Pigou s Wealth and Welfare: a centenary assessment

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1 Cambridge Journal of Economics 2014, 38, doi: /cje/bet072 Advance Access publication 7 January 2014 Pigou s Wealth and Welfare: a centenary assessment David Collard* Pigou s Wealth and Welfare offered a programme of action that was potentially very interventionist. Any economic policy should be assessed, he proposed, by its expected effect on the size, distribution and variability of the national dividend. His programme, though rough and ready, has proved to be more useful than the new welfare economics, which tended to leave distributional questions for others and efficiency questions to competitive markets. Pigou himself, however, took a conservative view of what might be done in practice. The impact of policies on the size, distribution and variability of income is still a central focus of both popular and technical interest. Some of the issues now recognised as important to well-being, such as welfare in unequal societies and the experience of unemployment, may be subsumed into Pigou s three criteria. Key words: Pigou, Welfare, Cambridge, Income, Distribution JEL classifications: A11, B13, H23, H40, I31 1. Introduction Pigou s Wealth and Welfare (1912) (hereafter, WW) was published four years after he was somewhat controversially appointed, at the age of 30, to Marshall s chair at Cambridge. The book was a product of the young Pigou: tall and handsome like a Viking, as recalled by a slightly later observer (Dalton, 1953, p. 57), a brilliant lecturer and debater and a protégé of both Marshall and Edgeworth. Though personally shy, he was not then the isolated character who was to tussle with Keynes over the analysis of unemployment in the 1930s. Indeed, at this stage he and Keynes were collaborators: Keynes had helped Pigou with the technical analyses in his Principles and Methods of Industrial Peace (Pigou, 1905) and his Edgeworthian paper (Pigou, 1908) on bilateral monopoly, and his assistance with WW is acknowledged in the preface. It was ironic, in view of their later controversy, that Pigou came to welfare economics via his analysis of unemployment, which continued to be a preoccupation. The present paper concentrates on the supply side of WW, as did Pigou himself. On the demand side, he had toyed with the notion of interdependent utilities (Pigou, Manuscript received 4 December 2012; final version received 5 July Address for correspondence: Penywyrlod, Pen y cae mawr, Usk. NP15 1LX; collarddavid@yahoo. co.uk * University of Bath. The Author Published by Oxford University Press on behalf of the Cambridge Political Economy Society. All rights reserved.

2 946 D. Collard 1903) but did not pursue the notion. And he had already (Pigou, 1910) made important technical contributions to the measurement of elasticity. But the discussion of desires and satisfactions in WW is rather perfunctory. Pigou s book was, of course, expanded into successive editions of his great tome, The Economics of Welfare (1920, hereafter, EW; later editions were published in 1924, 1929 and 1932). Dalton was not alone in preferring the sinewy beauty of WW to its plump successors. Even so, the earlier work has always been somewhat eclipsed by the later. It will be argued here that WW made a distinctive contribution to welfare economics and that Pigou s analytical structure, though old-fashioned to modern eyes, is still useful a century later. The very subject of welfare economics, it should be remembered, is one that Pigou carved out and made his own. This early book and its successors pushed the topic (now often described as public economics ) centre stage, where it has since remained. The structure of WW was simple and coherent. The consequences of policy for human well-being were to be measured with reference to national income: its size, its distribution and its variability. Thus, Pigou provided a framework, on his own admission a rough and ready one, for the assessment of policy interventions. Though they had their reservations, Pigou s reviewers were on the whole very positive. Edgeworth (1913), while raising a number of important technical points, found that the book abounds in new ideas. He was particularly enthusiastic, rather surprisingly in the light of the criticisms of others, about the splendid novelty of Pigou s marginal supply price. He did, however, regret that Pigou had insufficiently acknowledged his debt to Sidgwick. The best-known review, respectful but critical, was that by Allyn Young (1913). Young made some relatively minor complaints about Pigou s neglect of the relation between welfare and satisfaction and of longer-term population problems. But his most serious critique was of the curve of marginal supply prices I fail to see that its use is appropriate in the analysis of the extent to which competition tends to secure the maximum social dividend (Young, 1913, p. 681). In the decreasing returns case, he pointed out that rising factor prices simply represented transfers of purchasing power. JM Clark (1913) repeated Edgeworth s praise, though complaining about the benumbing effect of Pigou s style. Like Young, he trenchantly attacked Pigou s confusion between real costs and transfers. In this, Pigou must have thought he had taken his cue from Marshall (Principles, 1920, Book V, ch. viii, see also Appendix H). But Marshall was himself unhappy about Pigou s treatment (see Bharadwaj, 1972) and had not pursued the argument that competition might not lead to maximum advantage. Marshall s comments, on his own copy of WW, which were to be kept secret over Pigou s lifetime, were highly critical on this point. He believed that Pigou s curve of marginal supply price had no reality and greatly preferred his own treatment. Marshall followed Young in believing that Pigou had mistaken transfers for real cost and, in the case of increasing returns, that his analysis was far too static. He had, in Marshall s view, neglected the role of time, attempting to solve dynamic problems using static tools. Marshall s reasons for secrecy must remain a matter for conjecture: perhaps he was unsure of his ground; perhaps he did not wish to embarrass his protégé. In spite of Marshall s secrecy, Pigou was not, of course, unaware of these criticisms and very slowly and reluctantly retreated, correcting the decreasing returns case in the 1924 edition of EW and redefining the increasing returns case in Nevertheless, these important criticisms aside, Pigou s book was widely seen as a work of major importance.

3 2. Wealth and Welfare Pigou s Wealth and Welfare 947 Wealth and Welfare was a programmatic book: it had an agenda and a purpose. In his rather high-flown concluding section, Pigou wrote: The complicated analyses, which (economists) endeavour to carry through, are instruments for the bettering of human life. The misery and squalor that surround us, the injurious luxury of some wealthy families, the terrible uncertainty overshadowing many families of the poor these are evils too plain to be ignored. (Pigou, 1912, p. 488) So, what should be done? Surprisingly, Pigou was not greatly concerned with the size of economic welfare as such: what we wish to learn is, not how large welfare is, or has been, but how its magnitude would be affected by the introduction of causes, which it is in the power of statesmen or private persons to call into being. (Pigou, 1912, p. 4) Economic welfare was, of course, only one aspect of well-being in general, but Pigou asserted that any cause that increased economic welfare would probably increase total welfare. However, he first felt obliged to mount a ground-clearing defence of the relevance of economic policies. The threat came from two sources: evolutionary biology and statistical invariance. Could it not be, argued some evolutionary biologists, that well-being depended almost entirely on people s germ cells (or, as we would now say, their DNA)? If so, income would be irrelevant. Pigou s defence was an interesting one. Though acquired characteristics cannot be inherited, economic environments can: Environments, in short, as well as people, have children ideas, once produced or once accepted by a particular generation may remodel from its very base the environment which succeeding generations enjoy in this way a permanent change of environment is brought about. (Pigou, 1912, p. 59) Pigou also had to confront the eugenicists argument that redistribution would encourage the breeding of inferior stock. His counterargument was that, since better-off families produced fewer children, redistribution could actually improve the stock. So, taking these two points together, Pigou was not prepared to see the biologists make off with his subject matter. Neither was Pigou prepared to cede income distribution to the statisticians. He therefore devoted a short chapter to refuting what has become known as Pareto s law (Cours, 1896; Manual, 1906). Pareto had found a robust straight-line relationship between the log of income and the log of the number of persons exceeding that income, which implied an invariant distribution, such that improvements for the poor would depend entirely on increases in the dividend. There would then be no point in distributional policies. Pigou was deeply sceptical about such distributional invariance, especially when it involved redistribution to the poor, and it is now well known that Pareto s relationship holds good only at the top end of the income distribution. Having cleared the ground in this manner, Pigou felt able to put Marshall s concept of the national dividend (national income) at the centre of his analysis. A change in economic welfare would depend upon changes in its size, distribution and variability. Pigou summarised his criteria as follows (Pigou, 1920, p. x):

4 948 D. Collard (i) If a cause is introduced, which makes for an increase in the aggregate size of the net national dividend, provided that the absolute share of no group of members, in terms of the commodities which that group is accustomed to consume, decreases, the economic welfare of the community as a whole is likely to be augmented. (ii) If a cause is introduced, which makes for an increase of the absolute share of relatively poor groups of persons (in terms of the commodities which those groups are accustomed chiefly to consume), provided that the magnitude of the aggregate national dividend does not decrease, economic welfare is likely to be augmented. (iii) If a cause is introduced, which diminishes the variability, or inequality in time, of the dividend, and especially of that part of it which accrues to the poorer classes, economic welfare is likely to be augmented. Several points need to be noted. First, Pigou s criteria were meant to be operational. He starts with the status quo and introduces causes, the effects of which are, in principle, measurable. So it was important to get the measurement of the status quo right. Pigou devoted a great deal of time and space to clarifying the concept and measurement of the national dividend: the topic continued to absorb him in the decades ahead (e.g. see his little book, Income (Pigou, 1946), which became something of a bestseller). Second, Pigou decided to take the topic of variability out of the second and subsequent editions of WW as he was then planning a new book, Industrial Fluctuations (Pigou, 1927A). This was to become something of a habit, since a substantial amount of material on taxation was also deleted so as to be incorporated in his Study in Public Finance (Pigou, 1928A). Meanwhile the tome itself continued to grow. Though he directed his comments at the work of JS Mill and Marshall, it could also have been with Pigou in mind that Keynes wrote: Economists must leave to Adam Smith alone the glory of the Quarto, must pluck the day, fling pamphlets into the wind, always write sub species temporis, and achieve immortality by accident, if at all. (Keynes in Pigou, 1925 p. 36) Third, the Pigou of WW was much more restrictive about increases in the national dividend than the Pigou of EW. In the later book he was to write: Provided that the dividend accruing to the poor is not diminished, increases in the aggregate national dividend of the community, unless they result from coercing people to work more than they wish to do, carry with them increases in economic welfare. (Pigou, 1928C, p. 82) His earlier statement ((i) above) had embodied a kind of group Pareto optimality: increases in the national dividend were only to be approved of if no group was made worse off. This is less restrictive than full Pareto optimality, which requires everyone to be better off, for it applied to broad groups, not to individuals. Nevertheless, it would fail to sanction some outcomes that the later Pigou would have surely found acceptable, for example, an increase in the social dividend, which left the very poor better off but some higher income group worse off. Fourth, Pigou had spotted a useful (and modern) symmetry between inequality and variability: variability is simply inequality over time: economic welfare is larger the more evenly the available resources are divided the degree of evenness of distribution being measured by the standard, or mean square, deviation. It is obvious that the result thus achieved is equally applicable, when, for many similar men at one moment we substitute one man at many similar moments. (Pigou, 1912, p. 401)

5 Pigou s Wealth and Welfare 949 Pigou was explicit about giving greater weight to the variability of consumption by the poor than to the variability of consumption by other groups. Nevertheless, he devoted only 80 or so of WW s 480 pages to variability and what he had to say about it turned out to fit less well into EW than into the later Industrial Fluctuations. Fifth, the criteria are ceteris paribus. So, in themselves they are not particularly helpful in the many cases where some sort of trade-off is required. The most obvious class of cases is where a redistribution to the poor would lead to some (even a very small) loss of income to any other group. If the trade-off is to be made operational, we need both a value judgement and an empirical assessment of the consequences of policies. It will be seen that whenever such a trade-off was implied, Pigou tended to be conservative in his assessment. Though Pigou is rightly regarded as a partial equilibrium economist, not a general equilibrium economist, he does display some general equilibrium tendencies. He was familiar with Edgeworth s geometric analysis and had clearly read Pareto s Cours and Manual. Marshall too had, of course, been familiar with general equilibrium theory, but was dismissive of its usefulness. Pigou s early articles campaigning for free trade (Pigou, 1904, 1906) had essentially relied on a small general equilibrium model. Hicks was to observe it is funny what a general equilibriumist [sic] he [Pigou] is at bottom (Scazzieri et al., 2008, p. 88). In WW, Pigou took a subset of the conditions for a general optimum: the equality of marginal value products. He recognised the possibility of local optima but presumed that, in general, maximising the dividend required equal marginal value products and that this would normally be achieved by selfish behaviour under competitive conditions. Pigou then explored, as had Marshall, a number of cases in which competition might not lead to an optimum. The first three obstacles that he considered are to do with imperfect mobility, the imperfect divisibility of units and the variability of demand across industries. The analysis was painstaking and taxonomic. He concluded, for example, that increasing labour mobility would probably (though not certainly) bring marginal products into greater equality. Reducing the costs of labour mobility would probably increase the national dividend, but to give bounties may or may not be a good thing as there could be a double transference (WW p. 126). This qualification is an interesting one in view of Coase s (1960) critique of Pigou on externalities. The most arresting chapter in this section of WW, his pièce de resistance as it were, is chapter seven on the divergence between marginal social net product and marginal private net product. Here, since his suggestions were potentially very radical, Pigou was anxious to state that this reasoning involves no attack upon the view that interference with the free play of self-interest was undesirable (p. 148). Again, in view of Coase s later attack, it is very important to note that much of Pigou s discussion was about contracts, particularly what we now call the principal agent problem. It is very wide-ranging, covering agricultural tenancies, lessors and lessees, the owners of concessions (railways, gas and electricity) and the hiring of labour. Generally, the risk is that of underinvestment by the agent when the private marginal product of investment is less than the social marginal product. The degree of underinvestment depends on the detailed nature of the contract. Sometimes compensation will prevent underinvestment, though it could possibly lead to overinvestment. Pigou was very good on the incomplete nature of labour contracts, for example, where: Payment to an individual is made to correspond, not to the actual amount of service done by an individual, but with some rough index of this service. (Pigou, 1912, p. 58)

6 950 D. Collard Part of the divergence between social and private net products is therefore to do with the imperfection of contracts. But there will often be no contract in place or, indeed, possible. Thus, his oft-quoted observation: divergence may also occur, when the uncharged service or disservice rendered by B accrues, not to A, with whom he is in contractual relations, but to some quite different person. (Pigou, 1912, p. 159) Taking his cue from Mill and Sidgwick (Collard, 2010, chs 2 and 7), Pigou cited many examples of this kind of externality, some positive and some negative: afforestation, street lighting, smoke prevention, town planning, slum clearance, inventions and improvements, distant investments that would mainly benefit our heirs, intoxicants, hard factory work by women, wasteful advertisements under monopolistic competition, deception, forgery, adulteration, etc. In some cases it would be appropriate to give bounties, in some to levy what would become known as Pigovian taxes and in others to impose outright prohibition. Pigou therefore provided a powerful interventionist agenda, since such externalities could not normally be dealt with by contractual bargaining between the parties concerned: It is, however, possible for the State, if it so chooses to remove the divergence in any field by extraordinary encouragements or extraordinary constraints upon investments in that field. The most obvious forms, which these encouragements and restraints may assume, are, of course, those of bounties and taxes. (Pigou, 1912, p. 164) Having established a case for taxing or subsidising externalities, Pigou attempted a similar a case for a more general scheme of taxes and subsidies: it is possible to conceive, in respect of every industry obeying the law of diminishing returns, some general uniform rate of tax, the levy of which on the industry makes the marginal net product of resources in that industry more nearly equal to the marginal net product of resources in general than it would otherwise have been. In like manner, it is possible to conceive, in respect of every industry obeying the law of increasing returns, some general uniform rate of bounty, the grant of which would have this effect. (Pigou, 1912, p. 178) Potentially, Pigou s schema implied taking a strong interventionist line in microeconomic policy industry by industry, something not at all in the spirit of neoclassical economics. In the face of Pigou s own, albeit grudging, retreat and of the professional consensus that he was plainly wrong (in the decreasing returns case at least), it would be otiose to offer a defence. What I would say in mitigation is that Pigou was struggling with what was later to become a major issue in growth theory. Could interventions to favour increasing returns sectors increase economic growth? Pigou lacked the tools to deal with this issue, but at least he was aware that strategic policies could be adopted. Pigou was on much firmer ground when considering the effects of monopoly, monopolistic competition and discriminating monopoly on ideal output. Under monopoly, with linear schedules, output would be half competitive output and marginal value product would therefore be greater than under competition. Under monopolistic competition, output will be indeterminate but normally less than under competition. His discussion here (WW, Part II, chs 10 12) and subsequently in a series of articles in the late 1920s and early 1930s, which evolved from it (Pigou 1927B, 1928B, 1933), were an important if traditional element in the famous debates on increasing returns, stimulated by Sraffa (1926). Kahn s article Notes on Ideal Output was squarely based on Pigou s analysis (Kahn, 1935).

7 Pigou s Wealth and Welfare 951 Pigou s taxonomic discussion of discriminating monopoly is classic. Of his three degrees of discriminating monopoly, he considered only the third to be of practical importance: this is where the monopolist is able to charge different monopoly prices to different groups of consumers. The following is a typical result: under diminishing or constant returns, discriminating monopoly output will be less than ideal output; under increasing returns it may or may not be. His analysis of discriminating monopoly led him to take a position on the calculation of railway rates. At some risk of simplification, Pigou s argument was as follows. A charging policy based on ability to pay (the value of service principle ) would lead to a discriminating monopoly outcome, while marginal cost pricing (the cost of service principle ) would replicate the competitive condition. But Pigou had shown that under increasing or constant returns, discriminating monopoly output will lie between zero and the competitive ideal. Hence, the marginal cost principle should be adopted. On the other hand, with sharply falling costs, discriminating monopoly might provide some service where none at all would be provided under competition. So, knowledge of the cost functions over several ranges of output would be required. In principle, Pigou s approach to competition policy was rather radical: in many industries, neither simple competition nor monopolistic competition, nor simple monopoly, nor discriminating monopoly will lead to the maximisation of the national dividend. (Pigou, 1912, p. 237) He therefore had to take a general overview of the repercussions of his analysis for state intervention. What were the implications for policy? To begin with, the case for public intervention was only a prima facie one: It is not sufficient to contrast the imperfect adjustments of unfettered private enterprise with the best adjustments that economists in their studies can imagine. For we cannot expect that any state authority will attain, or will even whole-heartedly seek, that ideal. Such authorities are liable alike to ignorance, to sectional pressure and to personal corruption by private interests. (Pigou, 1912, p. 248) Like Sidgwick and Marshall before him, Pigou was not altogether unaware then of what was to become the public choice critique. Backhouse and Medema (2012) have demonstrated this beyond doubt. Nevertheless, Pigou left his set of fiscal recommendations largely intact, turning instead to the direct control of monopoly and direct state provision. Unfortunately, he seemed to lose his radical impetus at this stage. The public operation of industries, he concluded, is full of difficulty besides being inferior to public regulation and whether they should be publicly operated or publicly controlled cannot be determined in a general way. (Pigou, 1912, p. 289) Plainly, he was unenthusiastic about either and much preferred to rely upon fiscal policy in the form of taxes and bounties. Unfortunately, he failed to pursue the nuts and bolts of taxes and bounties apart from generalities about the shapes of cost curves and industry structures. In that respect, he fully deserved Clapham s jibe of empty economic boxes (Clapham, 1922). It is important to recognise that Pigou was not offering a welfare function but merely a set of criteria. While not using the term trade-offs, Pigou took the view in Part II of WW that there was fortunately no long-run trade-off between redistribution and the maximisation of the national dividend. This was because any redistribution

8 952 D. Collard that would reduce the national dividend would also reduce the supply of saving and hence investment and, in the long run, employment and the real wage. Curiously, much of Pigou s discussion of redistribution in WW was about manipulation of the wage rate: for example, a time rate rather than a piece rate would probably favour less-efficient and, therefore, otherwise poorer workers. Similarly, the spreading of short time working across workers in an industry, in the face of adverse demand, was probably preferable to the concentration of unemployment on a subgroup. Pigou considered the effect on the real wages of workers in general, of artificially raising the wage of workers in a particular industry. Such an effect was possible but unlikely if the product (a wage good) was largely consumed by the workers themselves. It was even less likely when the employer was able to employ a differential efficiency wage. Chapters 1 6 of Part III had thus far been concerned with manipulation of the real wage or the introduction of artificial wage rates. The crunch came in chapter 7 when he considered: under what conditions, a transference from the relatively rich to the relatively poor, brought about by interference with the natural course of wages at any point, will react favourably upon the national dividend. (WW, p. 343) Pigou recognised that if bargaining power was uneven or if there were positive effects on industrial efficiency, an artificial wage could raise the national dividend. And an artificial wage could substitute for Poor Law support. But it was unlikely to do so in practice: though in a few special cases success may be achieved, yet, generally speaking, a transference of resources from the relatively rich to the relatively poor, brought about by interference with the natural course of wages at any point, is unlikely to do otherwise than injure the national dividend and, therewith, in the end, the real income of the relatively poor. (Pigou, 1912, p. 343) Not much was to be hoped for then from wage policies. Direct transfers from the relatively rich to the relatively poor were more promising as there was now no presumption that they necessarily reduce the national dividend. Much depends, in Pigou s view, on how efficiently the poor invest resources in themselves. Unfortunately: the poor, as entrepreneurs of investment in themselves and in their children, are abnormally incompetent. (Pigou, 1912, p. 359) On the other hand, there are two classes of the poor to whom transfers could be made while actually increasing the national dividend: the temporarily sick and, in the form of education, young children: There can be little doubt that resources transferred from the relatively rich, for well-considered investment in these two classes of poor persons would yield a larger return than is obtainable from investment in machinery. (Pigou, 1912, p. 364) Pigou made a distinction between actual transfers and the expectation of transfers, to be referred to later as announcement effects. Voluntary transfers driven by altruistic motives or by the expectation of honours (Marshall s economic chivalry ; Marshall, 1920, p. 719) would, of course, have no adverse effect on saving. Neither would taxes on pure rents or capital gains, nor expenditure taxes, nor, perhaps, death duties. Anticipating his Study in Public Finance (Pigou, 1928A, ch. 10), taxes that discriminated against saving would be more injurious than those that did not. There are

9 Pigou s Wealth and Welfare 953 announcement effects for the poor also, of which the most obvious is a disincentive to work. In which case, it would be a good strategy to provide things in kind which the poor would not have provided for themselves: Public parks for the collective use of the poor, flowers for their private use general sanitary measures unemployment insurance. (Pigou, 1912, p. 383) These could all be provided without reducing the national dividend. On the other hand, differential transfers to poor persons would probably reduce national income unless relatively severe measures were taken (including the sending of the idle poor to penal colonies). At last we come to a case in which Pigou seemed to be prepared to contemplate a trade-off between distribution and the national dividend: the national minimum. A national minimum standard: is justified by analysis, in the sense that it can be shown to be conducive to economic welfare on the whole, if we believe the misery that results to individuals from extreme want to be indefinitely large; for, then, the good of abolishing extreme want is not commensurable with any evils that may follow from a diminution of the dividend. (Pigou, 1912, p. 395) The implied trade-off is explicitly utilitarian, buttressed by a sense of duty towards the weak: economic welfare is best promoted by the establishment of a national minimum, at such a level that the direct good resulting from the marginal pound transferred to the poor just balances the indirect evil brought about by the consequent reduction of the dividend. (Pigou, 1912, pp ) The minimum had, however, to be set at a pretty low level. Pigou s third criterion was the variability of the national dividend, measured by the mean square deviation. Because of diminishing marginal utility, welfare can be increased if consumption is spaced out more evenly over time (risk aversion, as we would now say, being analogous to inequality aversion). Pigou also recognised that idleness affects future employability, that the variability of consumption is usually associated with the variability of employment (itself an evil) and that variability exposes the worker to downside risk. In principle, consumption variability may be reduced by mutuality or insurance. Since people are irrational this leads to underprovision, making compulsory state schemes attractive. One source of the variability of consumption is the variability of the price level. Various proposals for steadying the price were under consideration at the time and Pigou drew upon these in his discussion. There is a brief, rather backwardlooking digression (WW, part IV, ch. 5) on the variability of the wages fund. Much of the material that follows eventually found its way into Industrial Fluctuations. Thus, chapter 6 of WW, which looked at variations due to variations in the bounty of nature and in export demand, grew into Industrial Fluctuations chapter 2. Similarly, chapter 7 on errors in business forecasts grew into chapters 6 and 7. Given this discussion of the causes of variability and its adverse effects on welfare, what was to be done? One possible solution is the provision of public works. Pigou quoted with approval the various reports from bodies advocating deliberate countercyclical policy on the part of government and local authorities. He even contemplated a system of bounties during the slump financed by taxation in the boom.

10 954 D. Collard It seems to the present writer rather a pity that Pigou virtually abolished variability from his welfare criteria after the first edition of EW. As a result, welfare economics came to be seen as quite separate from macroeconomics. This was unfortunate, since employment is important in individuals own assessments of their well-being. 3. Pigou and welfare economics Blaug (1968) has suggested that WW was virtually a blueprint for the welfare state. This is surely a very selective reading. Pigou is sometimes viewed as left or at least pink and possibly Fabian in his sympathies. Something of the sort is admittedly true of his structure. It is an interventionist structure, implying a policy agenda. But to anyone with socialist sympathies, Pigou constantly disappoints: he is always cautious and rarely radical in matters of redistribution or welfare provision. The great Liberal reforms at the beginning of the century, of course, predated Pigou s book. Backhouse and Nishizawa (2010, ch. 1) make the point that the Oxford LSE nexus (Toynbee, Ruskin, Hobson, Wells, the Webbs and Beveridge) was far more important than the Cambridge School in the emergence of the British welfare state. The basic reason for Pigou s caution lay in the nature of his welfare criteria. Redistribution to the poor was acceptable on diminishing marginal utility grounds provided that it did not reduce the social dividend. If any trade-off was to be considered, it could only be between desperate poverty and very small adverse consequences for the dividend. The really interesting questions arise, however, when the trade-off is non-trivial. The national dividend (or national income), usually expressed per capita, was and remains the most commonly used index of economic welfare. Pigou borrowed the concept from Marshall and made it his own, recognising the index number problem when tastes or distribution changed. The discussion in Part II, ch. 3 of WW can be a little tedious, but here Pigou, starting from the construction of price indices, was the first economist to deduce implied satisfaction from expenditure decisions. This was done in the spirit of revealed preference by assuming a representative consumer (l homme moyen) from each group and calculating price indices, which, of course, would vary inversely with real income. These issues, concerning the meaning of increases in real income, were later debated extensively in the literature generated by Kaldor (1939), Hicks (1939) and Scitovsky (1941 2). Pigou s treatment did not meet the high technical standards that came to be expected by Samuelson (1960), who commented that it was just as well that the rest of Pigou s EW did not depend on his discussion of the dividend. Nevertheless, he praised Pigou s more rudimentary treatment as masterly and classic. Pigou was content, as a fruit seeker, that his own treatment would do as a rough practical measure. The concept had its limitations, many of which were recognised by Pigou himself. It is now commonly supplemented by other indicators of well-being, such as the human development index, which allows for factors such as infant mortality and literacy. More radical alternatives, such as happiness indices, are discussed below. But per capita GDP, for all its faults, remains the primus inter pares. Changes in GDP and even fluctuations in its quarterly growth rates regularly make it into the main news headlines. Perhaps the best-known technical legacy of WW is the concept of Pigovian taxes, to correct for the difference between marginal social and private marginal net products. In view of the prominence of these in the modern literature, it sometimes comes as a surprise that Pigou did little to elaborate them either in EW or later in A Study in

11 Pigou s Wealth and Welfare 955 Public Finance. Coase (1960, p. 39) was right to point to a lack of clarity in Pigou s exposition: the main source of the obscurity is that Pigou had not thought his position through not being clear it was never clearly wrong. Coase s critique was widely accepted, i.e. that under competition, litigation would ensure that externalities would be internalised so that Pigovian taxes were not only unnecessary but actually harmful. This was a little unfair in that Pigou s corrective taxes were designed for situations in which contractual arrangements to remedy externalities could not be entered into: precisely those situations in which potential litigants were powerless and widely dispersed. His discussion of mobility (see this paper, p.5) showed he was perfectly aware that taxes or subsidies could overcompensate for a distortion. Medema (2009), though very sympathetic to the Coasean view, has recently argued that the difference between him and Pigou, when one has taken their small print into account, is not as great as was previously thought. The Coasean critique nevertheless put the proponents of Pigovian taxes on the defensive. But rescue was at hand in the form of environmental economics. For, as economists from the 1970s onwards increasingly emphasised environmental issues (see, e.g., Lecomber, 1979), the appropriate mix of regulation, Pigovian taxes and artificial markets became a central feature of international policy on climate change and related matters. A particularly striking externality concerns investments that will largely benefit future generations. Pigou discusses these briefly in WW (Part II, ch. 7), paying special attention to mortality. The issue is revisited in more detail in EW, which refers to a defective telescopic faculty (Part I, ch. 2). Pigou s discussion led to rather a large literature on the social rate of discount. The issue was famously taken up by Ramsey (1928), who, following Pigou, declared pure time discounting to be morally unacceptable. Long neglected, Ramsey s paper became a central part of optimal growth theory and is still relevant. For example, it was the basis for calculating the social rate of discount in the Stern Report on climate change (see Collard, 2010, ch. 20). Pigou, though traditionally viewed as a partial equilibrium economist, insisted on equal marginal (social) products across factor uses. Marginal equivalences more generally, as a set of necessary conditions for optimality, came to the fore in the so-called new welfare economics associated with Bergson s (1938) social welfare function. This enabled theorists to separate out efficiency conditions from distributional issues, using a Paretian general equilibrium framework. There would potentially be many Pareto optima, each associated with an initial income distribution. It was further shown, in the spirit of Edgeworth s recontracting mechanism, that every competitive-equilibrium is a Pareto optimum (the first theorem of welfare economics). Distributional weights could be added to taste, as it were. The case for redistribution could no longer rest on the utilitarian ground of diminishing marginal utility but required a value judgement. As for the marginal conditions, they could be investigated by an objective science. This was the view famously taken by Robbins (1932): the new scientific approach would eventually enable economic imperialists to apply their techniques to any area where resources were scarce. The new structure was, in itself, a politically neutral one. It could, in principle, be operated by a socialist planner who would set income distribution and then (making use of the second theorem of welfare economics) operate pseudo markets under a market socialist mechanism. Or it could enable scientific economists to set the distribution issue to one side and concentrate on the conditions for Pareto optimality. If the first theorem held, the task of economists was to ensure a competitive market; if

12 956 D. Collard there were market imperfections, there remained quite a lot for them to do. Or it could enable free-market economists to argue that markets on the whole behaved as if they were competitive. One has then only to add that the present income distribution is more or less acceptable for welfare economics to be reduced to a form of market admiration. It is hard not to conclude that the combination of general equilibrium theory and the new welfare economics led the subject up a technically brilliant but ultimately fruitless garden path, particularly when it became clear that, for efficiency, economic agents would be required to know all prices into the indefinite future (Debreu, 1959). It is interesting that Pigou s criteria came reasonably well out of Little s well-known and devastating critique of mid-century welfare economics. Though critical of utilitarianism, he was even more so of the new welfare economics. Little (1950, p. 275) proposed that welfare economics be based on the following sufficient condition for a desirable economic change: an economic change is desirable if (a) it would result in a good redistribution of wealth, and if (b) the potential losers could not profitably bribe the potential gainers to oppose the change. These are similar in spirit to Pigou s criteria, except that redistribution is now a value judgement rather than being based on utilitarianism and that Little had taken on board the Kaldor/Hicks/Scitovsky discussion. He also argued that the criteria could only be used in a rough and ready, commonsense way, which is precisely what Pigou had maintained. We have seen that Pigou was not unaware of the imperfections of government. It was because of these that Coase looked to the common law rather than the government for a corrective set of institutions to deal with externalities and other issues. His attack may be seen as part of an institutional critique of Pigou s approach, not just to externalities but to market failures more generally. Traditional economists tended to think of themselves as making technical recommendations to objective politicians who would act upon them. They knew very well that officials and politicians could be stupid or corrupt and that this had to be taken into account when devising policies (Backhouse and Medema, 2012). But the political system was essentially viewed as a black box, operating benignly on the whole and gradually improving in quality over time. The public choice approach, as popularised by Buchanan and Tullock (1962), applied the economist s self-interest assumption to politicians and even to the economists themselves. This was salutary and useful, even if rather cynical. The politics of the policy-making process (voting mechanisms, political parties, interest groups, etc.) then became part of the problem to be analysed. But a major question then arises about the nature of welfare economics. Once policy choice is endogenous, welfare economics apparently becomes a positive science and the would-be normative economist is reduced to analysing a process in which he himself is involved. Clearly this would not have satisfied Pigou, who saw economics as a way of enabling people to lead better lives, or Marshall (Pigou, 1925, p. 89), who wanted the Cambridge Tripos to send out into the world economists with cool heads and warm hearts. The economist with serious intent has to take the public choice critique into account: his or her recommendations are then the first move in a policy game. The critique does not render the economist powerless, just more streetwise. I have already remarked that Pigou allowed only a limited trade-off between his welfare criteria. Earlier writers (Bentham, Mill and Sidgwick) had been horrified by the potentially catastrophic implications for output of any attempt at redistribution. Pigou himself was extremely cautious about it. Yet the feasibility of a trade-off is a central issue in welfare economics and one of the most difficult to resolve. Pigou started to

13 Pigou s Wealth and Welfare 957 explore it in outline in WW and then in more detail in A Study in Public Finance. What set of commodity taxes, he asked Ramsey, would obtain a given revenue with the least loss of utility? Hence Ramsey s seminal paper (1927). Like his paper on optimal saving (also inspired by Pigou), this one was a slow burner and it failed to get detailed wider attention in the profession until Atkinson (1973) and Mirrlees (1971) provided an analysis for the income tax case. The more general problem, taking income and commodity taxes together, turned out to be extremely complex. The even more general problem, which must include the saving and work disincentives of social security and welfare payments, income taxes and commodity taxes, is almost intractable. It is not surprising that Pigou got little further than a taxonomy of the main effects. Pigou said little about the trade-off between the national dividend and his third criterion, variability, the topic to be hived off later to Industrial Fluctuations. His basic presumption, which must be broadly true, was that reductions in the variability of income and hence consumption would be of the greatest benefit to the poor. So, provided that limited measures, such as price stability, countercyclical spending by local authorities and assisted unemployment insurance, did not harm the national dividend, there was little cause to worry much about trade-offs. Omitting his third welfare criterion from EW did not then greatly damage the structure of the book. However, as already noted, a possible consequence was that business cycles and unemployment were hived off to an increasingly separate macroeconomics. Hence, standard welfare economics came to say little about one of the main factors affecting people s welfare. Although paying lip service to GE Moore ( good is good and that s all there is to it), Pigou was essentially a utilitarian. His case for redistribution was explicitly utilitarian. The implications of this could be quite radical. As he was to point out in A Study in Public Finance, if diminishing marginal utility was taken seriously, the least damaging way of raising a given revenue would be to lop off all higher incomes until the desired sum had been raised. But this would be to ignore disincentive effects, so a trade-off was required. The case for redistribution does not, fortunately, rest entirely on utilitarianism. Any inequality-averse function will do. For example, a Rawlsian, justice as fairness, approach would attempt to maximise the well-being of the least well-off. Sen (1973) explored different inequality-averse functions and their implications for the measurement of inequality itself. The degree of inequality aversion assumed obviously has implications for the optimal tax structure, discussed above. Utilitarianism then is not essential in making an argument for redistribution. Neither has it been necessary, since early in the twentieth century, to the analysis of demand. This is not to say that utility has disappeared from the economist s armoury. Utility functions are alive and moderately well, not just in the textbooks but in the learned journals. They are an important part of doing economics. But they do not generally claim to be measures of individual goodness or welfare or happiness. However, there has been something of a resurgence of an implied Benthamite utilitarianism in the recent body of research on happiness (see, e.g., Clark and Oswald, 1994; Layard, 2005). This research attempts to obtain objective measures of the subjective impact of factors such as divorce, unemployment, etc. It is utilitarian in spirit. By way of contrast, Sen (Sen and Nussbaum, 1993) had strongly attacked the utilitarian approach to well-being and suggested that it should, instead, be measured by people s functionings and capabilities. Both, in the end, come down to what people value. After all, Bentham allowed all manner of things, such as the pleasures of amity and goodwill, to enter into his utility function as well as the pleasures of consumption (see Collard, 2010).

14 958 D. Collard 4. Assessment Any overall assessment of WW has to take account of three things: its context in what one might call Cambridge welfare economics, its intrinsic merits and its place in Pigou s life s work as an economist. It is not too much to claim that there is an identifiable strand of welfare economics running through the work of Sidgwick, Marshall and Pigou. One such strand, relating to intergenerational economics, was identified in Collard (1996). It might be argued that Pigou simply took Sidgwick s utilitarianism and combined it with Marshallian techniques to produce a manual of applied economics. But Pigou was by no means a simple utilitarian or, as we have seen, a slavish adherent to Marshall s doctrines. If there is a Cambridge School of welfare economics, its locus surely lies in Pigou s WW and later in his EW. The defining characteristic of this school is the view that, in principle, active economic interventions can improve economic welfare (though in practice the interventions have tended to be rather conservative). It may be contrasted with the Chicago Virginia view that economic interventions on the whole tend to make matters worse, though, as is often the case, the contrast is less dramatic once the small print is taken into account (Medema, 2009, passim). In making a rounded assessment, a little more should be said about WW in the context of Pigou s contributions overall. So I close with a reminder that he was not merely a welfare economist but a pretty good all-rounder. Pigou was active at the top of the economics profession for nearly 50 years. He is now best known for EW and for his disputes with Keynes in the 1930s. He could be pedantic and excessively taxonomic and, unlike Keynes, did not have an attractive writing style; however, he made significant contributions across the board. Let us look briefly at some assessments of his other work. Edgeworth, reviewing Pigou s early book The Riddle of the Tariff (1903), commented that the power with which he wields the organon of economic theory is of the highest promise (Edgeworth, 1904) and he compared Pigou s work with the early work of Clerk-Maxwell in physics. Deaton commented that Pigou s work (1910, 1930), showing a linear relationship between price and income elasticities under independent utilities (Pigou s law) was still one of the best examples of indirect measurement by use of theory to be found outside of the physical and biological sciences (Deaton, 1975, p. 9). Pigou s 1918 article, despite his protestations, is widely acknowledged to be the first published statement of the Cambridge version of the quantity theory of money (the Cambridge k) (Pigou, 1918). Schumpeter (1953), complaining that no one had produced a synthesis of business cycle theory, remarked that Pigou s Industrial Fluctuations came closest. Solow (1980) has described Pigou s The Theory of Unemployment (1933) as masterly in its attempt to get to grips with elasticities and praised his realistic approach to the labour market, which had stressed rigidity, search, segmentation and bargaining. Samuelson (1941) assessed the methodology of Pigou s Employment and Equilibrium (1941) to be almost ideal and judged it to be one of the most important books of recent years. The intrinsic merits of WW have been examined in this paper. For all its faults, it still stands as a classic exposition of the nature and content of welfare economics. I have argued that Pigou s pioneering work provided a more robust structure for asking relevant questions about economic policy than the Paretian structure, which seemed to allow scientific economics to put income distribution to one side. Then, as now, a central question for welfare economists is the effect of policy changes not merely on per capita income, but on its distribution and variability.