VALUE JUDGMENTS AND REDISTRIBUTION

The interest in the question “Why are some people rich and some poor?” has always been motivated by something more than pure intellectual curiosity. A notable feature of the observed distribution of income has always been that it is unequal, and a natural second question is therefore “Can inequality be justified?” A possible response to this question is that it is one that should be answered by moral philosophers and not by economists, whose science does not provide them with the tools needed to answer it.

1.3.1 The Normative Economics of the Classical School

The natural starting point for economic theories of distributive justice is the distribution of income that is generated by the market economy. Although the main concern of the classical economists was with the positive analysis of income distribution, they were also concerned with ethical issues and with the evaluation of redistribution policy.

1.3.1.1 AdamSmith

A point of reference for the classical view of this issue is Adam Smith’s theory of the invis­ible hand.

He intends only his own gain, and he is in this, as in many other cases, led by an invisible hand to promote an end which was no part of his intention. Nor is it always the worse for the society that it was no part of it. By pursuing his own interest he frequently promotes that of the society more effectually than when he really intends to promote it.

Smith (1776; 1976, p. 456)

The most common interpretation of this passage is that private incentives operating in the context of a market economy promote an efficient use of resources in the sense of max­imizing “the annual revenue of society,” although this interpretation is not undisputed.^[29] Does it also promote a just distribution of income? There is no systematic discussion of this in the Wealth of Nations, although most readers of the book will find it reasonably clear that this was not his view. It is remarkable, therefore, to find in Smith’s other main work, The Theory of Moral Sentiments (1759), a paragraph in which he makes the claim that the rich, without intending to do so, promote the interests of the poor. His statement of this claim is also of interest because it contains the second of his three uses of the metaphor of the invisible hand.^[30] The rich, he says

... in spite of their natural selfishness and rapacity, though they mean only their own conve- niency, though the sole end which they propose from the labours of all the thousands whom they employ, be the gratification of their own vain and insatiable desires, they divide with the poor the produce of all their improvements. They are led by an invisible hand to make nearly the same distribution of the necessaries of life, which would have been made, had the earth been divided into equal portions among all its inhabitants, and thus without intending it, without knowing it, advance the interest of the society.

Smith (1759; 1976, pp. 184-185)

The proposition that the distribution of necessaries is almost the same as if the economic system had been designed with a view to an equal distribution is certainly a striking one, although one should note that there is no claim that the income that finances the con­sumption over and above that level is distributed in a similar fashion. The self-interest of the rich is claimed to guarantee a certain minimum income to the poor, but not to the extent of leading to equality of living standards. Almost regardless of one’s interpretation of the substantive content of this proposition, it is difficult to see that Smith provides any convincing support for it, and it is hardly surprising that this version of the invisible hand has had little influence on subsequent thinking about income distribution.

Going back to The Wealth of Nations, although it does not contain any systematic dis­cussion of the normative aspects of the distribution of income, there are many passages in the book that demonstrate Adam Smith’s concern with inequality and poverty as well his sympathy for the poor. One example is his positive attitude toward trade unions, which leads him to suggest that it is an inconsistency of economic policy to allow employers to collude while forbidding workmen to form trade unions (Smith, 1776; 1976, pp. 83—85). Another example that, although in itself of minor importance, is suggestive of his attitude, is his discussion of the system of the tolls that should be charged for different types of public transport. The principle that was most commonly used at Smith’s time was that of charging according to the weight of the carriage. He argued against this principle and in favor of the alternative of charging higher rates for luxury carriages and lower rates for carriages of necessity. Such a reform, he argued, would have the effect that “the indolence and vanity of the rich is made to contribute in a very easy manner to the relief of the poor, by rendering cheaper the transportation of heavy goods to all the different parts of the country” (Smith, 1776; 1976, p.

A clearer statement of Smith’s more general perspective on the distribution of income between rich and poor comes in a passage that follows a discussion of the effects of lower prices of necessities:

Is this improvement in the circumstances of the lower ranks of the people to be regarded as an advantage or as an inconveniency to the society? The answer seems at first sight abundantly plain. Servants, labourers and workmen of different kinds, make up the far greater part of every great political society. But what improves the circumstances of the greater part can never be regarded as an inconveniency to the whole. No society can surely be flourishing and happy, of which the far greater part of the members are poor and miserable. It is but equity, besides, that they who feed, cloath and lodge the whole body of the people, should have such a share of the produce of their own labour as to be themselves tolerably well fed, cloathed and lodged.

Smith (1776; 1976, p. 96)

It is clear from the context that Smith meant this statement to apply even to the case where the improvements in the standard of living of the lower ranks were achieved at some cost to the higher ranks of society.

What consequences did Smith draw for redistributive policy? Here, we must keep in mind that the instruments available for redistributive policy were limited in number in Smith’s time, so that his policy recommendations were mostly incidental, as in the pre­ceding passage concerning charges for public transport. His discussion of taxation in Book V of the Wealth of Nations is not very explicit when it comes to the redistributive effects of the tax system as a whole; he is content to discuss the main categories of taxes one by one with apparently little regard for the overall impact of the tax system. How­ever, this discussion is introduced by the presentation of four normative “maxims” of taxation, and in the first of these we find the following principle:

The subjects of every state ought to contribute towards the support of the government, as nearly as possible, in proportion to their respective abilities; that is, in proportion to the revenue which they respectively enjoy under the protection of the state.

Smith (1776; 1976, p. 825)

The principle may not be entirely clear to the modern reader and could be interpreted in two different ways. The first part of the passage indicates that the principle is one of ability to pay, whereas the second part might suggest that we should read it as a recommendation of the benefit principle, according to which taxes should be seen as payment for services rendered by the state. However, the most reasonable interpretation of the term “revenue” is “income”; a central service that the state provides is security of private income, so that income is both a measure of ability to pay and benefits received. Thus, the tax system as a whole should be as nearly as possible proportionate to income. It is important to note that this is not a recommendation for the form of an income tax— about which Smith has little to say—but for the more general design of the tax system as a whole.

1.3.1.2 Malthus and Ricardo on the Poor Laws

Although redistributive taxation played little role at the time of the early classical econ­omists, the form that support for the poor should take was a major issue of public policy.^[31] There was widespread concern over the established system of poor relief, which provided assistance both to those too sick or too old to work and to those who were able to work but found it difficult or impossible to earn a living. Malthus applied his theory of pop­ulation to this issue and argued that support for the poor would not in the long run improve their position in society. Because the provision of a minimum standard of living would encourage the poor to have more children, in the long run they would not be better off on an individual basis; there would simply be a larger number of poor people in society. In addition, the resulting increase of population would drive up the price of food and cause more workers to rely on poor relief:

They [the poor laws] may be said, therefore, to create the poor which they maintain; and as the provisions of the country must, in consequence of the increased population, be distributed to every man in smaller proportions, it is evident that the labour of those who are not supported by parish assistance will purchase a smaller quantity of provisions than before, and consequently more of them must be driven to apply for assistance.

Malthus (1803; 1992, p. 100)

Malthus therefore recommended the abolition of the poor laws to increase the incentives of the able-bodied poor to provide for themselves through their own work. In this he received strong support from other prominent economists, in particular from his friend David Ricardo. According to Ricardo, “the comforts and well-being of the poor” can­not be secured without some effort of their own, especially to regulate the increase in their numbers. But, he argued,

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The operation ofthe system of poor laws has been directly contrary to this. They have rendered restraint superfluous, and have invited imprudence, by offering it a portion ofthe wages ofpru- dence and industry.

The nature of the evil points out the remedy. By gradually contracting the sphere of the poor laws; by impressing on the poor the value of independence, by teaching them that they must look not to systematic and casual charity, but to their own exertions for support, that prudence and forethought are neither unnecessary nor unprofitable virtues, we shall by degrees approach a sounder and more healthful state.

Ricardo (1817; 1951, p. 107)

In a stark form the critique of the poor laws introduced a theme that was destined to become a major issue in the economic analysis ofpoverty and redistribution: The possible conflict between the objectives of justice (poor relief) and efficiency (labor supply). Later classical economists, in particular Nassau William Senior, who was chairman ofthe 1832 Royal Commission on the poor laws, strongly recommended a reform of the system that ensured that poor relief would never be organized in such a way as to make it more attrac­tive than to earn one’s living by regular work.

1.3.1.3 Mill

John Stuart Mill is known as one ofthe most prominent spokesmen for the philosophy of utilitarianism, which he expounded in particular in his book Utilitarianism (1863). One might expect then that in his Principles he would use the utilitarian approach to evaluate income inequality, but this perspective is in fact absent from his analysis. Like in the case of Adam Smith, we search in vain for a unified theoretical principle that can be used to evaluate income distribution from a normative point of view. On the other hand, there are numerous opportunities to gain insight into his views on distribution from his dis­cussion of more specific issues.

On such issue is that of inheritance. Although Mill supports each individual’s rights to the fruits of his own labor and property, he draws a line when it comes to income from inherited property. In a passage that may have been more controversial to his readers than he indicated (Mill, 1848; 1965, p. 218), he wrote that “although the right ofbequest, or gift after death, forms part of the idea of private property, the right of inheritance, as dis­tinguished from bequest, does not.” He therefore supported restrictions regarding inher­itance in the form of limits on how much an individual may be allowed to receive. His

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The last edition of the Principles that appeared during Mill’s lifetime was the 7th, which came out in 1871. Thus, he clearly had the opportunity to use material from Utilitarianism for this purpose. arguments for such restrictions run partly in the form of incentives: Although restrictions on how much a parent is allowed to leave to his children may weaken the parent’s desire to accumulate wealth, this is outweighed by the adverse incentives to work and save that arise for children who receive large amounts of wealth that they have done nothing to deserve. But he also defended the proposed restrictions by its distributional conse­quences. If children’s inheritance were to be limited to some maximum amount,

... the benefit would be great. Wealth which could no longer be employed in "over"-enriching a few, would either be devoted to objects of public usefulness, or if bestowed on individuals, would be distributed among a larger number.

Mill (1848; 1965, p. 226)

According to Mill, therefore, there is a social benefit associated with a more even distri­bution of wealth.^[32]

Another issue is that of the most desirable form of taxation. In his chapter “On the General Principles of Taxation” (Mill, 1848; 1965, Book V, Chapter II), Mill cited with approval Adam Smith’s four maxims on taxation. After having quoted them in verbatim, he commented that although their meaning is mostly clear, the maxim that is concerned with equality in taxation (and which was cited earlier) requires further examination because it is concerned with a concept that is often imperfectly understood. He then stated that the fundamental principle of equality in taxation is equality of sacrifice, which means “... apportioning the contribution of each person toward the expenses of govern­ment, so that he shall feel neither more nor less inconvenience from his share of the pay­ment than every other person experiences from his” (p. 807). He then went on to discuss the consequences of this general principle for the design of the income tax. Although expressing some sympathy for the idea of a graduated income tax, he concluded in favor of a linear tax in which, e.g., the first 50 pounds of income is tax exempt, whereas the excess income is taxed at a constant rate. He also recommended that saving be exempt from taxation, the main argument being that taxing the parts of income that are devoted to consumption and saving at the same rate involves a “double taxation of saving” and therefore a disincentive to saving and investment.

Mill’s tax policy recommendations emerge as a compromise between the abstract idea of equal sacrifice and more ad hoc considerations, but it is difficult to see to what extent his conclusions can be derived from the philosophical principles of utilitarianism. In his book Utilitarianism (Mill, 1863; 1969, pp. 254-255), there is a brief discussion of alternative concepts ofjustice in taxation, but the text is rather inconclusive: Mill described alter­native points of view that give support to a head tax, a proportional tax, or progressive taxation. He then stated that “[f]rom these confusions there is no other mode of extrication than the utilitarian.” However, he did not conclude as to the form of taxation that would follow from the application of utilitarian principles, and as we have seen this connection is not clear in his discussion in the Principles either.

It may seem surprising that John Stuart Mill, an intellectual known for his radical sym­pathies, should not have come out more strongly in favor of redistributive taxation. The main explanation is probably that he saw taxation as being of secondary importance in this regard in comparison to structural reforms aiming to expand the range of choice open to all layers of society. Such reforms would include better education for the lower classes, ending the restrictions on entry into various occupations as well the discrimination of women in the labor market. The latter issue was one that he considered to be of special importance. He wrote the influential book On the Subjection of Women (Mill, 1869), and in the Principles he wrote,

Let women who prefer that occupation [as a wife and mother]; adopt it, but that there should be no option, no other carriere possible for the great majority of women, except in the humbler departments of life, is a flagrant social injustice.

Mill (1848; 1965, p. 765)

It is notable that it was to take more than a century for the gender issue once again to make its appearance in the normative economics of inequality and income distribution.

1.3.2 The Neoclassical Economists: Efficiency and Justice

With the emergence of marginalism and the neoclassical school of economic theory there began a more systematic exploration of the optimality properties of the market allocation of resources and in particular the relationship between on the one hand the efficiency of the market economy and on the other hand the distributive justice of its allocation of resources. In the long-run perspective of the history of ideas, the neoclassical interest in these issues may be seen as a desire to clarify Adam Smith’s proposition that the invis­ible hand of the market led to a result that was in conformity with “the public interest.”

1.3.2.1 Walras

The three main protagonists of the marginalist revolution paid little attention to the role of the competitive market system in the determination of income distribution and even less to the ethical aspects of it. Among the three, however, Leon Walras is notable for raising an issue that goes back to Adam Smith’s theory of the invisible hand and the ability of the market mechanism to function in a way that is consistent with the public interest. Toward the end of his detailed analysis of exchange in a two-commodity world he wrote that

[the] exchange of two commodities for each other in a perfectly competitive market is an oper­ation by which all holders of either one, or of both, of the two commodities can obtain the greatest possible satisfaction of their wants consistent with the condition that the two commodities are bought and sold at one and the same rate of exchange throughout the market.

Walras (1874-1877; 1954, p. 143)

The context makes it clear that Walras meant the conclusion to apply beyond the simple case of two commodities and pure exchange, so it must be understood as a more general characterization of a competitive economy.

The characterization can be read as a modernized version of Smith’s statement about the invisible hand; however, it can be interpreted in two different ways. Several econ­omists have taken the view that the expression “the greatest possible satisfaction of their wants” refers to the collective society of all individuals; according to this interpretation, Walras said that the competitive equilibrium generates the greatest possible satisfaction of wants for society as a whole. In this perspective, Walras came out as a rather naive apol­ogetic for the free market system. The other interpretation is obviously that each indi­vidual can obtain the greatest possible satisfaction of wants for himself. There can in fact be no doubt that the second interpretation is the correct representation ofWalras’s position. On the one hand, he insisted that his analytical description of the competitive market has no broader normative significance:

Though our description of free competition emphasizes the problem of utility, it leaves the ques­tion of justice entirely to one side.

Walras (1874-1877; 1954, p. 257)

On the other hand, he emphasized the noncomparability of utility, so that he must have rejected the notion that there exists such a thing as wants satisfaction for society as a whole.

On the latter point, however, we have evidence that for Walras, at least in this case, old habits of thought died hard. In a letter to the German economist Wilhelm Launhard in 1885 Walras defended himself against the charge that he had maintained that compe­tition necessarily led to maximum satisfaction for society as a whole. Suppose, he argued, that commodities can be sold at a low price to the poor and a high price to the rich. The rich would then have to give up some consumption of “superfluous” goods, whereas the poor would be better able to afford necessities. “Consequently, there would be a large increase in utility” (Jaffe, 1965, vol. II, p. 50). Here, utility evidently refers to aggregate or social utility; hence, there is an assumption, contrary to the statement in the Elements, that individual utilities can be compared and aggregated.

In addition to this lapse from theoretical consistency, the modern economist might also question Walras’s use of the example of price discrimination for consumer goods to illustrate redistribution policy. Clearly, an example that would both be more striking and more realistic would be redistribution of income from the rich to the poor. The conse­quences in terms of the consumption of luxuries and necessities would be the same, and the connection with policies that were within the realm of the feasible would be much stronger.

In modern terminology, the conclusion to which Walras came close, although he did not manage to state it with great clarity, was that the market equilibrium was efficient although it did not necessarily result in a just distribution of resources and income. Although imperfectly formulated, this insight was a step forward in the understanding of the connection between the market mechanism as a system for efficient resource allo­cation and as a determinant of the distribution of income and welfare between individuals in society. The insight was to be further studied and clarified by the next generation of marginalist thinkers of whom the most important were Alfred Marshall and Walras’ suc­cessor in Lausanne, Vilfredo Pareto.

1.3.2.2 Marshall

What were Marshall’s views regarding the normative aspects of income distribution? In welfare economics, Marshall is chiefly remembered for his invention of the partial equilibrium concept of the social surplus (the sum of producers’ and consumers’ surplus), which can be measured as the area between the demand and marginal cost curves. Because this area achieves its maximum at the point of intersection between the two curves, i.e., at the competitive equilibrium, Marshall was able to con­clude that

a position of (stable) equilibrium of demand and supply is a position also of maximum satisfaction.

Marshall (1890; 1920, p. 470)

This is a conclusion very similar to that ofWalras, although Marshall was more careful in qualifying it to avoid misunderstandings. It is obvious that he meant the conclusion to apply beyond the simple case of an individual commodity to the general equilibrium of demand and supply, including the markets for the factors of production. And although the term maximum satisfaction was meant to apply to society as a whole, Marshall empha­sized that it is an aggregate measure that is built on the assumption that

all differences in wealth between the different parties concerned may be neglected, and that the satisfaction which is rated at a shilling by any one of them, may be taken as equal to one that is rated at a shilling by any other.

Marshall (1890; 1920, p. 471)

He then argued that if, e.g., it were the case that the producers as a class were much poorer than the consumers, “aggregate satisfaction” might be increased by a restriction of supply that would, assuming demand to be inelastic, increase the income of the pro­ducers. The terminology here is apt to be confusing because it seems strange to argue that aggregate satisfaction can be increased by moving away from a position of maximum sat­isfaction. But quite apart from the terminology, the underlying argument is clearly based on the utilitarian assumption of decreasing marginal utility:

It is in fact only a special case ofthe broad proposition that the aggregate satisfaction can prima facie be increased by the distribution, whether voluntarily or compulsorily, of some ofthe property of the rich among the poor.

Marshall (1890; 1920, pp. 471-472)

In his concluding chapter on “Progress in relation to the standards of life” he became at the same time more explicit and more cautious regarding the desirability of less inequality:

The drift of economic science during many generations has been with increasing force towards the belief that there is no real necessity, and therefore no moral justification for extreme poverty side by side with great wealth. The inequalities of wealth though less than they are often repre­sented to be, are a serious flaw in our economic organization. Any diminution of them which can be attained by means that would not sap the springs of free initiative and strength of character, and would not therefore materially check the growth ofthe national dividend, would seem to be a clear social gain.

Marshall (1890; 1920, pp. 713-714)

This is a forceful expression of the view that excessive inequality is a social evil, and one notes also Marshall’s claim that this moral judgment can claim the support of economic science. On the other hand, the desirability of a move toward increased equality must take account of the possibility that it might weaken productivity and economic incen­tives, a point of view that would become a cornerstone in the analysis of welfare state policies that was to occupy the work of many economists in the coming generations.

What would be the means that could be used to achieve reduced inequality? On this topic Marshall’s Principles has less to contribute. There is the emphasis on education as a means of improving one’s position in society but little attention to the possibility of com­pulsory redistribution that he alludes to. Foremost among the instruments of such redis­tribution is taxation, but there is hardly any systematic discussion of the principles of taxation in Marshall’s book, and what mention there is, is mostly incidental and for the most part relegated to footnotes or appendices. This is in marked contrast to the trea­tises of Smith, Ricardo, and Mill, in which issues of taxation (as well as public expendi­ture) occupied a major part of their presentation of the principles of economics. A possible explanation of this neglect on the part of Marshall is that he initially saw his Principles as the first of a work in two volumes, where the second volume was to con­tain the application of theory to several areas of economic policy; a sketch ofthe proposed contents of Volume 2 dated in October 1887 lists “Taxation” as one of six such areas, whereas in 1903, “Public finance” had become one of nine areas. When his Industry and Trade was finally published in 1919, these topics were no longer parts ofthe content of the book.^[33]

1.3.2.3 J. B. Clark

John Bates Clark was a pioneer of the modern marginalist thinking in the United States who introduced the concepts of marginal productivity and marginal utility both in aca­demic and more popular writings. But his 1899 book, The Distribution of Wealth, has become less known for its restatement of marginal productivity theory (which is its main focus) than for what Stigler (1941) referred to as its “naive productivity ethics.” In Clark’s view, the equality between factor prices and marginal value productivity was not just a descriptive theory of how the market worked; it was also the manifestation of a natural law. This view is expressed already on the first page of the preface:

It is the purpose of this work to show that the distribution of the income of society is controlled by a natural law, and that this law, if it worked without friction, would give to every agent ofpro- duction the amount of wealth which that agent creates.

Clark (1899, p. v)

This statement may be read simply as a characterization of factor market equilibrium under perfect competition, although it raises the issue of how an agent’s marginal pro­ductivity can be identified with “what he creates.” Clark maintained that this problem was less complex than many people thought, for it was essentially of the same nature as that which arose in a simple frontier society:

In particular, it is necessary to know that the primitive law which puts a man face to face with nature and makes him dependent on what he personally can make her yield to him is still, in essence, the law of the most complex economy.

Clark (1899, p. 37)

A further and crucial issue is whether the distribution that results from the operation of the law is just. On this point, there is a certain ambivalence in Clark’s exposition. On the one hand, he said that this question lies outside his enquiry, “for it is a matter of pure ethics” (p. 8). On the other hand, he argued that what he creates belongs to the agent by right, and that nobody can complain if he is paid according to what he creates. The competitive distribution of income is therefore both fair and consistent with social stability, for if some agents are paid less than what they create,

there would be at the foundation of the social structure an explosive element which sooner or later would destroy it.

Clark (1899, p. 9)

Although most modern economists will no doubt find Clark’s “productivity ethics” unconvincing, there are also elements in his thought that have been taken up by others. The most obvious parallel is the analysis by the philosopher Robert Nozick in his book Anarchy, State, and Utopia (Nozick, 1974). Nozick’s basic idea is what he calls the enti­tlement theory of distributive justice. Any distribution that reflects an acquisition of income or wealth that is considered to be fair, i.e., to have been fairly acquired according to certain axiomatic criteria, is just. Moreover, given such a distribution, there is no case for public redistribution ofincome. Although it is not linked to the marginal productivity theory ofincome distribution, Nozick’s theory evidently has some elements in common with the ideas of Clark.^[34]

1.3.2.4 Pareto

We have already encountered Pareto as an empirical researcher on income distribution. Although his influence in that area was significant, his contribution to welfare economics was more fundamental and of more lasting significance. It had important consequences for the way that economists thought about normative issues, including their views on income redistribution as a goal of economic policy.

The starting point for Pareto’s welfare economics was his study of utility and demand. Arguing in his Manual of Political Economy that only an ordinal concept of utility was required as a foundation for the study of consumers’ demand,^[35] he went on to point out that this concept of utility did not lend itself to interpersonal comparisons:

The utility, or its index, for one individual, and the utility, or its index, for another individual, are heterogeneous quantities. We can neither add them together nor compare them... A sum of utility enjoyed by different individuals does not exist; it is an expression which has no meaning.

Pareto (1909; 1971, p. 192)

From this it would seem to follow that the search for a criterion of aggregate utility or welfare would be in vain. However, Pareto went on to introduce his own criterion of social welfare or efficiency that we now call Pareto optimality:

We will say that the members of a collectivity enjoy maximum utility in a certain position when it is impossible to find a way of moving from that position very slightly in such a manner that the utility enjoyed by each of the individuals of that collectivity increases.

Pareto (1909; 1971, p. 261)

“Maximum utility” was clearly not a good name for this concept because it suggested precisely the type of aggregation that Pareto sought to avoid, but he may be excused for not inventing the term “Pareto optimality.”

Pareto showed that a competitive equilibrium satisfied the conditions for optimality in this sense. From the assumption of incomparability, it followed that his optimality cri­terion was unable to judge the welfare effects of a redistribution of income that led to diminished incomes for the rich and increased incomes for the poor because this would make the rich enjoy less utility and the poor more. If the economy were to find itself in a competitive equilibrium both before and after the redistribution of income, both states of the economy would satisfy the conditions for Pareto optimality, but the optimality cri­terion would not be able to rank the two situations relative to each other. Judgments about income distribution and redistribution in terms of justice or fairness should, according to this view, be regarded as occupying a position outside the field of economics as a scientific discipline. Although this interpretation is not very explicit in Pareto’s own work, it became a central proposition in the further elaboration of Paretian welfare eco­nomics that was carried out by a number of twentieth-century economists. But the acceptance of Pareto optimality as an important concept of welfare economics took a long time. As late as 1947 Paul Samuelson, after having presented the definition of Pareto optimality, could write that “it has not yet received attention from economists commen­surate with the importance which he [Pareto] attached to it” (Samuelson, 1947, p. 212).

1.3.3 Utilitarianism and the Economics of Redistribution

The insistence by Walras and even more strongly by Pareto on the subjective nature of utility might have been expected to lead to the total banishment of utilitarian philosophy from the normative analysis of income distribution. However, this did not happen. There were several reasons for this. One is that the work of Walras and especially Pareto did not become widely known in the international community of economists until well into the twentieth century. Another was that utilitarianism continued to hold a strong attraction for economists in search of a philosophical foundation for their egalitarian convictions and for the design of redistributive policy, particularly in the tax field.

1.3.3.1 Maximizing the Sum of Utilities

A good example of such an economist is Francis Ysidro Edgeworth. He adopted the view of the older utilitarians that social welfare should be seen as the sum of individual utilities but was critical of the use that they made of it, pointing out that it was difficult to see, in the absence of mathematical formalization, how their conclusions followed from their ethical premises. In his book New and Old Methods of Ethics (Edgeworth, 1877) he built on the analogy with the Weber-Fechner law in psychology, which stated that the per­ception of a sensual stimulus increases less than proportionally with the strength of the stimulus, to argue that utility must increase less than proportionally with income. From this he drew strong conclusions for the socially optimal distribution of income. In the case of a given total income to be divided between all members of society the optimal distri­bution would be one of complete equality, assuming that all individuals had the same utility function of income. He also analyzed the case of variable work effort and found that under certain assumptions those with the greatest capacity should do the most work.

A related approach was that of Pigou. In his Economics of Welfare (1920), he used an explicit utilitarian argument—although without reference to the Weber-Fechnerlaw— to argue in favor of redistribution of income from the rich to the poor:

... it is evident that any transference of income from a relatively rich man to a relatively poor man of similar temperament, since it enables more intense wants to be satisfied at the expense of less intense wants, must increase the aggregate sum of satisfaction. The old “law of diminishing [mar­ginal] utility" thus leads securely to the proposition: Any cause which increases the absolute share of real income in the hands of the poor, provided that it does not lead to a contraction in the size of the national dividend from any point of view, will, in general, increase economic welfare.

Pigou (1920; 1932, p. 89)

In other words, it is assumed that there exists a utility function of income that is concave and the same for everybody. In the following pages, the proviso of “similar temperament” is spelled out further. Pigou admits that under existing social conditions a rich man may in fact be able to produce more utility from any given amount of income than a poor man. But this advantage has come about through past inequalities of income and the standard ofliving and cannot therefore be used to argue against income equal­ization: In the long run, the poor who experience increased incomes will be as able as the current rich to generate utility from their income. The last part of the quotation intro­duces an important qualification: Policies that aim to redistribute income from the rich to the poor may have an adverse effect on incentives, in particular on the incentives to work and save. This may lead to a reduction of the national dividend or national income so that there will be less income available for distribution.

In analytical terms, we might restate this argument as saying that if there are no incen­tive effects of redistribution it should be carried to the point where the marginal utility of income is the same for all; in the case of identical tastes, this would imply complete equal­ization of incomes, as in the analysis of Edgeworth. If incentive effects are present, the optimal amount of redistribution would stop short of this point, with the gap between the marginal utility of income between rich and poor determined by the strength of the incentive effects.

1.3.3.2 Critique of Utilitarianism

The assumptions of identical utility functions, decreasing marginal utility, and interper­sonal comparability of utility all became the subject of critical scrutiny as Pareto’s work on demand theory and welfare economics became more widely known. Because these assumptions had been shown to be unnecessary for the study of consumer demand, they were also held to be inappropriate for making welfare judgments. Justifications of income redistribution such as that advanced by Pigou gradually came to be viewed as nonscien- tific and simply subjective expressions of one’s personal taste for income equality. On the desirability of redistribution, economics as a science would have to remain silent. This view was particularly forcefully put in the influential book by Lionel Robbins (1932).

Robbins’s influence is clearly discernible in the New Welfare Economics that was developed by several writers during the 1930s and 1940s. In the reformulation of welfare theory by Bergson (1938) and Samuelson (1947), a crucial role was played by the social welfare function that depicted social welfare as an increasing function of individual utility levels, represented by ordinal utility functions. The conditions for social welfare maxi­mization could then be stated as two set of conditions. One set described the conditions for Pareto optimal allocation of factors of production and consumer goods, whereas the other represented the conditions for optimal distribution between consumers as requiring equality of the social marginal utility of income—i.e., the increase in social welfare fol­lowing an increase in income—between individuals.^[36] Although the new formulation made clear the distinction between welfare judgments related to efficiency on the one hand and distributive justice on the other, the generality of the conditions that Samuelson (1947) referred to as the interpersonal optimal conditions was such that it became virtu­ally impossible to draw any conclusion regarding the socially desirable form of income redistribution. At the most general level of analysis, the only conclusion that could be drawn from the analysis was that the desirable extent of redistribution was determined by one’s ethical beliefs. Regarding the form of redistribution, however, the analysis had rather strong implications: To achieve a full optimum of social welfare, redistribution ought to be carried out by means of instruments that did not lead to violation of the effi­ciency conditions. The only instruments that could achieve this were individualized lump sum taxes and transfers (although some economists, e.g., Hotelling (1938), implic­itly assumed that the income tax was at least approximately equivalent to lump sum taxation).

1.3.3.3 A Comeback for Utilitarianism

Although the new welfare economics helped to clarify the relationship between econ­omists’ statements regarding efficiency and distributive justice, one might still ask whether the representatives of the new approach went too far in their rejection of the old welfare economics, which was based on a cardinal definition of utility and interper­sonal utility comparisons. This view has been argued by Cooter and Rappoport (1984), who maintained that the concepts of utility used by the post-Pareto ordinalist school and the older economists whom they refer to as the material welfare school were fundamen­tally different. The concept of utility employed by the material welfare school was not intended to represent the individual’s tastes but his needs, and these needs were assumed to be objectively observable as for instance in the form of physical fitness. To use this concept for interpersonal comparisons did not involve a comparison of subjective pref­erences but of empirically observable standards of living. The consumption goods that were bought using the individual’s income were used to produce his standard of living, but like other factors of production the goods obeyed the law of diminishing returns, which in this case was translated into the concept of diminishing marginal utility of income. It was this concept of utility that was used by economists like Edgeworth^[37] and Pigou to justify the recommendation of transfers to the poor and progressive taxation. The concreteness of the concept is well brought out in Hugh Dalton’s (1920) comment on Jevons’s (1871) discovery^[38] of the law of diminishing marginal utility.

From this law a practical conclusion of the greatest importance follows, namely, the extreme wastefulness from the point of view of economic welfare of large inequalities of income. It is obvi­ous to the modern economist that, from this point of view, a considerable equalization of incomes is desirable, provided that production is not checked thereby. But before Jevons wrote, this was by no means obvious, or at any rate it was not widely perceived.

Dalton (1920, p. 90)

Dalton’s use of the word wastefulness is suggestive. In the new welfare economics frame­work, this term would be meaningless, but in the approach taken by the material welfare school, it has a concrete interpretation in terms of a smaller quantity of aggregate welfare, which is due to the inequality of income. Given the way that income is distributed, it produces a smaller amount of material welfare or standard of living than that which would result from a more equal distribution.

A new justification for the utilitarian social welfare function arose in the early postwar period. It started with an article by William Vickrey (1945), which was apparently con­cerned with the possibility of measuring the marginal utility of income on the basis of the von Neumann-Morgenstern expected utility hypothesis. But in the middle of the article, Vickrey changed his focus to that of discussing the question of the socially optimal dis­tribution of income. His approach is nicely summed up in the following statement:

If utility is defined as that quantity the mathematical expectation of which is maximized by an individual making choices involving risk, then to maximize the aggregate of such utility over the population is equivalent to choosing that distribution of income which such an individual would select were he asked which of various variants of the economy he would like to become a member of, assuming that once he selects a given economy with a given distribution of income he has an equal chance of landing in the shoes of each member of it.

Vickrey (1945, p. 329)

The idea was developed further by several writers, including Marcus Fleming (1952) and John Harsanyi (1955b), neither of whom, however, referred to Vickrey’s work. Harsanyi’s article in particular showed how a utilitarian social welfare function, additive in individual utilities, could be derived from a set of axioms governing individual and social welfare judgments. Using this approach, one could go back to the issue raised by the earlier utilitarian economists and ask which distribution of a given amount of income would maximize social welfare. If social welfare can be expressed as an unweighted sum of individual utility functions, and if these functions are concave (representing risk-averse attitudes), the answer would once again be that the optimal distribution would be one of complete equality.

This implication was not emphasized by Harsanyi, whose interests centered on the logical foundations for this particular social welfare function, not in its implications for social organization and economic policy. Vickrey, on the other hand, developed these implications in some detail, pointing out both the optimality of equal distribution if total income could be taken as fixed and the qualifications needed when one takes account of the objection that the total amount of income cannot in practice be taken as independent of the way it is distributed.^[39] Therefore, he argued, “some degree of inequality is needed in order to provide the required incentives and stimuli to efficient cooperation of indi­viduals in the production process” (Vickrey, 1945, p. 329). From this observation, he proceeded to an attempt to determine the welfare maximizing amount of redistribution by calculating an optimal income tax function using the calculus of variations. He suc­ceeded in deriving the Euler equation for this problem but concluded that “even in this simplified form the problem resists any facile solution” (Vickrey, 1945, p. 331).

There is a direct line from Vickrey’s analysis to the modern theory of optimal income taxation as pioneered by James Mirrlees (1971). Mirrlees also adopted the utilitarian assumption of social welfare as the sum of individual utility functions (which he also assumed to be identical) but without the choice theoretic foundation adopted by Vickrey and Harsanyi; it is also notable that he does not refer to Vickrey’s (1945) article. In the Mirrlees model, individual utility functions depend on consumption (or income) and lei­sure. Lump sum taxation is ruled out as infeasible, and redistribution has to be carried out by means of a nonlinear income tax that distorts the choice between leisure and con­sumption. The shape of the optimal income tax function accordingly has to reflect the trade-off between equality and efficiency. By adopting some additional assumptions relative to Vickrey’s model, Mirrlees was in fact able to characterize the optimal income tax function, although in rather general terms. More specific results were derived by a simulation analysis of special cases. A surprising feature of the optimal tax schedule that emerged from these numerical experiments was that although the average tax rate was increasing in income, the marginal tax rate tended to stay approximately constant and if anything showed a tendency to decline with income.^[40] Mirrlees’s contribution has led to a long line of refinements and extensions of his analysis, including a critical exam­ination of the utilitarian foundations of the social welfare function. In the 1970s, the book by the philosopher John Rawls (1972) created a great deal ofinterest among economists who were interested in public policy analysis, and Rawls’s “maxi-min” criterion, by which the welfare criterion to be maximized is the utility of the least fortunate person in society, was applied to the problem of optimal income taxation by Atkinson (1973). His numerical results indicated that with this criterion the marginal tax rates and the degree of progression were likely to be considerably higher than in the case con­sidered by Mirrlees.

As an aside, it may be noted that a different argument for low marginal tax rates had earlier been discussed by Ragnar Frisch in an article published in Norwegian (Frisch, 1948). Frisch based his argument on the distinction between what he called the internal and external marginal productivity of labor. The external marginal productivity in a par­ticular sector refers to the effect on output in other sectors that is not taken into account in the employment decision. Frisch believed that this effect as a rule was positive, so that work effort tended to be too low in a market economy. This might call for a negative marginal tax rate,^[41] which, however, was not practically feasible, “at least not at the pre­sent time.” Instead, he suggested a zero marginal tax rate on the part of income that was directly related to effort, and the remainder of the individual’s income could be taxed according to a progressive scale.

1.3.4 Sacrifice and Benefit Theories

There are other ways to analyze the normative problems of redistribution than via social welfare maximization, and in this section, we consider two of these. Equal sacrifice theories caught the attention of economists around the end of the nineteenth century and were for a time influential in policy debates. Benefit theories of taxation whereby taxes are seen as payment for benefits received from the state have traditionally had a strong appeal to those who look for fairness in the relationship between the individual and the state.

1.3.4.1 EqualSacrifice

The utilitarian approach to income distribution and taxation is sometimes referred to as an equal sacrifice theory. In the simple case that forms the starting point for the utilitarian analysis, pretax incomes are given and the government aims to collect a given amount of revenue by using individualized lump sum taxes to maximize the sum of identical and concave utility functions of income. The resulting optimal distribution of after-tax incomes is one of complete equality of income where the marginal utility of income is the same for all. The solution represent a minimum of aggregate sacrifice because the outcome with equal marginal utilities of income is the maximum of total utility that can be obtained relative to the tax revenue that is to be collected. It is a solution of equal sacrifice between persons only in the sense of equal marginal sacrifice: The sacrifice ofthe last dollar paid in taxes is the same for all.

34

It might be expected that some economists who thought about the just distribution of the tax burden should come to think that this notion of equal sacrifice had limited appeal. In the case of substantial inequality of pretax incomes, the loss of utility from going from the pretax to the after-tax situation will obviously differ between individuals, and if one thinks that this is unjust it is natural to look for some alternative notion of equal sacrifice that could be applied to such nonmarginal changes in the distribution of income. This led to the development of equal sacrifice theories in the more specific sense, and in particular the theories of equal absolute and equal proportional sacrifice; theories that were first discussed analytically by Cohen-Stuart (1889) and Edgeworth (1897). The cri­terion of equal absolute sacrifice)^[42] can be formalized as:

Here, Y is pretax income and T is the amount of tax, while k is a constant that is the same for all taxpayers,^[43] so that the sacrifice of utility that results from taxation is the same for all individuals. To see how the amount of tax varies with income according to this principle, one may take the derivative of the left-hand side of the equation with respect to Y, treat­ing T as a function of Y. Solving for the marginal tax rate, we obtain:

One sees immediately that the assumption of decreasing marginal utility of income implies that the marginal tax rate is positive, but the assumption does not take us any fur­ther in supplying an argument for progressive taxation. To study the implications for pro­gressivity, one can use the result to derive the elasticity of income after tax with respect to income before tax. For progressivity, this should be less than one, but whether this is the case or not turns out to depend on whether the elasticity of the marginal utility of income is less than or greater than — 1. For the logarithmic function, where the elasticity is just — 1, equal sacrifice in this sense implies proportional rather than progressive taxation, as pointed out by Samuelson (1947, p. 227). From the point of view of the history of public finance, this conclusion is of particular interest because it was for some time widely believed that the principle of equal sacrifice combined with the assumption of decreasing marginal utility of income was sufficient to justify progressive taxation.^[44]

Although the principle of equal sacrifice may have some appeal to economic intui­tion, the main reason that it has disappeared from the modern discussion of optimal redis­tribution must be that its assumptions are difficult to reconcile with the maximization of a social welfare function. From that perspective, the straightforward utilitarian approach is much more appealing. In addition, the equal sacrifice theory lends itself less easily to gen­eralizations incorporating variable labor supply and the second best considerations intro­duced by the work of Mirrlees and others into the utilitarian framework. From this point of view, the equal sacrifice theory of income redistribution proved to be a sidetrack.^[45]

1.3.4.2 The Benefit Principle of Taxation

The utilitarian and related approaches to the issue of optimal income distribution con­sidered the question of the just or fair distribution of income in isolation from the dis­tributive effects of public expenditure. In the older literature, we have seen that Adam Smith recommended that the contributions of taxpayers should be in proportion to “the revenue which they respectively enjoy under the protection of the state,” and one inter­pretation of this rule is that taxes should be levied so as to correspond to the benefits that people received from the activities of the state. However, the further elaboration of the benefit principle of taxation mainly took place in the writings of a number of continental European economists during the late nineteenth and early twentieth centuries. Two dif­ferent types of claims were made for the implementation of the benefit principle of tax­ation. The first was that taxes levied on individuals according to the benefits that they received from the provision of public goods would somehow establish a price system for public goods or publicly provided goods that would correspond to competitive prices for private goods with similar efficiency properties. This idea suffers from the weakness that at least for public goods in the proper sense these prices do not provide individuals with the incentives to reveal their true preferences so that they cannot fill the functions of the price mechanism in the private goods part of the economy. The second claim, which is the one that is relevant for the normative analysis of redistribution policy, is that the benefit principle represents justice in taxation and that it therefore is important for nor­mative judgments about income distribution in a mixed economy. The best known state­ment of this position is that of Knut Wicksell (1896).^[46]

The concept of just taxation as used by Wicksell is quite different from that employed by economists in the utilitarian tradition. Wicksell sees the relationship between govern­ment and citizens as basically one of exchange, and one that should be carried out on terms that are fair. The starting point for his argument is that no public project should be carried out unless society’s aggregate willingness to pay is at least as high as its costs. Given that this condition is satisfied, it ought to be possible to distribute the costs in such a man­ner that every citizen makes a gain from the exchange, and this is the principle ofjustice in taxation: “No-one can complain if he secures a benefit which he himself considers to be (greater or at least) as great as the price he has to pay” (Wicksell, 1896; 1958, p. 79). From this he drew the conclusion that any political proposal about public projects should be voted on as a balanced budget tax-expenditure “package,” and that it should only be passed on the basis of a unanimous vote.

It may seem surprising that Wicksell with his reputation for political radicalism should favor a system that seems to exclude the possibility of income redistribution through the public budget. It is at this point that one has to keep his peculiar definition of “just taxation” in mind. Wicksell said explicitly that the principle does not take account of distributional issues. Given the distribution of income in society, Wicksell’s principle, as described here, does nothing more than assure that the adoption of any new public project does not harm any citizen.^[47] He also emphasized that this principle, if adopted in the Swedish society of his own time, would be in the interests of the lower classes who in his view were exploited by the higher income groups to contribute to the financ­ing of public projects that involved little or no benefit to themselves.

However, Wicksell recognized that for this principle to be fully convincing both from an economic and ethical point of view, it would have to be embedded in a broader frame­work of distributive justice: “It is clear that justice in taxation tacitly presupposes justice in the existing distribution of property and income” (Wicksell, 1896; 1958, p. 108). Onthis broader concept of justice, however, he has actually little to say, although he emphasized that too much redistribution may harm the upper classes in a way that is harmful to society as a whole because these classes “undeniably include a significant share of a nation’s intel­ligence and economic initiative” (Wicksell, 1896; 1958, p. 117).

Wicksell’s analysis was followed up by his countryman Erik Lindahl, whose mono­graph on the theory of taxation introduced the concept that later came to be known as Lindahl prices (Lindahl, 1919). In a later article, he discussed in more detail the argument that the benefit principle had a claim to be considered a standard ofjustice in taxation. Here, on the one hand, he emphasized the broader concept of distributive justice in which the benefit principle had to be embedded^[48]:

... justice in taxation is inextricably linked with justice in the distribution of property, since it would obviously be nonsense to speak of “a just portion of an unjust whole."

Lindahl (1928; 1958, p. 227)

On the other hand, Lindahl also argued that there did not necessarily exist any contra­diction between the principles of benefit and ability to pay because ability to pay could often be taken as a good indication of the benefit derived from public expenditure. On this point, Lindahl’s argument is reminiscent of Adam Smith’s first maxim of taxation, which indicated that it would be possible for taxation simultaneously to reflect both the individual taxpayers’ ability to pay and the benefits that they received under the pro­tection of the state.

1.4.