magnitude of sanctions, but only a distribution of them. In many contexts, however, sanctions are stipulated and well known in advance (d) Level of wealth of a party. The level of wealth of a party imposes a ceiling on the maximum sanction. Thus, the lower is the probability of sanctions, the lower is the maximum expected sanction, so that it might be impossible to deter a person from committing an act even if his benefit from it is quite modest if the probability of sanctions is small. For example consider a risk-neutral individual with wealth of $5.000 ho would obtain a benefit of $100 from an act. It would be impossible to deter this person from committing the act if the likelihood of sanctions is 1 percent, for then the highest expected sanction that he could face is 1% HS5,000=$50 The level of wealth of a party not only determines the maximum sanction that can be imposed on a party, it also may influence how he reacts to the risk of sanctions generally, for the degree of risk aversion is usually thought to depend on wealth. The more wealthy a party is, the less averse to risk, and thus the less he tends to be deterred by a given probability and magnitude of sanction 2.3 Optimal sanctions when the probability of their imposition is a given. Let me now address the question about the socially best magnitude of sanction, taking the probability of imposition of sanctions as a given. The assumption that the probability of sanctions is taken as given is relevant in many contexts, as those who decide on the magnitude of sanctions may not have control over enforcement effort. For example, a judge or administrative officer who sets the fine for a regulatory infraction may take the enforcement budget and its allocation as a given Further, in many areas of enforcement, the probability of sanctions for a particular type of infraction is set by overall policy and is not independently variable(see section 5 of chapter 22) In any case, the problem of determining the optimal sanction given the probability of sanctions is a subpart in a theoretical sense of the problem of finding the optimal probability and sanction for to find the optimal probability, one must in general find the optimal sanction for each probability If parties are risk neutral, optimal behavior will be induced if the expected sanction equals the expected harm, for then a party will compare his benefit to the expected harm Consequently, the sanction, when imposed, must exceed harm; in particular, the sanction is governed by a fundamental probability-related multiplier--the sanction must equal the harm multiplied by the inverse of the probability of its imposition. Thus, if the harm is 100 and the probability of sanctions is 50 percent, the sanction should be multiplied by 1/5=2, so the sanction should equal 200(and thus the expected sanction equals 100); if the probability of sanctions is 25 percent, the sanction should be multiplied by 1/25=4, so the sanction should equal 400(again the expected sanction equals 100); and so forth. In this way, parties will behave optimally; the situation will be as if they faced liability equal to the harm I will comment generally on the actual effect of sanctions(both monetary and nonmonetary)on deterrence in section 2.3 of chapter 21 If harm is h and the probability of proper imposition of the sanction is p, the magnitude of the sanction should be h multiplied by 1/p, so that the expected sanction is p(h/p)=h, resulting in optimal behavior under strict liability(and fault liability)
Chapter 20 – Page 7 magnitude of sanctions, but only a distribution of them. In many contexts, however, sanctions are stipulated and well known in advance. (d) Level of wealth of a party. The level of wealth of a party imposes a ceiling on the maximum sanction. Thus, the lower is the probability of sanctions, the lower is the maximum expected sanction, so that it might be impossible to deter a person from committing an act even if his benefit from it is quite modest if the probability of sanctions is small. For example, consider a risk-neutral individual with wealth of $5,000 who would obtain a benefit of $100 from an act. It would be impossible to deter this person from committing the act if the likelihood of sanctions is 1 percent, for then the highest expected sanction that he could face is 1% H $5,000 = $50. The level of wealth of a party not only determines the maximum sanction that can be imposed on a party, it also may influence how he reacts to the risk of sanctions generally, for the degree of risk aversion is usually thought to depend on wealth. The more wealthy a party is, the less averse to risk, and thus the less he tends to be deterred by a given probability and magnitude of sanction.11 2.3 Optimal sanctions when the probability of their imposition is a given. Let me now address the question about the socially best magnitude of sanction, taking the probability of imposition of sanctions as a given. The assumption that the probability of sanctions is taken as given is relevant in many contexts, as those who decide on the magnitude of sanctions may not have control over enforcement effort. For example, a judge or administrative officer who sets the fine for a regulatory infraction may take the enforcement budget and its allocation as a given. Further, in many areas of enforcement, the probability of sanctions for a particular type of infraction is set by overall policy and is not independently variable (see section 5 of chapter 22). In any case, the problem of determining the optimal sanction given the probability of sanctions is a subpart in a theoretical sense of the problem of finding the optimal probability and sanction, for to find the optimal probability, one must in general find the optimal sanction for each probability. If parties are risk neutral, optimal behavior will be induced if the expected sanction equals the expected harm, for then a party will compare his benefit to the expected harm. Consequently, the sanction, when imposed, must exceed harm; in particular, the sanction is governed by a fundamental probability-related multiplier -- the sanction must equal the harm multiplied by the inverse of the probability of its imposition.12 Thus, if the harm is 100 and the probability of sanctions is 50 percent, the sanction should be multiplied by 1/.5 = 2, so the sanction should equal 200 (and thus the expected sanction equals 100); if the probability of sanctions is 25 percent, the sanction should be multiplied by 1/.25 = 4, so the sanction should equal 400 (again the expected sanction equals 100); and so forth. In this way, parties will behave optimally; the situation will be as if they faced liability equal to the harm. 11I will comment generally on the actual effect of sanctions (both monetary and nonmonetary) on deterrence in section 2.3 of chapter 21. 12If harm is h and the probability of proper imposition of the sanction is p, the magnitude of the sanction should be h multiplied by 1/p, so that the expected sanction is p(h/p) = h, resulting in optimal behavior under strict liability (and fault liability)
Risk-averse case. If parties are risk averse, the optimal sanction tends to be lower than it when parties are risk neutral. The reasons are essentially as indicated above in section 1.2 First, because parties for whom the act is socially desirable will often commit it, they will bear risk, which is socially undesirable in itself. Second, if the sanction equals its optimal level in the risk-neutral case. risk-averse individuals will tend to be overdeterred. Lowering the sanction ameliorates both of these problems. 3 Comments.(a) Practical ability to impose high sanctions reflecting the probability of their imposition. The theme of this section is that sanctions should be scaled upward to reflect the likelihood of escaping liability. There are several problems, however, that may be faced in actually imposing such sanctions. First, there may be resistance to inflating sanctions on grounds of fairness; the notion that the magnitude of sanctions should be proportional to the gravity and moral quality of an act is a widely held notion of fairness, and this notion does not accord weight to the likelihood of escape from sanctions. For example, the fair punishment for an act such as littering might be thought quite modest(perhaps no more than $10 or $20) because an act of littering is not considered to be seriously harmful, even though the sanction called for by the principles discussed here would be substantial(such as $200) if the probability of catching a litterer is smalL. 14 a second problem is that there may be significant difficulty in determining the probability of sanctions. For example, if a restaurant violated an ordinance about safety in its kitchen, the sanctioning authority would have to take into account such factors as the probability of inspection of the restaurant, the probability that employees would make reports to authorities themselves, the probability that customers would notice something wrong, and the like. These determinations are often difficult and lend themselves to dispute, although, as with any type of determination, they can be performed more cheaply if demands for accuracy are reduced (b) Effect of wealth. It should be borne in mind that the wealth of the party may be too low(consider especially individuals with essentially no savings, or thinly capitalized firms) for the party to be induced to act optimally. If the likelihood of being caught is low and the magnitude of the harm high, it may be impossible to induce the party to act optimally, leading to a significant problem of underdeterrence 2.4 Optimal sanctions when the probability of their imposition is also optimally determined. One of the basic insights that apply to optimal law enforcement when the state high magnitude sanction policy is socially advantageous. The reasons are two-fold: A social chooses both the probability of imposing sanctions and their magnitude is that a low probability savings in enforcement effort can be achieved by allowing sanctions to be imposed only with a low probability; and sanctions can be raised to avoid dilution of deterrence from the low probability of sanctions. This strategy for conserving enforcement resources without sacrificing This can be shown along the lines sketched in note 3. Issues of faimess in sanctions are discussed in chapter 27. On fairness and the economic theory of law enforcement, see Polinsky and Shavell 2000a and Kaplow and Shavell 2002b, chapter 6 Note that that the rise in the sanction does not increase enforcement expenditures this is an aspect of the maintained assumption of this chapter that the imposition of monetary sanctions does not involve resources costs
Chapter 20 – Page 8 Risk-averse case. If parties are risk averse, the optimal sanction tends to be lower than it is when parties are risk neutral. The reasons are essentially as indicated above in section 1.2. First, because parties for whom the act is socially desirable will often commit it, they will bear risk, which is socially undesirable in itself. Second, if the sanction equals its optimal level in the risk-neutral case, risk-averse individuals will tend to be overdeterred. Lowering the sanction ameliorates both of these problems.13 Comments. (a) Practical ability to impose high sanctions reflecting the probability of their imposition. The theme of this section is that sanctions should be scaled upward to reflect the likelihood of escaping liability. There are several problems, however, that may be faced in actually imposing such sanctions. First, there may be resistance to inflating sanctions on grounds of fairness; the notion that the magnitude of sanctions should be proportional to the gravity and moral quality of an act is a widely held notion of fairness, and this notion does not accord weight to the likelihood of escape from sanctions. For example, the fair punishment for an act such as littering might be thought quite modest (perhaps no more than $10 or $20) because an act of littering is not considered to be seriously harmful, even though the sanction called for by the principles discussed here would be substantial (such as $200) if the probability of catching a litterer is small.14 A second problem is that there may be significant difficulty in determining the probability of sanctions. For example, if a restaurant violated an ordinance about safety in its kitchen, the sanctioning authority would have to take into account such factors as the probability of inspection of the restaurant, the probability that employees would make reports to authorities themselves, the probability that customers would notice something wrong, and the like. These determinations are often difficult and lend themselves to dispute, although, as with any type of determination, they can be performed more cheaply if demands for accuracy are reduced. (b) Effect of wealth. It should be borne in mind that the wealth of the party may be too low (consider especially individuals with essentially no savings, or thinly capitalized firms) for the party to be induced to act optimally. If the likelihood of being caught is low and the magnitude of the harm high, it may be impossible to induce the party to act optimally, leading to a significant problem of underdeterrence. 2.4 Optimal sanctions when the probability of their imposition is also optimally determined. One of the basic insights that apply to optimal law enforcement when the state chooses both the probability of imposing sanctions and their magnitude is that a low probabilityhigh magnitude sanction policy is socially advantageous. The reasons are two-fold: A social savings in enforcement effort can be achieved by allowing sanctions to be imposed only with a low probability; and sanctions can be raised to avoid dilution of deterrence from the low probability of sanctions.15 This strategy for conserving enforcement resources without sacrificing 13This can be shown along the lines sketched in note 3. 14Issues of fairness in sanctions are discussed in chapter 27. On fairness and the economic theory of law enforcement, see Polinsky and Shavell 2000a and Kaplow and Shavell 2002b, chapter 6. 15Note that that the rise in the sanction does not increase enforcement expenditures; this is an aspect of the maintained assumption of this chapter that the imposition of monetary sanctions does not involve resources costs
deterrence has the apparent implication that enforcement effort and probabilities of sanctions should be very low, but be accor ed by very high sanctions. Such a draconian conclusion will shortly be seen to hold if parties are risk neutral. But this strong conclusion does not hold if parties are risk averse(or if any of a variety of other factors are relevant, as will be noted later), even though the conclusion contains an important element of the truth about optimal policy under all circumstances Suppose that parties are risk neutral In this case, it is optimal for the fundamental strategy for saving enforcement resources just mentioned to be employed to the fullest extent meaning that the sanction should be as high as possible, equal to the entire wealth of an individual. To understand why, suppose that the sanction is less than maximal. Then the sanction can always be raised and the probability lowered proportionally, so that deterrence is not altered; but as the lower probability will mean a savings in enforcement costs, the change must raise social welfare. For example, suppose that the wealth of individuals is $10,000, the likelihood of $100. Now if the sanction is raised to $2, 000 and the probability of sanctions is lowered to s o sanctions is 10 percent, and the sanction is $1,000. Thus, in particular, the expected sanction is percent, the expected sanction and deterrence will be unchanged, and equal $100, but enforcement expenses will be lowered. Indeed, if the sanction is raised to the maximum, $10,000 and the probability of sanctions is reduced to 1 percent, deterrence will be unchanged and more enforcement expenses will be saved. The conclusion, therefore, is that sanctions should be raised until they are maximal best probability is such that the expected sanction equals the harm. In the example under at the What is the optimal probability of imposing the sanction? It might at first seem th discussion, this would mean that if the harm from the act is $100, the expected sanction should be the same, so that the probability p should satisfy p H $10,000=$100, implying that the best p is 1 percent. But in fact the optimal probability should be lower than 1 percent. In general, the optimal expected sanction is less than the harm. The reason for this conclusion, another basic insight about optimal enforcement when the probability of sanctions is chosen along with the magnitude of sanctions, is essentially that, because of the cost of enforcement, it is better to compromise and not achieve perfect behavior, but rather to permit a degree of underdeterrence in order to save enforcement resources. If the cost of enforcement is significant, it may be best to To establish this conclusion formally, observe that social welfare in the risk-neutral case, the benefits obtained from committing acts less harm and enforcement costs, is given by w=I(g/ h)fg)dg/ c(p), where dp) is the enforcement cost of setting the probability equal to p (It is assumed here for simplicity that an act causes harm with certainty, rather than only with a probability, and this will also be assumed in subsequent notes. ) Clearly, if s is not maximal, s can be raised to the income y of individuals, and p can be lowered to p(s/y), so that the expected sanction Ip(s/y)lv remains ps. Hence, the integral in W does not change but c(p) falls, so that W rises, meaning that raising s to y and lowering p increases welfare; thus the optimal sanction must be maximal. Note that this conclusion that the optin nction is maximal does not depend on the magnitude of the harm. Becker 1968 first suggested the conclusion(although much of his analysis presumes the sanction is not maximal)and it is noted explicitly in Carr-Hill and Stern 1979 and Polinsky and Shavell 1979 To amplify the point that some degree of underenforcement is desirable, suppose in the example that the expected sanction is $99 instead of S100--which would be the case if the probability is. 99 percent instead of I percent
Chapter 20 – Page 9 deterrence has the apparent implication that enforcement effort and probabilities of sanctions should be very low, but be accompanied by very high sanctions. Such a draconian conclusion will shortly be seen to hold if parties are risk neutral. But this strong conclusion does not hold if parties are risk averse (or if any of a variety of other factors are relevant, as will be noted later), even though the conclusion contains an important element of the truth about optimal policy under all circumstances. Suppose that parties are risk neutral. In this case, it is optimal for the fundamental strategy for saving enforcement resources just mentioned to be employed to the fullest extent, meaning that the sanction should be as high as possible, equal to the entire wealth of an individual. To understand why, suppose that the sanction is less than maximal. Then the sanction can always be raised and the probability lowered proportionally, so that deterrence is not altered; but as the lower probability will mean a savings in enforcement costs, the change must raise social welfare. For example, suppose that the wealth of individuals is $10,000, the likelihood of sanctions is 10 percent, and the sanction is $1,000. Thus, in particular, the expected sanction is $100. Now if the sanction is raised to $2,000 and the probability of sanctions is lowered to 5 percent, the expected sanction and deterrence will be unchanged, and equal $100, but enforcement expenses will be lowered. Indeed, if the sanction is raised to the maximum, $10,000 and the probability of sanctions is reduced to 1 percent, deterrence will be unchanged and more enforcement expenses will be saved. The conclusion, therefore, is that sanctions should be raised until they are maximal.16 What is the optimal probability of imposing the sanction? It might at first seem that the best probability is such that the expected sanction equals the harm. In the example under discussion, this would mean that if the harm from the act is $100, the expected sanction should be the same, so that the probability p should satisfy p H $10,000 = $100, implying that the best p is 1 percent. But in fact the optimal probability should be lower than 1 percent. In general, the optimal expected sanction is less than the harm. The reason for this conclusion, another basic insight about optimal enforcement when the probability of sanctions is chosen along with the magnitude of sanctions, is essentially that, because of the cost of enforcement, it is better to compromise and not achieve perfect behavior, but rather to permit a degree of underdeterrence in order to save enforcement resources.17 If the cost of enforcement is significant, it may be best to 16To establish this conclusion formally, observe that social welfare in the risk-neutral case, the benefits obtained from committing acts less harm and enforcement costs, is given by 4 W = I(g ! h)f(g)dg ! c(p), ps where c(p) is the enforcement cost of setting the probability equal to p. (It is assumed here for simplicity that an act causes harm with certainty, rather than only with a probability, and this will also be assumed in subsequent notes.) Clearly, if s is not maximal, s can be raised to the income y of individuals, and p can be lowered to p(s/y), so that the expected sanction [p(s/y)]y remains ps. Hence, the integral in W does not change but c(p) falls, so that W rises, meaning that raising s to y and lowering p increases welfare; thus the optimal sanction must be maximal. Note that this conclusion that the optimal sanction is maximal does not depend on the magnitude of the harm. Becker 1968 first suggested the conclusion (although much of his analysis presumes the sanction is not maximal) and it is noted explicitly in Carr-Hill and Stern 1979 and Polinsky and Shavell 1979. 17To amplify the point that some degree of underenforcement is desirable, suppose in the example that the expected sanction is $99 instead of $100 -- which would be the case if the probability is .99 percent instead of 1 percent
allow substantial underdeterrence to reduce costs of enforcement Indeed, because of the costs of enforcement, it is possible that it will be optimal for there not to be any law enforcement, for society to countenance harm in order to save the costs of law enforcement-- the game of enforcement may not be worth the candle. This can be demonstrated to be true, other things being equal, if the harm from the act is below a certain threshold Risk-averse case. In this case, the conclusion differs from that when parties are risk neutral. The main difference is that the optimal sanction is not maximal, in general, and may be much lower than maximal. For instance, in the example discussed above, the optimal sanction might be $300 rather than $10,000, the level of a person's wealth. The reason, roughly, is that the risk aversion of individuals means that their bearing the risk of sanctions constitutes a form of social cost. The optimal level of the sanction will depend, among other things, on the degree of risk aversion of parties; the more risk averse the parties, the lower the optimal sanction will tend With regard to the optimal probability, two points should be made. First, the optimal probability might be higher than in the risk-neutral case: If the sanction is, in effect, constrained Then the individuals who would be undesirably led to commit the harmful act would be those obtaining benefits of between $99 and $100 and doing harm of$100. Thus, they would be contributing only slightly to net social harm(harm minus benefit obtained)-for they would cause net social harm of less than SI each. On the other hand, the social saving in enforcement expenses from reducing the enforcement probability is proportional to the probability reduction. For this reason, it is always desirable for the probability to be lowered some amount below l percent, so that the expected sanction is below $100. Formally, differentiate W in note 16 with respect to p and set this equal to 0, yielding s(h ps f(ps)=cNp) Because the right side is positive, h>ps must hold (whether or not s is optimal, equal to y) Another reason that the optimal sanction may not be maximal is that higher sanctions may induce violators to spend additional resources to avoid punishment; see Malik 1990. Further reasons will be given in later Further insight into the risk-averse case can be gained by considering why, precisely, the argument applying in the risk-neutral case for optimality of maximal sanctions fails when parties are not risk-neutral Consider any situation in some reduction of the probability to a level p that will leave the nisk Even thor '$1,000 and a probability of imposition of averse individuals indifferent between bearing the $10,000 sanction with probability p and instead bearing the $1, 000 sanction with probability 10 percent. But, due to risk aversion, this p will be less than l percent, perhaps it will be. I percent. At the new p and the $10,000 maximal sanction, deterrence will, by construction, be preserved Parties who commit the harmful act will be just as well off as they were when they faced the $1,000 sanction with probability 10 percent, and enforcement resources will have been saved(indee even more resources will have been saved than in the risk-neutral case, when p falls only to l percent ). So why will not social welfare necessarily have been raised? The answer is that the state's revenue from sanctions will have fallen, as the expected sanction will be lower(such as. 1%H $10,000=$10 for each person who commits the act, instead of $100) decline in revenue might offset the savings in enforcement costs, and, if so, will result in higher taxes and thus tend to The formal problem in the risk-averse case is similar to that sketched in note 3, namely, to m w= F(g*F(, s))U0)+I[(li p)U +g)+pUv+g! s)lfg)dg 产(y,S) over s and p, where g*(v,s)is defined by(1 I P)U(+8)+PU(+8!s)=U0). A\so, mis problem is solved in !(1!F(g*)(h!ps)! dp), where is the initial income of each person, so the second term is taxes. Essentially Polinsky and Shavell 1979. For further analysis, see Kaplow 1992
Chapter 20 – Page 10 allow substantial underdeterrence to reduce costs of enforcement. Indeed, because of the costs of enforcement, it is possible that it will be optimal for there not to be any law enforcement, for society to countenance harm in order to save the costs of law enforcement -- the game of enforcement may not be worth the candle. This can be demonstrated to be true, other things being equal, if the harm from the act is below a certain threshold. Risk-averse case. In this case, the conclusion differs from that when parties are risk neutral. The main difference is that the optimal sanction is not maximal, in general, and may be much lower than maximal. For instance, in the example discussed above, the optimal sanction might be $300 rather than $10,000, the level of a person=s wealth. The reason, roughly, is that the risk aversion of individuals means that their bearing the risk of sanctions constitutes a form of social cost.18 The optimal level of the sanction will depend, among other things, on the degree of risk aversion of parties; the more risk averse the parties, the lower the optimal sanction will tend to be.19 With regard to the optimal probability, two points should be made. First, the optimal probability might be higher than in the risk-neutral case: If the sanction is, in effect, constrained Then the individuals who would be undesirably led to commit the harmful act would be those obtaining benefits of between $99 and $100 and doing harm of $100. Thus, they would be contributing only slightly to net social harm (harm minus benefit obtained) -- for they would cause net social harm of less than $1 each. On the other hand, the social saving in enforcement expenses from reducing the enforcement probability is proportional to the probability reduction. For this reason, it is always desirable for the probability to be lowered some amount below 1 percent, so that the expected sanction is below $100. Formally, differentiate W in note 16 with respect to p and set this equal to 0, yielding s(h ! ps)f(ps) = cN(p). Because the right side is positive, h > ps must hold (whether or not s is optimal, equal to y). 18Another reason that the optimal sanction may not be maximal is that higher sanctions may induce violators to spend additional resources to avoid punishment; see Malik 1990. Further reasons will be given in later chapters. 19Further insight into the risk-averse case can be gained by considering why, precisely, the argument applying in the risk-neutral case for optimality of maximal sanctions fails when parties are not risk-neutral. Consider any situation in which the sanction is less than maximal -- consider for instance a sanction of $1,000 and a probability of imposition of sanctions of 10 percent. Now raise the sanction to wealth, $10,000. Even though individuals are risk averse, there will be some reduction of the probability to a level p that will leave the risk-averse individuals indifferent between bearing the $10,000 sanction with probability p and instead bearing the $1,000 sanction with probability 10 percent. But, due to risk aversion, this p will be less than 1 percent, perhaps it will be .1 percent. At the new p and the $10,000 maximal sanction, deterrence will, by construction, be preserved: Parties who commit the harmful act will be just as well off as they were when they faced the $1,000 sanction with probability 10 percent, and enforcement resources will have been saved (indeed, even more resources will have been saved than in the risk-neutral case, when p falls only to 1 percent). So why will not social welfare necessarily have been raised? The answer is that the state=s revenue from sanctions will have fallen, as the expected sanction will be lower (such as .1% H $10,000 = $10 for each person who commits the act, instead of $100). This decline in revenue might offset the savings in enforcement costs, and, if so, will result in higher taxes and thus tend to lead to lower welfare. The formal problem in the risk-averse case is similar to that sketched in note 3, namely, to maximize social welfare 4 W = F(g*(y, s))U(y) + I[(1 ! p)U(y + g) + pU(y + g ! s)]f(g)dg. g*(y, s) over s and p, where g*(y,s) is defined by (1 ! p)U(y + g) + pU(y + g ! s) = U(y). Also, y = z ! (1 ! F(g*))(h ! ps) ! c(p), where z is the initial income of each person, so the second term is taxes. Essentially this problem is solved in Polinsky and Shavell 1979. For further analysis, see Kaplow 1992
not to be high due to the risk aversion of individuals, say to be in the range of $300, then the only way to achieve a particular level of deterrence is through use of greater enforcement than would be needed were the sanction maximal. Second, the optimal probability could also be lower than in the risk-neutral case: If the sanction must be fairly low due to risk aversion, the effectiveness of raising the probability is reduced, leading to the possibility that the optimal probability could be lower than in the risk-neutral case, or that it might not be worth controlling the activity at all, even though it would be in the risk-neutral case A further point is worth mentioning. The reason that has been discussed why some risk averse parties bear risk is that it may turn out to be desirable for them to commit harmful acts and they will do so. However, as we know, there are other reasons for risk-bearing--and thus for sanctions to be less than maximal --notably, legal errors that result in the imposition of innocent partie 2.5 Comment on the misleading notion that sanctions are analogous to market prices-- that willingness to face sanctions for harmful acts implies that committing such acts is socially correct. It is commonly stated that if a party is willing to pay a sanction, or face an expected sanction, then it is not socially incorrect, indeed it is socially desirable, for him to commit an act, such as to pollute, since the willingness to bear the expected sanction signals that his benefit is higher than the expected sanction. The analogy to paying a price for a good is said to apply, whereby, if a party is willing to pay the price of a good, the purchase is inferred to be socially desirable, since the willingness to pay the price implies that the value that the part places on the good must exceed its production cost. This line of thinking is offered both as a criticism of the economic way of thinking by some, and as a point of interest, asserted to be correct, by economists However, this view represents an incorrect interpretation of economic analysis of optimal law enforcement. As has been explained above, optimal law enforcement is characterized by underdeterrence -and perhaps by substantial underdeterrence - due to the costliness of enforcement effort and limits on sanctions. For example, the probability and magnitude of sanctions against pollution may fall significantly short of discouraging as much pollution as would be ideal -- because of the costs of raising the likelihood of enforcement and because of limits on the magnitude of sanctions. Consider a firm that faces a maximum sanction equal to its assets of $100,000, that could take a precaution that costs $10,000 and would prevent pollution harm of $25,000, and that would be sanctioned for pollution only with a probability of 5 percent due to the high cost of detecting the source of the pollution. This firm might well find it in its private interest to pollute--its savings from not taking the precaution of $10,000 is double the maximum possible expected sanction of 5% H$100,000=$5,000. But the firms failure to take the precaution would most definitely be socially undesirable-- pollution causes harm of $25,000 yet saves prevention costs of only $10,000. It is often the case that when parties choose to commit harmful acts and the likelihood of sanctions is low, it would be socially best that they do not commit the acts; they commit the acts only because the social cost of enforcement effort esults in inadequate expected sanctions Note, however, that if enforcement is certain, the conclusion may be different. For example, if we imagine pollution taxes to be imposed with certainty in some context(because it is administratively easy to do so), then by setting the tax equal to the harm due to pollution, the
Chapter 20 – Page 11 not to be high due to the risk aversion of individuals, say to be in the range of $300, then the only way to achieve a particular level of deterrence is through use of greater enforcement than would be needed were the sanction maximal. Second, the optimal probability could also be lower than in the risk-neutral case: If the sanction must be fairly low due to risk aversion, the effectiveness of raising the probability is reduced, leading to the possibility that the optimal probability could be lower than in the risk-neutral case, or that it might not be worth controlling the activity at all, even though it would be in the risk-neutral case. A further point is worth mentioning. The reason that has been discussed why some riskaverse parties bear risk is that it may turn out to be desirable for them to commit harmful acts and they will do so. However, as we know, there are other reasons for risk-bearing -- and thus for sanctions to be less than maximal -- notably, legal errors that result in the imposition of sanctions on innocent parties. 2.5 Comment on the misleading notion that sanctions are analogous to market prices -- that willingness to face sanctions for harmful acts implies that committing such acts is socially correct. It is commonly stated that if a party is willing to pay a sanction, or face an expected sanction, then it is not socially incorrect, indeed it is socially desirable, for him to commit an act, such as to pollute, since the willingness to bear the expected sanction signals that his benefit is higher than the expected sanction. The analogy to paying a price for a good is said to apply, whereby, if a party is willing to pay the price of a good, the purchase is inferred to be socially desirable, since the willingness to pay the price implies that the value that the party places on the good must exceed its production cost. This line of thinking is offered both as a criticism of the economic way of thinking by some, and as a point of interest, asserted to be correct, by economists. However, this view represents an incorrect interpretation of economic analysis of optimal law enforcement. As has been explained above, optimal law enforcement is characterized by underdeterrence -- and perhaps by substantial underdeterrence -- due to the costliness of enforcement effort and limits on sanctions. For example, the probability and magnitude of sanctions against pollution may fall significantly short of discouraging as much pollution as would be ideal -- because of the costs of raising the likelihood of enforcement and because of limits on the magnitude of sanctions. Consider a firm that faces a maximum sanction equal to its assets of $100,000, that could take a precaution that costs $10,000 and would prevent pollution harm of $25,000, and that would be sanctioned for pollution only with a probability of 5 percent due to the high cost of detecting the source of the pollution. This firm might well find it in its private interest to pollute -- its savings from not taking the precaution of $10,000 is double the maximum possible expected sanction of 5% H $100,000 = $5,000. But the firm’s failure to take the precaution would most definitely be socially undesirable -- pollution causes harm of $25,000 yet saves prevention costs of only $10,000. It is often the case that when parties choose to commit harmful acts and the likelihood of sanctions is low, it would be socially best that they do not commit the acts; they commit the acts only because the social cost of enforcement effort results in inadequate expected sanctions. Note, however, that if enforcement is certain, the conclusion may be different. For example, if we imagine pollution taxes to be imposed with certainty in some context (because it is administratively easy to do so), then by setting the tax equal to the harm due to pollution, the