6110
OPTIMAL TECHNIQUES OF REDISTRIBUTION
Christopher Curran ©
Associate Professor, Emory University Department of Economics
© Copyright 1997 Christopher Curran
Contents
8. Achieving a Desired Income Distribution
9. Modification of the Tax Shedule
10. Other Reasons for Using the Tax System to Achieve Distributional Goals
14. Efficiency of the Legal Rules
Bibliography on Optimal Techniques of Redistribution (6110)
Legal scholars have often argued that a legal system in providing a "level playing field" for consumers and producers should be designed to help in society's efforts to achieve an optimaldistribution of income. This essay reviews research by law and economics scholars thatchallenges this premise. Using neoclassical welfare economics most of these scholarsconclude that there exists a taxation scheme that achieves a desired income distribution and ispreferred by all members of society to any plan for redistributing income using the legalsystem. An implication of this research is that economic efficiency and not fairness is theappropriate criteria for evaluating any legal rule.
Keywords: income redistribution, taxation
JEL Classification: K0, H2
In this essay we examine the issue of whether income redistribution goals are more efficientlyachieved by using the tax system or by incorporating these goals into the design andimplementation of a legal system. As stated, this question takes as given that some amount ofincome redistribution is desirable and ignores the extensive literature on (1) the desirability ofincome redistribution and (2) the effectiveness of income redistribution in combating poverty.While the problem that remains -- that of developing the most cost effective method ofachieving the desired income distribution -- has a strong production flavor, the answer hasimportant implications both for the study and practice of law. If the arguments of Kaplow andShavell (1994) and others are correct, then law and economics scholars should adopt theirsuggestion that "it is appropriate for economic analysis of legal rules to focus on efficiencyand to ignore the distribution of income in offering normative judgments." Kaplow andShavell (1994, p.677) . If their analysis is flawed or if, as some authors suggest, traditionalneoclassical economics models contain serious deficiencies, then the arguments of Calabresi(1991) , Kronman (1980) , Kennedy (1982) , and Arlen (1992) that the courts should considerincome distribution when evaluating legal rules have merit.
It is not unusual for legal scholars to assume that courts ought to be concerned with the properdistribution of income. Indeed, given that allowing the courts to consider issues of incomedistribution in judging cases will increase the demand for the services of lawyers and the legalsystem, it would be surprising if legal scholars were unanimous in concluding that courtsought to ignore the implications of legal policies on the income distribution. (See, forexample, Polinsky and Shavell (1991) .) Moreover, Friedman's (1981) and Lott's (1987) papersimply that a court should consider a party's wealth when that consideration leads to optimaldeterrence. Rather than reviewing all of this literature, this essay focuses on articles directlyaddressing the issue of whether it is more efficient to use the legal system or taxation toredistribute income. Heavy reliance on neoclassical economic theory and (usually)mathematical models characterizes the articles contributing to this discussion.
While Shavell (1981) is the first law and economics scholar to address the issue of the mostefficient way to redistribute income, his arguments draw directly from the optimal taxationliterature of the 1970s. (See Auerbach (1985) and Stiglitz (1985) for thorough reviews of theoptimal taxation literature and Drèze and Stern (1985) for a review of the cost-benefitliterature.) Shavell acknowledges his particular intellectual debt to two articles in thisliterature. In the first, Mirrlees (1971) demonstrates that commodities whose demand areindependent of income should not be taxed (with a fixed per unit tax) when there is anoptimal income taxation system in place. In the second, Hylland and Zeckhauser (1979, p.266) demonstrate that "in the optimal arrangement, distributional objectives are achievedthrough the tax system alone." Moreover, Hylland and Zeckhauser conclude that, in thepresence of the optimal income tax, government programs should be adopted based purely onefficiency criteria. Shavell's 1981 paper reaches a conclusion that echo's that of Hylland andZeckhauser. In particular, Shavell (1981, p. 414) argues that "despite imperfect ability toredistribute income through taxation, everyone would strictly prefer that legal rules be chosenonly on the basis of their efficiency."
The conclusions of Shavell (1981) are contrary to those made by earlier legal scholars.Scholars such as Ackerman (1973) , Kennedy (1976) , Michelman (1978) , and Kronman(1980) argue that an important role of legal institutions is to redistribute income. Indeed, Kronman (1980, p.510) argues that the choice between using the legal system and usingtaxation to redistribute income depends on "contextual considerations that are likely to varyfrom one situation to the next." Kronman suggests that all of the alleged problems with usingcourts to redistribute income are equally likely to be problems with taxation. For instance,critics of using the courts to redistribute income claim that there is no reason to believe thatjudges can correctly assess the distributional consequences of any particular decision.Kronman counters that difficulty in applying egalitarian rules in individual cases does notmean that we cannot use egalitarian principles when designing the legal system. To the claimthat the legal system should "remain neutral between the aims and activities of its citizens" Kronman (1980, p. 502) , Kronman responds that taxation is no more neutral than are thecourts and the relative neutrality of the two methods of redistributing income is an empiricalissue. Kronman responds in a similar manner to claims that regulation is more injurious to itsintended beneficiaries and is more expensive to administer than is taxation by asserting thatthese are empirical issues than cannot be resolved through the use of theory alone, aconclusion not supported by Shavell (1981) .
Not only does Shavell's research offer conclusions contrary to earlier research, it appears tohave been ignored by legal scholars during the ten years following its publication. Calabresi(1991) , Donohue (1989) , Ellis (1982) , and Kennedy (1982) , all discuss the role of the legalsystem in achieving the proper distribution of income without mentioning Shavell's 1981seminal article. Abraham and Jeffries (1989) , who argue that information about a defendant'swealth should not be considered in determining punitive awards, do not reference Shavell . Intheir defense, the connection of Shavell's conclusion to the issue that Abraham and Jeffriesdiscuss is not obvious. Abraham and Jeffries argue that the consideration of a defendant'swealth is not germane to the issue of punitive damages and invites jury speculation aboutissues about which they have no information. They argue that traditional arguments that thelegal system needs punitive damages in order to deter individuals from inflicting harm forpersonal satisfaction and to neutralize the effects of underenforcement are incorrect. WhileAbraham and Jeffries do not point out the connection, their arguments echo those of both Hylland and Zeckhauser (1979) and Shavell (1981) that distributional goals are best achievedthrough the tax system while government programs - including legal regulation - shouldignore distributional goals in favor of efficiency criteria. Thus, by Hylland and Zeckhauser'sand Shavell's logic one would consider the defendant's wealth only in cases wealth iscorrelated with deterrence, a conclusion that matches Abraham and Jeffries' result.
Arlen (1992) appears to be the first author to acknowledge Shavell's 1981 article. While themodel that Shavell (1981) develops assumes that people are risk neutral, he points out that hisresults are independent of this assumption. Arlen argues, incorrectly it turns out, that Shavell'sconclusions do not hold when individuals are risk averse. The most recent contributions tothis literature are in direct response to what Kaplow and Shavell (1994) and Miceli andSegerson (1995) perceive as a general misunderstanding of Shavell's 1981 article by legalscholars, including Arlen (1992) . In what follows, we discuss Shavell (1981) and Kaplow andShavell (1994) together because of the similarities in the two articles. We then review Miceliand Segerson (1995) . Since the model in Miceli and Segerson (1995) corrects and placesArlen's results in the context of the Shavell model, we include Arlen (1992) in this discussion.
The arguments in Shavell(1981) and Kaplow and Shavell (1994) are essentially identical.These authors argue that all efforts to redistribute income - be these efforts through the legalsystem or through the tax system - distort work efforts (see Hausman (1981) for an empiricaljustification of this point). Redistributing income through the legal system creates additionalinefficiencies in the activities affected by the legal rules. Thus, we should be able to constructa new tax schedule that we can combine with efficient legal rules that will have the samedistortions of work effort but none of the inefficiencies that arise when we use the legalsystem to redistribute income.
8. Achieving a Desired Income Distribution
Since this result is key, we consider it here in some detail. Shavell (1981) and Kaplow andShavell (1994) assume that individuals are risk neutral maximizers of expected utility, whichis equal to their income net of taxes, expected liability costs, expected damages, and the costsof work effort and care taking. The tax schedule is a function of income while the expectedliability and damages are functions of the level of care taken by the individual. In order tosimplify the analysis, these authors assume that (1) an individual's income is a linear functionof his work effort and (2) in the aggregate the government returns all taxes collected.Following existing literature, they define the efficient level of care as that care level thatminimizes sum of the total costs of care and the expected accident costs. As Shavell (1981, p.416) and Kaplow and Shavell (1994, p. 678) note, the level of care that is efficient isindependent of an individual's income. These authors show that we can replace any regimehaving an inefficient legal rule and a tax schedule with a regime with an efficient legal ruleand a properly modified tax schedule that raises the same level of taxes. More importantly,they also show that all members of society prefer the regime with the efficient legal rule.
9. Modification of the Tax Schedule
The modification to the tax schedule under the inefficient legal rule offers some insight intowhat drives these results. The modified tax schedule is equal to the tax schedule in theinefficient regime plus the total accident costs in the inefficient regime minus the totalaccident costs in the efficient regime (see Kaplow and Shavell (1994, p. 678) ). Substitution ofthe new tax schedule into the expected utility function yields the results that the expectedutility is the same in the efficient regime (with the modified tax schedule) as it is in theinefficient regime. Moreover, this new tax schedule yields a greater level of revenue.Remember that the modified tax schedule is equal to the old tax schedule plus the efficiencysavings that come from switching to the efficient legal rule. Thus, if we rebate this savingsuniformly to the population in the form of a lump sum (negative) tax, no one's incentive towork is affected and everyone is better off by the amount of the rebate in taxes.
10. Other reasons for Using the Tax System to Achieve Distributional Goals
Kaplow and Shavell (1994, pp. 674-6) offer several other, more traditional reasons forfavoring the use the tax system over the legal system to redistribute income. First, the taxsystem can allocate the impact of income redistribution on all of the rich and all of the poor.By contrast, using the legal system to redistribute income yields haphazard results. The legalsystem can only affect those individuals involved in a lawsuit. Moreover, in many casesconsumer response are bound to mute or completely negate efforts to use the courts toredistribute income. For instance, individuals bound by contracts will adjust prices to takeaccount of efforts by the courts to redistribute income. Similarly, corporations may well beable to pass on to consumers the income redistribution efforts by the courts. Second, Kaplowand Shavell (1994, p. 675) argue that claims that the legal system should be involved inincome redistribution efforts because the political system is unable to achieve the ideal amountof income redistribution do not stand close examination. In particular, the legal systemoperates under the influence of the politicians and there is no reason to believe that efforts bythe courts to redistribute income in ways not intended by the politicians will escape theirscrutiny. Thus, Kaplow and Shavell (1994, p. 677) conclude that their analysis "suggests that itis appropriate for economic analysis of legal rules to focus on efficiency and to ignore thedistribution of income in offering normative judgments."
Miceli and Segerson (1995) offer the most complete analysis of the issue of role of incomedistribution in setting efficient levels of care. These authors analyze the role of risk aversion inthe Shavell (1981) and Kaplow and Shavell (1994) model. In doing so, they correct andreconcile Arlen's (1992) results with the other models. Miceli and Segerson argue that of thethree potential optimal choice criteria - Pareto efficiency, the Pareto criterion, and aggregatewelfare - Pareto efficiency the proper one to use. They define Pareto efficiency by thefollowing choice problem:
Max U i subject to U v U v o (1) where U i is the utility level of the injurer, U v is the utility level ofvictim, and U v o is some arbitrarily fixed level of utility for the victim. The Pareto criterion hasthe same definition as (1), except that U v o is set equal to the victim's original utility level,U(W v o ). Finally, aggregate welfare is the solution to the following choice problem:
Max U i + U v (2) where is some weight placed on the victim's utility. Miceli and Segerson(1995, p. 194) illustrate the three concepts with the utility possibilities frontier (UPF) shownin Figure 1 . The UPF contains all of the Pareto optimal points. As illustrated in Figure 1 , thePareto criterion and the aggregate welfare each pick points that are subsets of the Paretooptimal points. The authors prefer to use Pareto optimality as their choice criterion for tworeasons. First, unlike the other concepts, Pareto optimality does not involve interpersonalcomparisons of utility. Second, we can specify any income distribution by varying U v o .
Miceli and Segerson (1995, p. 197) define P(X) to be the probability of an accident (where P'> and P'' < 0); X, the injurer's care level; m, the damages that the victim suffers if there is anaccident; W i and W v , the injurer's and victim's preaccident wealth levels, respectively; D, thedamages paid by the injurer in case of an accident; and T, a (positive or negative) transfer fromthe injurer to the victim that occurs independent of whether an accident occurs. As Miceli andSegerson (1995, p. 197) note, the addition of the variable T allows them to "decoupledistribution and cost minimization issues." They then split the analysis into two distinct parts.In the first they derive the first-best care levels while in the second they analyze the ability ofvarious liability rules to give individuals the incentives necessary to take these first-best carelevels.
Miceli and Segerson (1995) show that in the presence of fully working insurance markets, thefirst-best care standards are independent of both injurer's and victim's wealth levels as long asthe policy maker is free to choose the care standard and the amount of the transfer, T. Only inthe case where the policy maker can only set the care standard is the care standard a functionof the injurer's wealth. For instance, Arlen (1992) implicitly assumes in her analysis that theamount of the transfer, T, and the amount of damages, D, are preset such that T = D = 0. Figure 2 illustrates the case when the policy maker can only set the care standard. The solidcurve labeled UPF 1 is the utility possibilities frontier that faces the policy maker who is free toset the care standard and the amount of the transfer. Since the policy maker's choice set isrestricted, the utility possibilities frontier available to the policy maker who can only set thecare standard must lie inside the unrestricted UPF at all points except the point where T and Dby coincidence equal the levels that would occur in the unrestricted case. In Figure 2 thedashed line labeled UPF 2 represents the restricted UPF, while point A represents the one pointwhere T and D equal the values they would have in the unrestricted case. Clearly, there existsolutions on UPF 1 where both the victim and the injurer can achieve higher utility levels thanthey can on the restricted UPF 2 .
14. Efficiency of the Legal Rules
By choosing appropriate liability rules society attempts to induce injurers to take the efficientlevel of care. The potential success of society in achieving this goal while concurrentlyattempting to reach an ideal distribution of income depends on the number of policy toolsavailable to the policy makers. Miceli and Segerson (1995, pp. 200-202) analyze the efficiencyof strict liability and negligence under various assumptions about the choice variablesavailable to the policy makers. As they note, the efficient care level solves Max U i subject toU v U v o and X maximized U i (3) given the liability rule. Miceli and Segerson demonstrate that,when policy makers can set the care standard X, the damage award D, and the transfer fromthe injurer to the victim T, both strict liability and negligence rules are efficient. The reason forthis result is that the policy makers have three tools - X, D, and T - with which to achievethree goals - income distribution, cost minimization, and efficient incentives for the injurer.Thus, the policy makers can set X to minimize total social cost, D to give the injurer theproper incentives, and T to redistribute income, resulting in society attaining a pointsomewhere on UPF 1 , as shown in Figure 2 . In contrast, if one or two of the three controlinstruments are not available to the policy makers, then society can achieve the three goalsonly by coincidence.
The results presented by Shavell (1981) , Miceli and Segerson (1995) , and Kaplow and Shavell(1994) comprise an existence theorem -- if society decides to redistribute income, there existsa tax schedule for redistributing income that everyone prefers to any other way ofredistributing income, including the use of legal rules or institutions. As Kaplow and Shavell(1994, p.675) note, the importance of this result to legal scholars is that it demonstrates that itis appropriate to evaluate legal rules only on the basis of efficiency criteria.
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© Copyright 1997 Christopher Curran