THE POSITIVE ECONOMICS OF INCOME DISTRIBUTION

It has sometimes been claimed that one of the fundamental questions that has motivated the systematic study of economics is “Why are some countries rich and some poor?” This may well be correct when we consider the motivations of some of the leading economists.

It took in fact considerable time before this question moved to the forefront of eco­nomics; indeed, it may be asked whether it has ever reached the forefront. Some thoughts on this question are contained in Part 4.

1.2.1 The Classical School: Factor Prices and the Functional Distribution of Income

By the classical school of economics, we shall, in line with standard usage in the history of economic thought, refer to the economists from Adam Smith to John Stuart Mill who dom­inated economics during the century from the 1770s to the 1870s. The members of this school were chiefly English and Scottish, although there were also economists in Germany, France, and other countries who felt a strong affinity to Adam Smith and his successors.^[12]

Regarding the positive study of the distribution of income, the theoretical approach of the classical economists focused mainly on the functional distribution of income, i.e., the distribution of income between the main factors of production, and it was doubt­less this distribution that Ricardo had in mind when he made his remark about “the principal problem.” How these “main factors” were to be defined was of course a matter of judgment, but the classical economists saw them as being labor, capital, and land, whose incomes were wages, profits, and rent.

The theory ofthe functional distribution did not, in contrast to the neoclassical theory that was developed a century later, build on a unified theoretical structure. It is therefore natural to present the theory in three parts, corresponding to the three main categories of income.

1.2.1.1 Wages

In Adam Smith’s great work, An Inquiry into the Nature and Causes of the Wealth of Nations (1776), the first chapter presents us with his famous example of technical pro­gress and division of labor in a pin factory. In a factory that he has seen, the compli­cated process of the production of a pin has been broken down into “about 18” separate operations, with the result, according to his calculations, that each of 10 men can produce 4800 times as many pins in a day as a single worker operating on his own without specialization and division of labor. One might think that this dramatic increase of productivity would lead to a corresponding increase in wages, but this is a conclusion that Smith is in fact unwilling to draw. He points out, first, that the division of labor depends on the extent ofthe market. Although specialization may by itself be expected to lead to higher productivity and wages, the demand side of the market limits the extent of specialization. In the highlands of Scotland, the typical farmer is often miles away from the nearest artisan and therefore has to be his own butcher, brewer, and baker, and even the artisans who are located in the small towns cannot afford to be highly specialized.

This idea seems to have been part of the conventional wisdom among economic and social writers at Smith’s time. In a passage that reminds one of the later work of Malthus, Smith said that “every species of animals naturally multiplies in proportion to the means of their subsistence” (Smith, 1776; 1976, p. 97). In this connection, he refers to Richard Cantillon, who in his book Essai sur la nature du commerce en general (1755) had argued that the standard of subsistence toward which the level of wages would gravitate must be sufficient for a working family to have four children. For experience shows, Cantillon said, that only two out of four children will be able to survive into adulthood and on average two new adults are required to ensure the reproduction of the working class.

The theory of subsistence wages received its most famous statement in the work of Thomas Robert Malthus, whose Essay on the Theory of Population (1798) became one of the most influential books on economics ever written. Among the public at large, the book became best known for its dramatic representation of the race between population and economic progress. This was illustrated by on the one hand the natural tendency of population to grow as a geometric series, whereas food production, due to decreasing returns in agriculture, would only be able to grow as an arithmetic series. Thus, the in­crease of population would be held down by the shortage of food, and the income of workers would accordingly converge to the subsistence level.

Malthus’s theory was widely accepted by the other classical economists. Gradually, however, it came to be modified regarding the essential content of the concept of sub­sistence. According to later thinking, a temporary increase of wages might not actually revert to the initial equilibrium level because psychological and social adaptation to a higher level of income might dampen the desire for larger families. The level of subsis­tence would then have to be reinterpreted as a social rather than a biological minimum amount of income, and this could well be imagined to rise over time. Technological pro­gress, on the other hand, had no place in Malthus’s view of the determination of wages.

² Malthus’s Essay came out in six editions during his lifetime. The most substantial changes in its contents occurred with the publication of the second edition, which in many respects must be considered a new book. Among Malthus scholars it has therefore been common to refer to the first edition as the “First Essay” and to the second and subsequent editions as the “Second Essay.”

The Malthusian theory of wages emphasized the supply side of the labor market, and little was said about labor demand. However, the reason why wages might tem­porarily rise above subsistence must be seen as being caused by shifts in demand, so that in an expanding economy, a series of shifts in demand might cause wages to be above subsistence even for long periods of time. The classical economists’ favorite example of an expanding economy was the United States (which at the time when Smith wrote was referred to as the British colonies in North America), where the extension of the country’s territory implied a continually increasing demand for labor and there­fore an upward pressure on wages.

According to the modern way of thinking about wage determination, wages, at least in a competitive economy, are determined by the intersection of the supply and demand curve for labor. This analytical apparatus was unknown to the classical econo­mists, but their theory can nevertheless be interpreted in these terms. The long-run equi­librium can be characterized by the intersection of a horizontal supply curve and a downward-sloping demand curve, whose position depends on the supply of other factors of production. If there is an increase in the supply of capital or land, the labor demand curve shifts to the right. In the short run labor supply is approximately inelastic, so that wages rise. But the rise in wages calls forth increased supply through an expand­ing population. The labor force accordingly increases until a new long-run equilibrium is reached where wages have come back to the level of subsistence, sometimes refer­red to as the natural price of labor. This dynamic process was described by Ricardo as follows:

It is when the market price of labour exceeds its natural price, that the condition of the labourer is flourishing and happy, that he has it in his power to command a greater proportion of the nec­essaries and enjoyments of life, and therefore to rear a healthy and numerous family. When, how­ever, by the encouragement which high wages give to the increase of population, the number of labourers is increased, wages again fall to their natural price, and indeed from a re-action some­times fall below it.

Ricardo (1817; 1951, p. 94)

1.2.1.2 Profits

Profit was regarded by the classical economists as the rate of return on capital, defined as the rate of interest plus a risk premium that varied with the nature of the capital.

He may therefore be willing to forego a part of his money profit, in consideration of the security, cleanliness, ease, or any other real or fancied advantage which one employment [for his funds] may possess over another.

Ricardo (1817; 1951, p. 90)

This is very similar to Adam Smith’s theory of compensating wage differentials (to be discussed later), implying a symmetric treatment of equilibrium in the markets for labor and capital. But this broad concept of the rate of return does not in fact play much role in the work of Ricardo or any other classical economist.^[13]

Although there were considerable differences among individual economists in their treatment of profits, we can still piece together a fairly unified theory from their writings. One basic question that the classical economists discussed was what it was in the working of the economic system that gave rise to a positive rate of profit. Nassau Senior (1836) provided a theory that combined the assumptions of a positive rate of time preference and the higher productivity of more roundabout methods of production. In equilibrium, cap­ital must earn a rate of profit that compensates the investor—who is assumed to be iden­tical to the saver—for his abstinence from current consumption. This is a formulation that foreshadows the later neoclassical theory of the rate of interest, in particular that of Bohm-Bawerk (1884-1889). In addition, the rate of profit contains a compensation for the risk undertaken by the investor. On the assumption that the investor is averse to risk, the risk premium must be positive, but because the degree of risk varies between projects and industries, the risk premium, and therefore the rate of return on capital, will show considerable variation, even assuming pure competition.

According to the classical theory, therefore, profit must be seen as the reward per unit of capital that accrues to the individual capitalist. But for a complete theory of the distribution of income from capital, one would also need a theory of the individual distribution of the ownership of capital because the income from capital accruing to the individual capitalist will be equal to the rate of return times the amount of capital owned. The determination of the ownership structure was an issue that did not receive much attention from the classical economists, and therefore their theory of the distri­bution of income within the capitalist class must be considered to be incomplete. On the other hand, this was an issue that did not seem to be of much concern to them. The question that formed part of Ricardo’s “principal problem” was the determination of capital’s share of national income, not the subdivision of this share among individual capitalists.

1.2.1.3 Rent

Rent was the income of the landowners, defined as the rental rate per unit of land times the number of units in the possession of the individual landowner. The most influential state­ment of the theory of rent was contained in Ricardo’s Principles (1817). Land varies in terms of its quality or productivity. The price of corn (Ricardo’s term for agricultural produce more generally) is determined by the cost of the labor and capital required to produce a unit of corn on the land with the lowest quality, i.e., the land on the margin of cultivation. On this land rent is zero. But because the nature of the product that is grown on this land is assumed to be the same as on lands of higher quality, all corn will sell at the same price, so that a positive rent will exist on all inframarginal units of land. Rent is determined by the cost of labor and capital used on the margin of cultivation, and the position of this margin is determined by the price of corn. Therefore, Ricardo concluded, “Corn is not high because a rent is paid, but a rent is paid because corn is high” (Ricardo, 1817; 1951, p. 74). An increase in the demand for corn would imply an extension of the margin of cultivation, an increase in the labor and capital cost of production, and consequently a higher corn price. This would increase total rental income in the economy.

As in the case of profits, the theory of the functional distribution of income is of lim­ited use when it comes to the analysis of the distribution of income within the group of landowners. An increase in the demand for corn will raise the rental rate for all land­owners, but the distribution of the rental income between them will depend on the dis­tribution of the ownership to land. On this distribution, regarding both capital and land, the classical theory is mostly silent.

What is likely to happen to the functional distribution of income in a growing econ­omy? Ricardo’s view of this issue is best explained by starting from his theory of rent. Beginning with a time when wages are above the level of subsistence, population will expand, the demand for corn will increase, and the margin of cultivation will be extended. The share of rent in national income will accordingly go up, and so will the share of labor, even after the wage rate has returned to its level of subsistence. The implication of this is that profits will fall and eventually, because of a weakening of the incentive to invest, bring the process of expansion to a halt. The economy will then have reached its stationary state, but the process toward this state may be delayed because of “improvements in machinery... as well as by discoveries in the science of agriculture” (Ricardo, 1817; 1951, p. 120). Thus, Ricardo saw technology as an essential determinant of the functional distribution of income, and to this would have to be added the social adaptation of the level of subsistence income if, during a process of expansion, workers became adjusted to a higher standard of living.

1.2.1.4 The Structure of Wages

In the classical theory of factor prices and the functional distribution of income, the fac­tors of production were mostly treated as homogeneous so that the analysis could be carried out at a high level of aggregation. At the same time, it was recognized that the assumption of homogeneity was a theoretical abstraction that was particularly severe when it came to the distribution of wage income because it was obvious that wages were not in fact uniform across different professions. There could in principle be two reasons for this. On the one hand, differences in wages could be caused by competitive forces. On the other hand, they could be caused by the absence of competition, either by private restraints on the process of competition or by government regulations, the “policies of Europe,” as Adam Smith used to call them.

Adam Smith’s competitive theory of the wage structure is now known as the theory of compensating variations. The general idea is that wages will reflect the particular circum­stances pertaining to different professions. For any particular line of work, these circumstances could be such as to imply that the wage is either above or below the average for all profes­sions. Smith mentioned several causes of wage inequality. One of these is the “ease or hardship” of the employment. Ablacksmith earns less in the course of a 12-h day than a miner does in 8 h, for the work of a blacksmith is less dirty and dangerous, and it is carried out in daylight and above the ground. Some professions are particularly honorable, and because honor is part of the reward, wages are correspondingly lower. Other professions are held in general disgrace, which has the opposite effect. The most detested of all workers is the public executioner, but relative to the hours worked, no one is better paid than he.

Smith also argued that wages will vary with how difficult and expensive it is to learn the profession, with “the constancy or inconstancy of employment,” and with the amount of trust placed in the worker. His fifth and final cause of wage inequality is the probability of succeeding in one’s profession. If one trains to become a shoemaker, it is virtually certain that one will be able to earn one’s living by making shoes. But if one is educated as a lawyer, Smith claimed, only one in 20 will be able to do well enough to live by it. To aim at the profession of a lawyer is accordingly a lottery, and because there are so few winning tickets, these must carry very high prizes. However, the wage differ­ences in this respect are in fact less than a rational consideration of the probabilities would imply because most people, and particularly the young, have a tendency to overestimate the probability of success. Smith suggested that this explains why so many of the young among “the common people” are ready to enlist as soldiers or go to sea.

Regarding the wage implications of education and training, Smith compared educa­tion to investment in machinery:

A man educated at the expence of much labour and time to any of those employments which require extraordinary dexterity and skill may be compared to one of those expensive machines. The work which he learns to perform, it must be expected, over and above the usual wages of com­mon labour, will replace to him the whole expence of his education, with at least the ordinary profits of an equally valuable capital.

Smith (1776; 1976, p. 118) This is a remarkable early statement of the main idea underlying human capital theory, which was yet to take almost 200 years to be developed more fully.

Smith’s theory of the wage structure is based on the assumption of perfect competi­tion or, in his terminology, “the system of perfect liberty.” But he recognized that this was not in every respect a realistic description of actual labor markets. The guild sys­tem that regulated the entry of labor into some occupations as well as government reg­ulations that limited the regional and industrial movement of labor could lead to wage differences that were larger than they would have been under perfect competition.

It is not entirely clear how the theory of the wage structure can be reconciled with the long-run tendency toward subsistence wages. Smith’s theory ofthe wage structure must obviously be interpreted as one of equilibrium wage differentials. But then, if the sub­sistence wage is to be interpreted as the average wage, some wages must be permanently below the subsistence wage, which hardly makes sense. On the other hand, if the sub­sistence wage is to be understood as a long-run minimum level, it must be the case that the average wage for all workers will actually be above the subsistence level, and this con­clusion is not easy to fit in with the classical theory of the long-run equilibrium theory of wages.

Smith’s theory of the competitive wage structure came in for a good deal of criticism and modification by a later generation of classical economists, in particular byJohn Stuart Mill (1848). Mill argued that although Smith’s theory might be a realistic one for the case of perfectly free competition with “employments of about the same grade” and “filled by nearly the same description of people,” this case is very far from the labor markets that one actually observes:

The really exhausting and the really repulsive labours, instead of being better paid than others, are almost invariably paid the worst of all, because performed by those who have no choice.... The more revolting the occupation, the more certain it is to receive the minimum of remuneration, because it devolves on the most helpless and degraded, on those who from squalid poverty, or from want of skill and education, are rejected from all other employments.

Mill (1848; 1965, p. 383)

Mill concluded that Smith’s hypothesis that wages tended to rise with the net disadvan­tages associated with different occupation was wrong, and that, on the contrary, the true relationship rather was one where “the hardships and the earnings” stood in an inverse relationship to each other. In a similar vein, John Cairnes (1874) coined the term “noncompeting groups” to describe a situation in which individuals in the labor market were prevented by lack of education and skills and the constraints imposed by their class background to compete for positions over a wide range of occupations. In other words, inequality of opportunity led to inequality of wages as well as of net advantages, i.e., wages adjusted to take account of other characteristics of the different employments.

1.2.1.5 TheLawsofDistribution

We have seen that the classical economists possessed a fairly sophisticated theory of the functional distribution of income. Their theory of the personal distribution was less advanced and restricted mainly to the framework of compensating wage differentials as developed by Smith and criticized by Mill. Regarding nonlabor income, their ability to analyze the personal distribution of income was limited by the absence of a theory of the distribution of ownership. A common attitude seems to have been that the distribu­tion of ownership to capital and land was determined by historical processes that lay out­side the scope of economic science. Thus, Mill claimed that in regard to the subject of Book I of his Principles, which is concerned with production, the “laws and conditions of the production of wealth partake of the character of physical truths.” By contrast, Book II on distribution is concerned with a subject of a quite different nature:

The distribution of wealth... depends on the laws and customs of society. The rules by which it is determined, are what the opinions and feelings of the ruling portion of the community make them, and are very different in different ages and countries.... But the laws of the generation of human opinions are not within our present subject. They are part of the general theory of human progress, a far larger and more difficult subject of inquiry than political economy.

Mill (1848; 1965, p. 200)

It is clear from the context that Mill meant this statement to apply to all aspects of the distribution of income and wealth. However, he was also careful to emphasize that although the causal factors behind the distribution of income had to be studied in a broad context, including noneconomic considerations, the consequences of different distribu­tional arrangements “must be discovered, like any other physical or mental truths, by observation and reasoning.”

1.2.1.6 TheMarxianPerspective

The basic structure of Karl Marx’s positive economic theory is consistent with the teaching of the classical economists, especially Smith and Ricardo. As in their work, his main interest in the theory of income distribution lay in the functional distribution of income and less in the distribution of income between persons. He adopted the the­ory of subsistence wages but added an additional component, which was absent in the work of Smith and Ricardo, viz, the existence of unemployment. According to Marx, even the subsistence level of wages would not be low enough to secure full employ­ment in the capitalist system, and the result of this was the development of what he named “the industrial reserve army” of the unemployed who live in extreme poverty and misery. He also argued that the existence of this reserve army is in fact in the inter­est of the capitalists. The reason is that there are significant fluctuations in economic activity that also imply large fluctuations in the demand for labor. The reserve army serves as a depository of labor on which the capitalists can draw without having to bid up wages, which they would have been led to do in a situation of full employment. Inequality and poverty therefore serve the interests of the ruling class, i.e., the capitalists.

Marx emphasized strongly that a central feature of the capitalist system was its ability to accumulate capital and generate economic growth. So what happens to the reserve army of the unemployed with the accumulation of capital? There are two effects that work in opposite directions. On the one hand, a more capital intensive technology increases the productivity of workers and tends to push wages up. On the other hand, the new technology also increases industrial concentration, and this effect lowers labor demand and pushes wages down. In the context of an increasing population, the net result of these effects may well be that employment increases, but the industrial reserve army will also increase, both in absolute and relative terms:

The greater the social wealth, the functioning capital, the extent and energy of its growth, and, therefore, also the absolute mass of the proletariat and the productiveness of its labour, the greater is the industrial reserve army. The same causes which develop the expansive power of capital, develop also the labour-power at its disposal. The relative mass of the reserve army increases therefore with the potential energy of wealth.

Marx (1867-1894; 1995, pp. 360-361)

According to Marx, therefore, and in sharp contrast to the view commonly held by the classical economists, unemployment was a permanent feature of the capitalist economic system and was central for a proper understanding of the distribution of income and wealth.

Apart from the emphasis on unemployment, a central concept of Marx’s analysis of the distribution of income is exploitation. At the bottom of this concept is the view that labor is the fundamental factor of production in the sense that all nonlabor inputs can be derived from past labor: “As values, all commodities are only definite masses of congealed labor time” (Marx, 1867-1894; 1995, p. 16). The worker’s productivity is a reflection of his labor-power. But he is only paid the subsistence wage, which is less than the value of what he produces. The difference between the two is the worker’s unpaid work for the benefit of the capitalist. This is the profit or surplus value that defines the capitalist’s exploitation of the worker.

Regarding the distribution of income from capital, a central element in Marx’s theory is the tendency—or the law, as he calls it—of the rate of profit to fall as capital accumu­lates. The effect of this would be to diminish the importance of capital income. On the other hand, Marx also believed that this would go together with increasing concentration in industry and a strengthening of the monopoly element in capital income, and this would serve to counteract the first effect. Monopoly also explains his emphasis on abso­lute rent in addition to the Ricardian differential rent. Absolute rent arises because the absence of competition in landed property prevents rent from being brought down to zero on land at the margin of cultivation.

Marx did not limit himself to the presentation of his arguments in terms of abstract reasoning but also provided vivid examples of the living conditions in contemporary industrial society, above all in England where he lived during the last three decades of his life and where he wrote Capital. In this he was also able to draw on the insights and knowledge of his friend and collaborator Friedrich Engels. Engels’s study of the condi­tions of the English working class (Engels, 1845) provided important material for Marx’s own work, but is also a significant contribution in its own right. Engels, who worked as a manager in an industrial firm in Manchester that was partly owned by his father, was appalled by the living conditions of the workers that he saw in the industrial towns in England. In his book, he attempted to give a detailed description of their incomes, hous­ing, and health, arguing that at least at this stage of the Industrial Revolution, workers were worse off than they had been before. He based his work both on his own obser­vations and on various contemporary reports, and the book is notable for its extensive use of statistical data to describe social and economic conditions among the working­class poor.

1.2.2 Neoclassical Economics: The Marginalist Approach to the Distribution of Income

The marginalist revolution and the birth of neoclassical economics marked a new style of economic theorizing in which, in contrast to the classical writers, the new generation of economists attempted to anchor their analysis in the behavior of individual economic agents, using the theory of optimization and the mathematical tools of the differential calculus. But it also marked a new view of the workings of the market economy. Par­ticular stress has traditionally been laid on the greater attention to demand as a determi­nant of prices, but the differences were also substantial when it came to the study of income distribution. Toa large extent, the development of a new approach to income distribution was driven by the internal logic of theoretical innovation, but there can be little doubt that it was also motivated by the social and economic development that became increasingly visible toward the end of the nineteenth century. As an example we may take Leon Walras, who criticized Malthus for the lack of logic in his theory of population, in particular for his neglect of the role of technological progress. He also pointed out the failure of Malthusian theory to explain the actual increase in living stan­dards for all classes in society. Thus, after having been impressed by the progress dem­onstrated at the World Exhibition in Paris in 1867, he wrote an article where he emphasized the benefits that advances in technology had brought to the working class and confronted them with the “ridiculous theory” of Malthus, predicting the workers’ eternal poverty and misery.

1.2.2.1 The Marginalist Revolution and Its Forerunners

Although the marginalist revolution is usually identified with the early 1870s, there were important forerunners of neoclassical economics who in some respects were actually more advanced in their analytical approach than their successors. Foremost among the early champions were Johann Heinrich von Thiinen and Herrmann Heinrich Gossen in Germany and Antoine Augustine Cournot and Jules Dupuit in France. In the present context, it is von Thiunen and Gossen that have a special claim to our attention.

Von Thunen’s main work Der Isolierte Staat (The Isolated State, 1826, 1850) is remark­able in this connection particularly for his early formulation of marginal productivity the­ory, which he applied both to capital and labor use. Thus, for a producer who attempts to maximize profits, he derived the conditions that the value of the marginal productivities of labor and capital must be equal to the wage rate and interest rate, respectively, and he used this approach to study geographical variation of the choice of capital intensity in a spatial economy. Von Thiunen considered the result of equality between marginal value productivities and factor prices also to be a theory of income distribution, but as such it is obviously incomplete in that it takes no account of the supply side of factor markets, thus leaving the formation of factor prices unexplained (except for the special case where fac­tor supplies are given). Nevertheless, this was an important building block for the theory of factor prices that was to be developed later.^[14]

Hermann Heinrich Gossen’s long-neglected book on economic theory (Gossen, 1854) is famous mainly for its early formulation of the theory of the utility-maximizing consumer and its derivation of “Gossen’s law” that at the optimum the ratio between marginal utility and price must be the same for all consumer goods. In the central version of his theory, income is taken as given so that it does not include any theory of factor supply, but he did in fact present an extension of his model in which he claims that the supply of labor can be derived from the condition that the marginal utility of con­sumption is equal to the disutility of work. Together, von Thilnen and Gossen provided important elements for the theory of factor price formation and income distribution, but it was yet to take a long time before their approach had been developed into a logically consistent theory of income distribution.

What historians of economic thought commonly refer to as the marginalist revolution is associated with three authors and three books: William Stanley Jevons’s Theory of Polit­ical Economy (1871), Carl Menger’s Grundsbtze der Volkswirtschaftslehre (1871), and Leon Walras’s Elements d'economie politique pure (1874-1877). The central concern of the three main protagonists of the marginalist revolution in the 1870s was to establish the theory of subjective value as the main causal factor for the understanding of price formation. This led them to focus first of all on the determination of prices for consumer goods, but they also extended the theory to apply to the formation of factor prices. The equality of mar­ginal value productivities and factor prices as following from profit maximization is particularly explicit in Walras (1874-1877; 1954, Lesson 36). Walras also emphasized that a theory of the average rate of wages—which he considered to be the main focus of the classical economists—is not very useful; the analysis of wages must be based on a disag­gregated view of the labor market with occupation-specific wage rates. However, neither Walras nor the other two went very far in the analysis of income distribution. Although they considered the application of the marginalist method to the analysis of wages and interest rates, they did not proceed to a study of how the theory could be used to explain inequality in society. For this we have to wait for the work of a later generation of mar­ginalist or neoclassical economists, and in the coming decades, a number of writers made important contributions. Here, we shall focus on the work of Alfred Marshall and Knut Wicksell, who both in different ways left their mark on the development of economics during the next century.

1.2.2.2 Alfred Marshall

The contrast between the work of Leon Walras and Alfred Marshall has frequently been characterized as that between general and partial equilibrium theory. That is clearly true regarding their style of theoretical analysis. But in addition, it is striking how much their great treatises differ with regard to the reliance on institutional and empirical material. Thus, when Marshall approached the issue of what determines the demand for labor, he did it by way of a numerical example in which a sheep farmer decides how many shep­herds to hire at a given rate of wages, hiring more workers as long as an additional shep­herd’s marginal value product exceeds the wage rate. He emphasized that the theory that “the wages of every class oflabor tend to be equal to the net product due to the additional labor of the marginal laborer of that class” does not in itself constitute a complete theory of wages because a number of other aspects both of factor and product markets need to be taken into account.^[15] On the other hand, “the doctrine throws into clear light the action of one of the causes that govern wages” (Marshall, 1890; 1920, p. 518).

As Walras before him, Marshall also argued that phrases such as “the general rate of wages” were apt to be misleading, for

... in fact, there is no such thing in modern civilization as a general rate of wages. Each of a hundred or more groups of workers has its own wage problem, its own special set of causes, nat­ural and artificial, controlling the supply-price, and limiting the number of its members; each has its own demand-price governed by the need that other agents of production have of its services.

Marshall (1890; 1920, p. 533)

There is an interesting contrast here to the work of Adam Smith and John Stuart Mill in that the wages of labor are analyzed from the start within the framework of multiple (although interrelated) labor markets, whereas the classical economists discussed the gen­eral rate of wages, later adding on a somewhat ad hoc discussion of wage differentials. The supply and demand framework instead provided a general approach to the study of wage formation, which could be used to analyze both the general level of wages (assuming, contrary to Marshall, that there is such a thing) and the wage differentials between occu­pations. However, Marshall also discussed the theory of compensating wage differentials, blending elements from the partially conflicting views of Smith and Mill.

Although Marshall must clearly be considered to be one of the founding fathers of the marginal productivity theory of wages,^[16] his theoretical perspective was much wider than this terminology may indicate. Among his significant theoretical innovations in the study of wages and the distribution of labor income should be counted his early formulation of the theory of human capital. He noted that

[t]he professional classes especially, while generally eager to save some capital for their children, are even more on the alert for opportunities of investing it in them.

Marshall (1890; 1920, p. 533)

Although investment in children by means of education and training will increase their productivity and thereby their opportunity to earn good wages, there are some serious imperfections in the market for human capital. One of these is the weakness of employers’ incentives to invest in human capital. This capital becomes the property of the worker, so that the employer’s opportunities of reaping the gains of any investment that made in the worker is severely limited, hence arises the crucial role of the parents, which is limited by “their power of forecasting the future, and by their willingness to sacrifice themselves for the sake of their children” (Marshall, 1890; 1920, p. 561). But although the parents play an important role in overcoming the adverse incentives of employers, this role has also other and more unfortunate consequences. Because the opportunities and insights of the professional classes are not shared by the members of the “lower ranks of society,” their investment in their children is inadequate, and this evil is cumulative:

The worse fed are the children of one generation, the less will they earn when they grow up, and the less will be their power of providing adequately for the material wants of their children; and so on to following generations.

Marshall (1890; 1920, p. 562)

Another point that Marshall repeatedly stressed is the dependence of productivity on wages. High wages lead workers to be better fed and better educated and so increase their productivity. Marshall suggested that this mechanism may be an important part of the explanation of the historical increase in wages, contrary to the predictions of at least the simple version of the Malthusian theory.

Both his emphasis on a disaggregated view of the labor market and his early insistence on the importance of human capital and efficiency wages make Marshall a very important contributor to the theory of income distribution, at least as regards the distribution of labor income. About the distribution of income from capital he has less to say. He applied marginal productivity theory to the study of the rate of interest, but because he did not offer any theory ofthe distribution ofthe ownership of capital (and land), the distribution of income from capital becomes an unsolved issue. The contrast to labor income is an interesting one: Because the discussion of the marginal productivity of labor is usually framed in the context of man-years of labor (as in the shepherd’s example), and because the measurement of the distribution of labor earnings uses annual income as its basis, the distribution of wages becomes identical to the distribution of earnings. Thus, the mar­ginal productivity theory becomes a much more important element in the theory of the distribution of labor income than in the study ofthe distribution ofincome from capital.^[17]

1.2.2.3 Knut Wicksell

The Swedish economist Knut Wicksell is an important figure in the history of the mar- ginalist revolution and the rise of the neoclassical school of economic theory. Whereas the earlier marginalists—apart from von Thiinen—had focused most of their attention on the analysis of consumption, Wicksell’s main interest was in production and investment decisions. It is worth noting that his initial interest in economics was kindled by his concern for social problems and the issues raised by unchecked population growth. In Volume 1 of his Lectures on Political Economy (1901-1906), he argued that virtually every problem in economics had to be studied in the context of a changing population; however, the population issue in fact plays relatively little role in his more formal aca­demic writing.

Wicksell is especially well known for the first clear and precise formulation of the production function as a central tool in the analysis of production and investment deci­sions (including the original introduction in economics of what became known as the Cobb-Douglas function). He made explicit the idea of factor substitution, and the assumption of continuous substitution between factors of production was adopted by later economists as a defining characteristic of neoclassical economics. In a more rigor­ous fashion than his contemporaries, he showed that profit maximization involved the equality between marginal value products and factor prices. Like Marshall, he stressed the incompleteness of marginal productivity theory as a theory of income distribution because it did not take the supply side into account. He did not really manage to integrate supply and demand in a formal analysis of income distribution, but in his dis­cussion of practical issues, he showed a clear understanding of the nature of their inter­action. Although he emphasized the role that technological progress had played in increasing the marginal productivity of labor, he held the view—in sharp contrast to Walras—that it was doubtful whether real wages had shown any increase during the preceding 200 years, whereas rent in his opinion had “successively doubled and redoubled.” The explanation for this he found in the growth of population during the same period:

Such an increase [in population] must, other things being equal, continually reduce the marginal productivity of labour and force down wages; or—what comes to the same thing, though the connection is easily overlooked on a superficial view—prevent the otherwise inevitable rise in wages due to technical progress.

(Wicksell (1901-1906; 1934, p. 143)

As a purely theoretical proposition, this statement shows a very clear understanding of the respective roles played by supply and demand in the determination of wages. On the other hand, its empirical connection with actual economic developments during WickselTs lifetime is highly questionable and can only be interpreted as being strongly colored by his neo-Malthusian convictions.^[18]

A further important theoretical issue in the neoclassical analysis of production and distribution concerns the problem of product exhaustion: Would the payments to the factors of production according to marginal productivity theory exhaust the value of output? Earlier, Philip Wicksteed (1894) had shown with reference to Euler’s theorem of homogeneous functions that this would happen if firms’ production functions were linearly homogeneous. The problem with this application of the theorem was that it implied constant marginal and average cost, so that the scale of production for each firm was indeterminate. Wicksell pointed out that the problem would be solved by the assumption that production functions went through phases of increasing, constant, and decreasing returns to scale. This corresponds to the case of an average cost function, which first decreases and then increases. At the minimum point of the U-shaped cost curve there are constant returns to scale, and this is in fact the point to which the long- run equilibrium of the industry will converge, given the assumption of free entry. Fac­tor prices correspond to marginal value productivities, and the payments to the factors of production exhaust the value of the product with pure profits being zero. But even in the case where product prices are given, as when they can be taken to be determined in world markets, this theory of distribution is incomplete in the absence of a theory of factor supply.

1.2.2.4 General Equilibrium Theory

The work of the neoclassical economists—from that of the early pioneers to the first and second generation of the marginalists in the closing decades of the nineteenth century— became consolidated in the later version of the theory of general equilibrium that was developed around the middle of the next century. The main achievements of this development have often been associated with the introduction of new methods of math­ematical methods in economics and with the analysis of existence and stability of equi­librium, but in a broader perspective one must also include the deeper understanding of the general interdependence in the economy that it led to. A particularly important aspect of this interdependence was the relationship between the prices of consumer goods, fac­tor prices and the distribution of income and wealth. But the connection between resource allocation and the distribution of income was not given much attention in mod­ern general equilibrium theory; in the influential presentation of the theory by Debreu (1959), the term distribution does not even appear in the index. In one respect, however, the modernized version of the Walrasian system provided a more satisfactory treatment of distribution. Dalton (1920) had criticized the marginal productivity theory of distribution for not giving a satisfactory account of the distribution of income from capital and land. The theory treated only the determination of the rate of interest and the rent from land, but the distribution of capital and rental incomes had to be concerned with the interest rate times the ownership of capital and with the rental rate times the holdings of land.^[19] This shortcoming of the theory is resolved in the modern theory by the introduction of the notion of endowments. Consumers are assumed to be endowed with initial resources (in principle both consumer goods and factors of production) as well as shares of the profits of the different firms in the economy, so that prices do indeed determine the dis­tribution of income or wealth. On the other hand, part of Dalton’s criticism remains valid because endowments and profit shares are taken to be exogenous, and no account is provided of their origin.

One reason why the new mathematical formulation of general equilibrium theory paid little explicit attention to the problem of income or wealth distribution was that in its ambition to achieve a high degree of generality, it rid itself of the distinction between consumer goods and factors of production. Formally, consumer goods were defined as commodities that entered the budget constraints as positive numbers, whereas factors of production were commodities represented by negative numbers. Moreover, the focus of the theory was on the competitive case, so that there was no scope for treating the formation of factor prices, e.g., wages, as being any different from the formation of prices for consumer goods. Labor was just like any other commodity and wages no dif­ferent from all other prices.

In applications of the general equilibrium framework the situation was different. In international trade theory, the effect of international trade on the domestic distribution of income had long been a central focus of the theory, and in the 1940s and 1950s, the anal­ysis of the connection between the prices of factors and goods moved to the forefront of the theoretical development in the field; the classic contributions were Stolper and Samuelson (1941) and Samuelson (1953). The focus of this literature was on the func­tional distribution of income, in particular on the shares of labor and capital, whereas the analysis of the personal income distribution was mostly by implication, as in the study of sectoral shifts following changes in world market prices.

Another field in which one might expect the general equilibrium framework to be important for the study of income distribution is public economics. But this has hardly been the case. One explanation for this is that in contrast to international trade theory, public economics has always had a strong concern with the effect of taxes on factor sup­ply, whereas in international economics one has often been content with assuming factor supplies to be given. The extension of the framework of analysis to incorporate variable factor supply leads to significant complications, and this may be the main reason why the best-known use of the general equilibrium approach in public economics is Harberger’s (1962) analysis of the incidence of the corporation income tax. Harberger’s model turned out to be a fruitful one for analyzing a number of problems in tax incidence analysis. On the other hand, the reason why it was easy to use was precisely because, in analogy with international trade theory, it ignored the study of the effects of taxation on the supply of capital and labor, issues that have otherwise been treated as central in the theory of public economics.

1.2.2.5 Imperfect Competition

The early neoclassical economists and the later general equilibrium theorists focused their analysis of the market economy on the case of perfect competition. In the case of the labor market, the assumption was that both workers and employers took the equilibrium mar­ket wage as given, whereas the forces of competition made any out-of-equilibrium wage rate adjust until the supply of labor was equal to demand. It was within this framework that theorists discussed the dual role of wages—and more generally of factor prices—in allocating factors of production among alternative uses and determining the distribution of factor incomes.

That the case of perfect competition was not a realistic one particularly in the labor market was already acknowledged by Adam Smith in his discussion of the determinants of wages (Smith, 1776, Book I, Chapter VIII). He emphasized that wages are influenced both by private and public restraints on competition. The guild system limits the access to certain occupations and thereby pushes up the level of wages relative to that of other lines of employment, and the government tolerates these regulations. Another point that he makes is that in bargaining over an employment contract, the natural advantages are with the employers. There are fewer employers than workers, so that it is easier for the employers to collude to keep wages low than it is for workers to combine to push wages up. Smith wrote long before the time of strong trade unions, and he remarked that although there are many laws that forbid workers to organize themselves for the purpose of obtaining higher wages, there are none that prevent employers in colluding for the opposite purpose. He also pointed out that if a conflict occurs, the employers can hold out much longer than the workers. A factory owner will often be able to live well without workers for a year or two, whereas a worker will find it difficult to survive for a week or a month if not employed. The implication is evidently that in many labor markets wages will be lower than they would have been in a situation of perfect competition with bar­gaining power being symmetrically distributed.

It took a long time before Smith’s insights were taken into account in the neoclassical theory of the market economy. Pigou’s Economics of Welfare (1920) discussed the func­tioning of the labor market with careful attention to the role of various institutions that interfere with competition in one way or the other. Because the relationship of the parties in the labor market is one of imperfect competition, there is an unavoidable indetermi­nateness in regard to the level of wages. In Appendix III to his book (Pigou, 1920; 1952, pp. 813-814), he provided a diagram that shows the deviation of the equilibrium wage from the competitive level,^[20] but he did not attempt to identify exactly what determines the imperfectly competitive wage level.

The year 1933 saw the publication of the two books that moved the concepts of monopolistic and imperfect competition into the core of economic theory. The Theory of Monopolistic Competition by Edward Chamberlin had its focus on the markets for con­sumer goods, whereas Joan Robinson’s Economics of Imperfect Competition also contained an analysis of imperfectly competitive labor markets with obvious implications for the distribution of income (which, however, she did not discuss except in passing). Pigou’s indeterminateness was removed by the assumption of completely asymmetric bargaining power by the two parties to the labor contract: Employers were assumed to be mono- psonists, and workers took wages as given. This led to an equilibrium in which wages were in general below the level of the marginal value products, with the gap between them reflecting the elasticity of supply. The larger the value of the elasticity of supply, the smaller would be the gap between the two, and the less would be the degree of exploitation. The implications of imperfect competition in the labor market were also considered by Hicks (1932), whose book among a number of other issues also contained an extensive discussion of the role of trade unions. In regard to the theory of income distribution, however, Hicks’s main interest was in the functional rather than the personal distribution of income. Thus, one of his most influential contributions in the book was the analysis of the effects of various types of technical progress on labor’s share of national income.

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The general indeterminateness of the outcome of wage bargaining, which was stressed by Pigou, also played a central role in the theory developed by the Danish econ­omist Frederik Zeuthen in his book Problems of Monopoly and Economic Warfare (1930).^[21] His theory is set in the framework of a bilateral monopoly model in which a firm bargains with a trade union and where neither party has any outside option; the employer has no alternative use of his capital, and workers have no alternative employment opportunities. While recognizing the basic indeterminacy of the equilibrium solution, Zeuthen explored the factors that would determine the features of the bargaining process and the likely outcome. Both parties realize that failure to reach agreement will result in a conflict—a strike or a lockout—that will be costly to both of them. Zeuthen saw the bargaining process as a series of proposals and counterproposals, where proposals of high wages would make employers willing to risk a conflict, and this would put downward pressure on wages. Proposals of low wages, on the other hand, would make the union more willing to risk a conflict and thereby tend to push wages upward. At some inter­mediate wage level, both parties will consider the risk of pushing for a better alternative to be equally large, and this will be the equilibrium wage. Zeuthen’s theory was an impor­tant contribution to better understanding of the role of bargaining and labor conflicts and a significant extension of the neoclassical theory of labor markets and income distribution.^[22]

1.2.2.6 Human Capital Theory

An unsatisfactory aspect of the marginal productivity theory of distribution—quite apart from its neglect of the supply side of factor markets—was that it offered little explanation of why some factors of production were more productive than others. One might argue that this was simply a question of technology and the way that factors were combined in the production process, but particularly in the case of labor, it is hard to escape the belief that some individuals are in some sense inherently more productive than others. How­ever, some of the differences in productivity might be due to education and training. This point was already made by Adam Smith, and we have also seen that Alfred Marshall sug­gested a possible explanation for this in the investment that parents made in their children, both with the time that they themselves devoted to them and with the resources that they spent in giving the children a good education. This would result in higher wages for the children who benefited but possibly also in increased inequalities of wage income.

Another writer who pursued the idea of investment in human beings was the German statistician Ernst Engel. In his 1883 book on the cost value (Kostenwerth) of human beings, he calculated the cost of training a boy to practice his father’s profession in the lower, middle, and upper classes of society (corresponding to lower, middle, and higher education).^[23] However, he did not have a theoretical framework that allowed him to explore the analogy between investment in human and physical capital, and he did not discuss the implications of his approach for the distribution of income, implicitly rul­ing out the possibility of mobility between income classes.

In the twentieth century, the ideas of Smith and Marshall were taken up by the economists of what came to be called the human capital school. Although important contributions were made by Theodore Schultz (1961), the theoretical foundations were laid by Gary Becker (1962, 1964). In particular, Becker’s 1964 book marked the begin­ning of an extremely influential line of research, which also took up important issues regarding the distribution of income. As set out in Becker and Chiswick (1966), the amount of investment in human capital at the individual level is determined by the intersection of the supply and demand curve (or the marginal benefit and the marginal cost curve). Both supply and demand curves must be expected to vary among individ­uals. Different supply curves may reflect the income and wealth of parents and access to capital markets, whereas the position of the demand curve may represent individual characteristics like inherent ability and attitudes to risk. In Becker and Tomes (1979), the framework is extended to an intergenerational setting where children’s endowments are partly determined by the investments made in them by their parents. This is clearly related to the ideas of Marshall regarding the long-term effects of invest­ment in children.

As with all theoretical innovations, the growth of the human capital field can to some extent be explained by developments internal to the discipline of economics. However, it is also natural to point out explanations that reflect changes in the econ­omy. Studies of economic growth had led to increased attention to changes in the effi­ciency of labor as a determinant of growth. Perhaps, more to the point in the present connection are the consequences of an increasing level of education in the labor force, which made the distinction between income from capital and labor seem a less central element in a realistic theory of income distribution. A society in which an increasing number of workers had become human capitalists required a new perspective on the distribution of income.

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1.2.2.7 Risk Taking and Income Distribution

The difference of riskiness of income between occupations figured as one element in Adam Smith’s theory of compensated wage differentials. In the choice between a safe and a risky occupation (shoemaker and lawyer in Smith’s example), the expected wage in the risky occupation would have to be higher than in the safe one to compensate indi­viduals for their additional risk bearing. To the extent that individuals assessed the prob­abilities correctly, these ex ante expectations would be translated into ex post income inequality: The incomes of lawyers would have a higher average but greater variance than the wages of shoemakers.

The possibility of formal modeling of choice in risk-taking situations was greatly stimulated by the axiomatic foundation of expected utility theory developed by von Neumann and Morgenstern (1947). Although it took some time for the theory to find applications in the analysis of real economic problems, its use in the theory of income distribution was one of the earliest. The classic article in the field is by Milton Friedman (1953), who used his earlier work with Leonard Savage (Friedman and Savage, 1948) to explain income distribution as the result of rational choice under uncertainty. A distinctive feature of the Friedman-Savage theory is the assumption that they make about attitudes to risk. Although the assumption of risk aversion is a natural one for explaining real-world features like portfolio diversification and insurance, it does not explain the simultaneous existence of gambling. To resolve this difficulty, Friedman and Savage assumed that the utility function of income had both concave and convex segments, i.e., ranges of both decreasing and increasing marginal utility. In Friedman’s income distribution theory, individuals at the beginning of their lives choose between alternative income streams; at the level of abstraction of Friedman’s analysis, these streams could be generated from labor as well as capital income. Although individuals have equal opportunities ex ante, the income lotteries in which they engage imply that some will find themselves ex post with high incomes, and some will end up in low-income groups. The special shape of the utility function gives rise to a distribution of income that, Friedman argued, is consistent with observed patterns, in particular as documented in his own empirical work with Kuznets (Friedman and Kuznets, 1945). He also argued that indi­viduals will be motivated as participants in a democratic society to introduce redistrib­utive mechanisms that insure them against the consequences of the most adverse outcomes. According to this theory, therefore, both income inequality and redistributive policies emerge as results of individuals’ free choice in a situation of equality of oppor­tunity and will reflect their attitude to risk, in particular the relative importance of risk averters and risk lovers. The less risk-averse individuals are, the greater will be the inequality of income in society.

A further development of this framework is due to Kanbur (1979), whose analysis builds on a much more specific structure than that used in Friedman’s article. In Kanbur’s framework, risk-averse individuals choose between the safe occupation of a worker and the risky occupation of an entrepreneur. In equilibrium, the two occupations must be equally attractive, i.e., have the same expected utility, and this implies that the expected income of the entrepreneur must be higher than that of the worker. Kanbur explored the comparative statics of the model and showed that when account is taken of general equi­librium effects on the distribution of individuals between occupations, there is no longer any simple connection between risk aversion and inequality. In a companion paper, Kanbur (1981) studied the role of taxation in the determination of the equilibrium dis­tribution of the population between the two occupations.

On this point, Kanbur’s study is related to the older analysis of taxation and risk taking that goes back to the classic article by Domar and Musgrave (1944). Their analysis of a model of portfolio choice showed that under certain assumptions, particularly that of full loss offset, income taxation induces individuals to take more risk than they otherwise would have done. Their choice of more risky portfolios obviously has the implication that their wealth ex post will have a larger variance than it would have had in the absence of income taxation. With full loss offset, income taxation functions in part as insurance against variations in capital income, and this insurance acts as an encouragement to risk taking. Ex post, therefore, one would expect higher taxation to generate more inequality in the distribution of income from capital.

1.2.3 NonmarginalistApproaches

The marginalist revolution of the 1870s left its mark on the style of economic theorizing for a long time; indeed, it remains a dominating influence on contemporary economics. As we have seen, it also played a central role in the theory of income distribution. But at the same time, other contributions were made that do not easily fit into the marginalist framework. A common feature of the alternative approaches is that they pursued an inductive rather than a deductive line of investigation. Some of these will be discussed later.

1.2.3.1 Statistical Approaches: The Pareto Distribution

Although the marginalist theory held out the promise of a theoretically more firmly based theory of the personal distribution of income, the late nineteenth century also saw the introduction of a more inductive theory of income distribution, founded not on a priori theorizing but on inference from statistical data. The pioneering contribution was due to Pareto, whose work caused a good deal of discussion and controversy during several decades after its initial publication.

Vilfredo Pareto was Walras’s successor in the chair of economics at the University of Lausanne. Like Walras, he was a firm believer in the mathematical method, and he saw it

¹⁴ The Domar-Musgrave article did not use the expected utility hypothesis. For a reformulation and sharp­ening of their theory along expected utility lines, see Mossin (1968).

as his main task to extend and refine the general equilibrium approach that Walras had developed, including the theory of factor price formation. When it comes to income dis­tribution, however, Pareto’s fame rests not on his refinements of Walrasian theory but on his formulation of what has become known as Pareto’s law.^[24] Many economists only know Pareto from footnotes in textbook treatments of utility theory and welfare eco­nomics and may be forgiven for thinking of him as a pure theorist. But Pareto was an immensely productive researcher who wrote on a wide variety of topics, both theoretical and empirical, and not only in economics. He is a significant figure in the history of soci­ology and wrote also on statistical theory, economic history, and political science. His studies of income distribution, set out in a number of articles and in his book Cours d'econ- omie politique (Pareto, 1896-97) drew on his knowledge both of economics and mathe­matical statistics and, in the matter of interpretation, also on his insights in sociology.

What posterity has come to know as Pareto’s law was not derived from a theoretical model; instead, it was based on a detailed study of incomes statistics for a number of coun­tries and time periods. Pareto’s analysis of these data led him to the hypothesis that all statistical income distributions have a common shape that one can characterize as follows. Suppose that we draw up a list of all incomes in society from the lowest to the highest. Starting from the median income, we know that 50% of the income earners have an income above the median. We then move up to a level ofincome that is 1% higher than the median and ask what percentage of the population has an income above this level. Obviously, the percentage is validity for his law. Such a claim naturally proved provocative to many who believed that governments should see it as one of their objectives to bring about a more egalitarian distribution of income. On the one hand, Pareto seemed to claim that the dis­tribution of factor incomes was given; on the other hand, he also went out of his way to point out that, given the skewness embedded in the Pareto distribution of incomes, pro­gressive taxation could only be counted on to provide a rather insignificant redistribution of income in favor of the poor. This was seen by many as proof of Pareto’s alleged reac­tionary attitudes, although this view is not supported by statements such as

... even with taxes at an equal percentage of incomes, the rich contribute far less to public expen­ditures than the poor, whereas they benefit much more from them. For whom, if not for the vain rich, are funds expended on armaments and the like?

Pareto (1895); quoted from Chipman (1976, p. 115)

However, it was the early presentation of Pareto, rather than his later and more cautious statements, that caught the attention of other economists, and a considerable amount of work was devoted to examining and criticizing his law of income distribution. Thus, in his Economics of Welfare (1920), Pigou devoted a whole chapter (Part IV, Chapter II) to a critical examination of Pareto’s law. In the preceding short chapter, Pigou had sketched the principles underlying the equity-efficiency trade-off (to use a more modern expres­sion), arguing from a utilitarian perspective that any cause that increases the “national dividend” without lowering the absolute share of the poor, or increases the absolute share of the poor without reducing the national dividend, must increase welfare. By contrast, the welfare effect of any measure that increases one of these quantities but diminishes the other is ambiguous:

Plainly, when this kind of disharmony exists, the aggregate effect upon economic welfare, brought about by any cause responsible for it, can only be determined by balancing in detail the injury (or benefit) to the dividend as a whole against the benefit (or injury) to the real earnings of the lower classes.

Pigou (1920; 1932, p. 645)

Pigou then went on to point out that, according to one “interesting thesis,” there was no need to be concerned about these cases of disharmony: Pareto’s alleged law of income distribution implied that because the relative shares of the different income groups were at least approximately constant, the only way to ensure an increase in the absolute share of the poor was to increase the national dividend. Pigou was clearly skeptical of the con­clusion and also expressed strong doubts with respect to several aspects of Pareto’s work. He criticized the empirical basis for Pareto’s generalization, but a more important point that he raised concerns the basis for assuming a given distribution relating to all sources of income. Pareto’s distribution is skewed to the right, and Pigou argued that in the case of labor income one would rather like to assume that the distribution of “capacities” follows the normal distribution.^[25] He also pointed out, however, that capacity is a multidimen­sional concept, and that although manual and mental capacity might both be normally distributed, their joint distribution would not be, and this fact might go some way toward explaining the form of the Pareto distribution. On the other hand, the reference to capac­ity, whether manual or mental, does not explain the distribution of income from capital or property, which is largely determined by inheritance, the importance of which depends in a crucial manner on the nature of legal and political institutions. The view that the distribution of income, and in particular the share of the poor, cannot be affected by measures of economic policy therefore becomes untenable.

Toward the end of the chapter Pigou quotes Pareto as remarking about his own dis­tribution that

[Some] persons would deduce from it a general law as to the only way in which the inequality of incomes can be diminished. But such a conclusion far transcends anything that can be derived from the premises. Empirical laws, like those with which we are here concerned, have little or no value outside the limits for which they were found experimentally to be true.

Pigou (1920; 1932, p. 655)

So it appears that Pigou’s criticism of Pareto to some extent missed its target. That it still was felt to be necessary to devote a chapter to it in 1920 must be explained by the popular attention that Pareto’s original formulation had attracted. The idea that the distribution of income was determined by a sort of immutable law appeared to have far-reaching con­sequences for the feasibility—or rather infeasibility—of redistributive policies.

Pigou was not the only economist to be critical of Pareto’s law of income distribution. Edgeworth (1896) at an early stage of the debate argued that Pareto’s contribution bore strong similarities to previous work by the English statistician Karl Pearson. Pareto reacted strongly to what he saw as an accusation of plagiarism and gave a heated reply in which he remarked that “it must have displeased Mr. Edgeworth to see me poach on territory which is apparently reserved for Professor Pearson, just as political economy is reserved for Professor Marshall” (Pareto, 1896). Further exchanges did little to soften the tone of the debate, and as late as 1926, 3 years after Pareto’s death, Edgeworth wrote about Pareto’s reaction that it “is of interest as throwing light not only on the character of the curve, but also on that of its discoverer” (Edgeworth, 1926; 2003, p. 492).

Pareto’s formulation of his law as well as the later controversies to which it gave rise constitute an interesting episode in the history of economic thought, and the Pareto dis­tribution continues to play a role in the empirical study of income distribution. Although it has received a good deal of criticism, it has also been hailed as a milestone in the empir­ical study of income distribution.^[26]

1.2.3.2 Other Statistical Approaches

The tradition established by Pareto’s work to look for regularities or empirical laws in the distribution of income was continued by a number of later writers. A characteristic feature of this literature is that the authors do not attempt to found their hypotheses on the neoclassical theory of factor market equilibrium but start instead from some observed empirical regularity, just as Pareto did. Just a few examples of this approach will be given here.

Roy (1950, 1951) claimed that observed earnings distributions could be reasonably approximated by the lognormal distribution and argued, echoing Pareto, that “[t]here must be some rational explanation of the fact that all these earnings’ distributions have such similar shapes” (Roy, 1950, p. 490). He attempted to discover this explanation by studying a number of industrial cases in which workers performed a standard and iden­tical task and where individual output was easy to measure. These included tasks like packing boxes of chocolate, stitching shoes, and pressing gramophone records. Alto­gether, for the 12 different cases studied, it turned out that the lognormal distribution performed slightly better than the normal. To the extent that people are paid according to output, this result could go some of the way toward explaining the earnings distribu­tion in terms of the distribution of individual skills. In Roy (1951), he studies the the­oretical case of a “primitive” society in which people can choose to work in two or more occupations and where their skills differ between occupations. He then discussed how different skill correlations give rise to different statistical earnings distributions (always assuming that earnings are proportional to output), emphasizing the central role played by the lognormal distribution. Champernowne (1953) considered a dynamic model in which it is assumed that every income earner has a probability of a rise or fall in income between one period and the next, which is proportionate to his income in the first period. He showed that over time this will result in convergence toward the Pareto distribution. In a comment on this article, Lydall (1959) argued that this stochastic process was implau­sible for labor incomes and showed that the Pareto distribution could be generated on the alternative assumption that in an industrial firm each supervisor controls the same number of persons and is paid according to the total income of those below him. A similar assumption about the pyramidal structure of organizations was employed by Herbert Simon (1957) in his analysis of the compensation of executives.

A different and more macroeconomic approach was taken by Kuznets (1955), whose goal was to explain the long-term trends in the inequality of income in the economy as a whole. Although on the basis of data for the United States, England, and Germany, he found that income inequality had decreased after the end of the First World War, he suggested that this period had been preceded by one of increasing inequality. In his view, the period of widening income gaps began with the Industrial Revolution in the late eighteenth century; for England he suggested that it ended around the middle of the nineteenth century and for the others a few decades later.¹ His explanation for this development was based on the shifts from the agricultural or traditional sector of

¹⁸ Setting the date of the change from the first to the second phase at roughly 1850 for England, Kuznets suggested that Marx’s view of the inevitable rise of inequality of income under capitalism may have been an overgeneralization from observations of the last stages of the first phase. the economy to the nonagricultural or modern sector, where income from capital plays a larger role for the distribution ofincome. Initially, inequality is larger in the modern sec­tor than in the traditional one, and this generates an increased inequality of income for society as a whole as the modern sector expands. Over time, however, as the modern sector becomes more mature a variety of forces combine to reduce inequality there, par­ticularly through an increased share of the lower-income groups and a lowering of the income from capital. Consequently, overall inequality diminishes. In his own words:

One might thus assume a long swing in the inequality characterizing the secular income structure; widening in the early phases of economic growth when the transition from the pre-industrial to the industrial civilization was most rapid; becoming stabilized for a while; and then narrowing in the later phases.

Kuznets (1955, p. 18)

This hypothesis is what has become known as the Kuznets curve in the form of a bell­shaped curve describing the relationship between per capita income and the degree of inequality. It should be emphasized, however, that Kuznets was careful to point out the inadequacy of the empirical evidence for the hypothesis, particularly in regard to the earlier phase of economic growth.

The various statistical approaches to the study of income distribution are attempts to rationalize the observed distribution of income by using some stylized facts or assump­tions about the generation of income to explain observed patterns of the distribution of income. To call these approaches, nontheoretical might be somewhat misleading; how­ever, it is clearly the case that they are not founded on theories of optimizing behavior and market equilibrium.

1.2.3.3 Institutional Theories of Income Distribution

There have always been economists who were skeptical of the central role played by for­mal models in economic theory. In the area of income distribution, we have seen that even a prominent theorist like John Stuart Mill argued that “the laws of distribution” must be understood in a political and social context, and because this context was deter­mined by institutions, the understanding of the distribution of income and wealth would have to take proper account of institutions in addition to the mechanism of demand and supply. Karl Marx emphasized that the distribution ofincome in the society of his time reflected the particular phase of social development that he called capitalism. Along sim­ilar lines, the German historical school, led by Wilhelm Roscher and Gustav Schmoller, downplayed the role of theory in favor of an approach based on a detailed study of his­torical data. If successfully carried out, this line of research would presumably be less able than, e.g., the marginal productivity theory to offer explanations with a claim to universal validity; on the other hand, it might hold out a promise of generating more insights with relevance for the particular society being studied.

It was especially in the United States that institutional approaches to the study of the economic system received a position that made many regard it as an important alternative to the theoretical approach of the neoclassical school of economists. Thorstein Veblen is widely regarded as the founder of American institutional economics, but his approach— more satirical than analytical—in books like The Theory of the Leisure Class (1899) and The Theory of Business Enterprise (1904) was too idiosyncratic to attract many direct fol- lowers.^[27] Neither he nor the other most prominent members of the institutional school, John R. Commons and Wesley C. Mitchell, paid particular attention to the distribution of income except for a general emphasis on the importance of power relations and evo­lutionary processes. The chief importance of the institutional school may have been as critics of the neoclassical theory in its focus on rational behavior and competitive equi­libria. But the lack of general propositions in the work of the institutional school con­tributed to its gradual decline as an influence on modern economics.

An interesting question that arises in the study of the effects of institutions on the economy is: What constitutes an institution? Here, Veblen adopted a broad definition that encompassed “settled habits of thought common to the generality of men.” A modern version of this idea came with Gary Becker’s work on the economics of dis­crimination (Becker, 1957), in which racial discrimination in the labor market is assumed to arise from a common preference for not working alongside people with a different skin color. In pursuing the implications of this idea, Becker may be said to have followed the guidelines for economic research recommended by the institutional economists; how­ever, the tools that he used in this work were entirely neoclassical.

Regarding the inequality of wage income, important contributions have been made by specialists in labor economics and industrial relations. It is natural to group these with the institutional economists because like them they emphasize the crucial role of insti­tutions for the understanding of the distribution of income, specifically the distribution of wage income. In the United States, the work of Dunlop (1944, 1958) described wages as determined by the interaction between company owners, management, and workers as represented by trade unions.^[28] ThebookbyPhelps Brown (1977) collects anumberofhis studies of wage inequality in different countries and under different economic systems.

His work is notable for the attempt to explain inequality of pay by drawing both on eco­nomic and sociological approaches, paying attention to such factors as social class and status, discrimination, intergenerational mobility, and mental ability.

1.2.3.4 The Role of Property Ownership and Inheritance

The role of inheritance as a determinant of income distribution has received relatively little attention in the theoretical literature. In the world of the early neoclassical econo­mists and the later general equilibrium theorists, the subject did not fit easily into their models. The time dimension—essential to get a grip on inheritance—could indeed be added through the introduction of time-dating consumer goods as well as factors of pro­duction, but this failed to provide a convincing picture of the nature of inheritance. In the world of general equilibrium theory, as described, e.g., in the book by Arrow and Hahn (1971), property ownership was represented by “endowments,” initial holding of goods and factors of production that were taken as exogenous. But models of this type are unable to explain the passing on of property from parents to children and the persistence of inequality between generations. The nature of these intergenerational transfers is determined by the rules of inheritance, which will therefore have an important influence on the distribution of income and wealth. But as Dalton remarked almost a century ago,

Many thinkers of high reputation still talk, or remain silent, about the law of inheritance, as though it had fallen immutable from heaven into the Garden of Eden.

Dalton (1920, p. 285)

Meade (1964) considered the development of the personal distribution of wealth on the background of what he saw as the likely development of the functional distribution of income. In his view, the dominating technological trend was toward “automation,” which would imply a significant reduction in the demand for labor and falling wages. This would lead to a shift in the functional distribution of income away from labor and in favor of income from property. Because, as he pointed out, income from property is much more unequally distributed than income from labor, this shift would imply a greater overall inequality in the population. This trend toward increased inequality in the distribution of income might in Meade’s view be reinforced by demographic factors, such as higher rates of growth for large than for small fortunes (due to better opportunities for diversification), the genetic inheritance of earning power, and the tendency toward assortative mating (the rich marrying the rich). As later pointed out by Stiglitz (1969), it could also be influenced by the rules governing inheritance, either by law or custom. If all wealth goes to the firstborn (primogeniture), this leads to a more unequal distribution of wealth than the alternative of dividing wealth equally among one’s children.

Inheritance is of obvious importance not only for material wealth but also for human capital. We have seen that this point had already been emphasized by Marshall (1890), and some decades later Cannan argued that the individual qualities required both to earn a good income from labor and to manage one’s property wisely were passed on from one generation to the next, so that this tended to stabilize the degree of inequality over time. However, this tendency was not without exceptions:

The able members of the poorest class are constantly rising to the top, and the particularly incom­petent members of the richest class are constantly falling to the bottom; but all the same, among the bulk of mankind there is a continuous hereditary transmission of inequality of income, the importance of which it is foolish to ignore.

Cannan (1914; 1928, p. 217)

The role of inheritance in determining the degree of inequality in the ownership of prop­erty is obviously an important one and requires attention to the broader subject of what Mill called “the laws and customs of society.” Perhaps, his warning, that this was a much larger and more difficult subject than economics, played some role in the development that led economists largely to neglect this important aspect of the distribution of income and wealth.

1.3.