just h). In sum, the formula for the optimal sanction under the fault rule, is as follows. Let g, h, and m be the gain, harm, and maximal sanction that can be imposed on an individual. Then the optimal sanction s = s(g,h,m) is apparent: if g $ h, then s = 0; if g < h and m < g, then s = 0; if g < h and m $ g, then s $ g. Therefore, all individuals whose acts would be desirable commit them, all those who can be deterred from committing undesirable acts are deterred, and no one actually suffers punishment