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Pigou wrote more than a dozen books and over 100 articles. After he transitioned from being a Cambridge student to a Fellow, he won the Adam Smith Prize at Cambridge in 1903 for an essay which was revised and published in 1905 as the Principles and Methods of Industrial Peace (Pigou 1905). This essay, which also formed the basis of his eight lectures for the 1903-1904 Jevons Memorial Lectures at University College London on Associations of Employers and Employed, Arbitration and Conciliation, is of interest to intellectual historians for the framing of labour market problems with reference to ethics: ‘The problem of this book is ethical—to determine what principles and methods ought to be employed in the settlement of industrial differences ... But the solution of the ethical problem can only be reached with the help of an investigation of actual and recent experience’ (Pigou 1905: ix).

While he recognised that the issue of industrial peace ‘is not confined to the narrow circle of economists’ (ibid.: vi), the analysis is still rich in economic ideas, with the explicit and formal use of economic analysis reserved for the appendices. At its most general level, the Principles and Methods of Industrial Peace reflects Pigou’s view that social problems are themselves ethical in character. The particular role of economic analysis—in the case of this book—was generally derived from Marshall’s Principles, but Edgeworth’s Mathematical Psychics was influential too. As such, Pigou was consciously aligning his views on the relevance and purpose of economics with those of his teacher, Marshall. Indeed, even the subject of this book was suggested to him by Marshall (ibid.: vii). The book is also of historical interest for its focus on an issue that subsequently featured prominently in Pigou’s formal definition of economic welfare, namely improving the living standards of the working poor and their families.^[1] It also features an important theme of his subsequent work on welfare economics, notably the complexities associated with balancing efficiency, in this case, efficiency in the setting of wage rates, with broader redistributive goals.

Pigou critically assessed the protectionist policies of the British Colonial Secretary, Joseph Chamberlain, in his booklets, The Riddle of the Tariff (Pigou 1903a) and Protective and Preferential Import Duties (Pigou 1906a), and in his subsequent essays in the Fortnightly Review, ‘The Known and the Unknown in Mr Chamberlain’s Policy’ (Pigou 1904a), and the Edinburgh Review, ‘Mr Chamberlain’s Proposals’ (Pigou 1904b) and ‘Protection and the Working Classes’ (Pigou 1906b). All of these essays are critical of protective tariffs and imperial preference, with Pigou estimating the loss of national income due to tariffs and noting that redistribution in response to preferential tariffs tended to favour landlords (Pigou 1904a [2002], (1904b) [2002]), and rejecting the proposition that protection increases economic stability (Pigou 1906a). Collard (2002: xii-xiii) astutely pointed out that while the polemical tone of these papers is readily evident to the reader, the level of analysis with which they are supported would not be out of place in the Economic Journal. The issue was important to Pigou, who joined Edgeworth, Marshall and 11 other prominent economists in signing a joint letter that was published in The Times on 15 August 1903, under the heading ‘Economics Professors and the Tariff Question’, which questioned the logic of protectionism.^[2]

During this early period of his career, Pigou also devoted time to core issues in equilibrium economics that laid the formal foundation for his subsequent work on welfare theory. In ‘Some Remarks on Utility’, (Pigou 1903b) Pigou considered the relationship between demand and utility when an individual’s assessment of the marginal value of their consumption changes with variations in the consumption of others. In modern Pigouvian language, it investigated whether demand-related externalities exist when goods are not common across society as a whole, but are common amongst a subclass of society that one may aspire to, such as diamonds and tuxedos among the wealthy elite. His conclusion was that such externalities do indeed exist but that they represent a relatively small influence on an individual’s consumption and can be ignored in a first approximation study of individual demand. He returned to the subject again at the end of the decade, demonstrating that, instead of simply ignoring this influence because it is ‘small’, it can be considered analytically as a demand externality.

Finally, and importantly, Pigou continued his interest in ethics and philosophy. This was no passive interest either. Rather, it was an area of study that he took seriously. In 1908, three of Pigou’s earlier articles from the International Journal of Ethics, namely ‘The Problem of Good’, ‘The Ethics of the Gospels’ and ‘The Ethics of Nietzsche’, plus one article from the Independent Review, namely ‘The Optimism of Browning and Meredith’, were republished in his book The Problem of Theism and Other Essays, which also included three new chapters: ‘The General Nature of Reality’, ‘The Problem of Theism’ and ‘Free Will’. It should also be noted that the chapter entitled ‘The General Nature of Reality’ is particularly notable for drawing out the methodological issues of social enquiry that derive from philosophical thought and which pertain to Pigou’s subsequent method of science, in that it recognises that at least part of the independent reality that social scientists deal with concerns the spirits of living men. Consequently, in the lead-up to Pigou being appointed a professor, his preparations for serious reflection on economics were preceded by philosophic reflection on the nature of what is good, the nature of science and the tools of economic analysis. In other words, he was laying the philosophical grounding for his seminal works in the field of welfare economics.

Less than two years after succeeding Marshall, Pigou contributed two papers to the Economic Journal that had notable legacies. First, ‘A Method of Determining the Numerical Value of Elasticities of Demand’ (Pigou 1910) contained the proposition that the own price elasticity of demand for a s pecific good is related proportionally to the income elasticity of demand for that good, which subsequently became known as ‘Pigou’s Law’ (Deaton 1974). Once this proportionate relationship is derived, own price elasticity of demand can then be estimated indirectly from empirical estimates on income elasticity of demand. Pigou started by assuming that individuals on a similar income have a similar utility for the good in question and, using an additive representation of utility, he investigated the consequences of the law of one price for the total utility and marginal utility as income changes. Second, in ‘Producers’ and Consumers’ Surplus’ (Pigou 1910 [2002]) Pigou developed his analytical apparatus to systematically account for externalities (although without using the term): both demand-related externalities, where an individual’s demand is influenced by others’ consumption of consumer goods, and supply-related externalities, where the supply of a good affects the well-being of people who are not a direct party to the exchange of the good in question. The efficiency consequences of these factors are discussed in that paper, as are corrective measures.^[3]

Pigou’s first truly great work, Wealth and Welfare (Pigou 1912), investigates the relationship between wealth, which he characterises as the national dividend, and welfare, which he considers with reference to two general propositions. First, welfare concerns states of consciousness only, but, as consciousness is too difficult a concept to work with analytically, Pigou presents ‘economic welfare’ as a part of a broader conception of welfare, one that can be considered with reference to the ‘national dividend’. Second, that welfare can be considered by categories such as ‘greater or lesser’. While welfare and economic welfare are broadly correlated, they are not synchronised to the point where a change in economic welfare necessarily yields an equal change in welfare, but in a probabilistic sense, and without information to the contrary, Pigou’s starting point is that increases or decreases in economic welfare can be considered with respect to changes in the national dividend.

Within this context, Pigou (1912: 66) contends that an increase in economic welfare is associated with three conditions: (1) ‘an increase in the size of the national dividend’, which we may call the ‘wealth-efficiency’ condition; (2) an ‘increase in the absolute share of the national dividend accruing to the poor’, which we may call the ‘distributive fairness’ condition; and (3) a ‘diminution in the variability of the national income, especially of the part accruing to the poor’, which we may call the ‘macroeconomic stability’ condition. For welfare in general the key question for Pigou was the relative ‘harmony’ and ‘disharmony’ between each of these three conditions. Economic welfare is enhanced, at least in a probabilistic sense, when an outcome meets one or more of these three criteria and there is no disharmony with the remaining conditions. But Pigou does not rule out the possibility of economic welfare improving even in the face of disharmony, such as when disharmony is only evident in the short run. On the issue of distributive fairness, the utilitarian foundation to his thinking on interpersonal comparison is clear, as he accepts that the marginal utility of money to a poor man is greater than that of a rich man, but he is extremely cautious in the use of that principle. On the question of macroeconomic stability, Pigou is concerned that lower-income workers are disproportionately affected by economic downturns, so policies that diminish fluctuations are welfare enhancing. Once such downturns occur, however, he advocates ‘equalising actions’ in the form of public works to offset the welfare losses from recessions and depressions. When people who would otherwise have been unemployed,

can be turned to some task of ‘actual and substantial utility,’ it [the cost of equalising action] may be comparatively small. This class of consideration helps to determine from how large a quantity of equalising action economic welfare would benefit. In all circumstances, however, advantage can be obtained from some quantity of equalising action (Pigou 1912: 476—477).

It is while addressing the issues related to the wealth-efficiency condition that the theoretical apparatus developed provisionally in ‘Producers’ and Consumers’ Surplus’ found full expression in an analysis of market failure, predicated on the view that money is the measuring rod of utility (i.e. a cardinal conception of utility). The resulting analysis revolutionised thinking about the potential for government to correct market failures through what we now call Pigouvian taxes, when negative externalities from a particular activity result in overinvestment in that activity.^[4] The significance of Pigou’s work here is readily evident from the force and quality of the counter-theses that emerged in response, with the old (cardinal) welfare economics of Pigou being contrasted with the new (ordinal or Paretian) welfare economics of Hicks and the Coase (1960) critique of Pigou’s analysis of market failure and social costs through the development of what became known as the Coase Theorem, that is, clearly defined, and legally enforceable, property rights have the potential, in many instances, to eliminate the need for correction of market failure by public authorities.

In response to the second edition of Irving Fisher’s The Purchasing Power of Money (Fisher 1913), Pigou wrote ‘The Value of Money’ (Pigou 1917) for the Quarterly Journal of Economics. This article is significant because it was the first time that the Cambridge equation version of the quantity theory of money, in which the real value of a unit of legal tender is given by the proportion of real economic activity held in real cash balances, was published in print. Pigou does not claim too much by way of originality for the development of this equation, as it is implicit in Marshall’s reflections and testimony on the subject, but it does reveal a difference in approach to theory between the master and pupil. Specifically, Marshall was not inclined to introduce mathematical formulation into economic theory, whereas Pigou was more willing to do so, but by complementing, in the case under consideration, the equation with textual discussion that canvasses the circumstances when the price-quantity relationship typically associated with the quantity theory will fail to hold (McLure 2013b).

Pigou then set about building upon the framework developed in Wealth and Welfare to produce The Economics of Welfare (Pigou 1920), which was published in four editions and became an integral part of the Cambridge tradition in economics. Pigou’s considerations on the variability of the national dividend were published as a new book Industrial Fluctuations (Pigou 1927a) which, amongst other things, stressed the correlation between pessimistic judgement and the phase of the business cycle. His discussion of public finance would be reproduced in The Political Economy of the War (Pigou 1921) and later extended into A Study in Public Finance (Pigou 1928a).

In the 1920s, Pigou also contributed substantively to two related debates, mainly between colleagues at Cambridge University, which were published in the Economic Journal.⁸ The first may be called the ‘empty boxes’ controversy, which commenced with John Clapham’s famous article ‘Of Empty Economic Boxes’ (Clapham 1922) in which it is contended that Marshall’s treatment of the concept of increasing and decreasing returns and Pigou’s treatment of the same in The Economics of Welfare were empty theoretical constructs because ^[5]

they were devoid of any clear linkage with real-world phenomena. In that debate, Pigou rejected Clapham’s point, suggesting that these ideas are not boxes per se, but part of a larger system of economic thought that guides practical enquiry. However, Dennis Robertson, Pigou’s Cambridge colleague, was not satisfied with Pigou’s defence (Boianovsky 2014), as he concluded that Pigou had overestimated the extent of efficient output by treating fixed costs as if they could be broken down into variable costs. This criticism is reminiscent of Allyn Young’s (1913) suggestion that Pigou’s industry-wide cost analysis in Wealth and Welfare was flawed because rents that firms realise from increasing returns are incorrectly attributed to the marginal net product of resource inputs.

The second debate may be called the ‘costs’ controversy, which was sparked by the publication of Piero Sraffa’s landmark paper on ‘The Laws of Returns under Competitive Conditions’ (Sraffa 1926). It pointed out that Marshall’s treatment of increasing and decreasing costs were inconsistent with competition because it ignored interdependencies between the economic output of firms and industries that impacts on the costs of all firms. Pigou took Sraffa’s assessment very seriously by reflecting on when partial analysis, which sets aside general interdependencies, can provide a reasonable approximation (in the case of internal economies) and when it cannot be set aside (in the case of external economies). His mature solution to the issue, provided in ‘An Analysis of Supply’ (Pigou 1928b), was to replace Marshall’s notion of a r epresentative firm for an industry, which recognised that firms are distributed around the representative firm with different costs structure (as a result of the different age and evolutionary state of each firm within an industry), with the idea of an ‘equilibrium firm’ given under competitive conditions, which, as Newman has accurately observed, ‘is Marshall’s representative firm with the representativeness with respect to size left out’ (Newman 1960: 591). Using comparative statics, Pigou argued that when industry output is in an initial equilibrium there is a tendency for individual firms to expand and contract, with no significant net effect on size because expanding firms offset contracting firms. Similarly, when there is a change in the conditions of demand that leads the industry to adjust to a new equilibrium, new output and supply price will also have adjusted in the same way, with any tendency for individual firms to expand and contract again offsetting each other. In that way, the size of the firm is effectively set aside in equilibrium theory. All that is required to permit increasing, constant or decreasing returns that are internal to the firm is that one firm, which need not be representative in terms of size, is representative in the sense that it, like the industry, is in an equilibrium state. However, this abstraction was not welcomed by all, with Robertson suggesting that ‘Pigou’s equilibrium firm is, it seems to me, even more “ghostly”.. .than Marshall’s representative firm’ (Robertson I960: 601).⁹

In the 1930s, Pigou’s enduring interest in the problem of unemployment came to the fore with The Theory of Unemployment (Pigou 1933a), which Keynes argued seemed ‘to get out of the Classical Theory all that can be got out of it’ (Keynes 1936 [1973]: 260). In this work Pigou developed his analysis of unemployment by modelling a sequence of real interdependencies in the microeconomy associated with the demand for the provision of raw materials, the short-run demand for wage goods, and the aggregate demand for labour. Pigou then extended his analysis to consider the interdependence between real and monetary influences on labour markets. The central analytical mechanism for dealing with these interdependencies throughout the book was the notion of the elasticity of demand for labour. The Theory of Unemployment was drafted during the Great Depression, with one of Pigou’s goals being to establish the relationship between the nominal and real elasticities of demand for labour in the macroeconomy. His analysis, which incorporated broad statistical observations and intuitive reasoning, led him to provisionally conclude that the elasticity of demand for labour with regard to the money wage would be ‘not less numerically than -1.5’, from which he concluded that a 10% cut in money wages would, other things being equal, result in more than a 10% expansion in the aggregate volume of labour demanded (Pigou 1933a: 106). Pigou, however, emphasised the importance of other things being equal and cautioned that other influences may tend to deepen depressed conditions and that, as a result, the ‘expansive effect of the reduction would be partly or wholly masked’ (ibid.). In addition to questions related to the elasticities of demand for labour, Pigou also examined shifts in the demand for labour in The Theory of Unemployment.

The consequent theoretical controversies with Keynes during the 1930s led to Pigou’s continued analysis of the issues raised by Keynes in The General Theory.¹⁰ Pigou’s immediate response was to produce ‘Real and Money Wage Rates in Relation to Unemployment’ in 1937, a controversial article which Keynes viewed as ‘the work of a sick man’ (Keynes quoted in Collard 2011: 27), a comment due in part to Pigou’s ill health at the time, but also because of a disagreement with Pigou’s assumptions concerning the monetary system ^{[6] [7]}

and the flexibility of real wages. However, Pigou continued to develop his analysis concerning employment in the wake of The General Theory, culminating in Employment and Equilibrium: A Theoretical Discussion (Pigou 1941)— which has been beautifully characterised by David Collard as a ‘late flowering’ (Collard 2013: 14), perhaps because Pigou had developed a small macroeconomic model that, among other things, included an employment multiplier which he regarded as probably positive (a nod to Keynes) and a money wage multiplier which he regarded as probably negative (a nod to his earlier The Theory of Unemployment).

The article ‘The Classical Stationary State’ (Pigou 1943), from which emerged Pigou’s real balance effect (now popularly known as the ‘Pigou effect’), followed, as did Lapses from Full Employment (Pigou 1945), and, five years later, the pamphlet Keynes’ ‘General Theory’: A Retrospective View (Pigou 1950), in which Pigou accepted certain elements of Keynes’s work but, as Collard (1981:127) has noted, he also maintained several reservations as well. Finally, it should be noted that Pigou continued to work long after his retirement at the age of 65. The work produced after this time included studies on income (Income: An Introduction to Economics (Pigou 1946) and Income Revisited (Pigou 1955)), British economic history (Aspects of British Economic History 1918-1925 (Pigou 1947)) and money (The Veil of Money (Pigou 1949)).

• [1] ‘It is prima facie desirable that arbitrators should seek somewhat to modify the general distribution ofwealth awarding to poor workpeople higher wages than the trend of economic forces would naturallybring about, provided that these wages seem likely to come from the pockets of relatively wealthy persons’(Pigou 1905: xi). Takami (2014) provides an interesting reconstruction of the intellectual environmentthat Pigou faced at Cambridge, including discussion of the potential influence of the Fabian Society andsocialism more generally on Pigou’s thinking up to 1912.
• [2] The letter is reprinted in Coats (1992: 314—315).
• [3] The relationship between ‘Some Remarks on Utility’ (Pigou 1903b) and ‘Producers’ and Consumers’Surplus’ (Pigou 1910 [2002]) is considered in McLure (2010).
• [4] Indeed, today the manifesto of the so-called Pigou Club, established by Gregory Mankiw (2006), advocates the imposition of a Pigouvian tax on gasoline to combat, amongst other things, global warming androad congestion.
• [5] These episodes are discussed in some detail by Aslanbeigui (1996).
• [6] Modern historians of Marshallian economics, such as Neil Hart (2013), are even more critical of Pigou,suggesting that his work on costs and the equilibrium firm closed off the evolutionary dimension ofMarshall’s work to the economics profession, with the result being that important evolutionary themes inMarshall were not to be developed further.
• [7] The definitive ‘rational’ treatment of this historical issue was undertaken by Ambrosi (2003).