Revisiting J. H. Clapham’s ‘Empty Economic Boxes’

This blog post revisits the economic historian J. H. Clapham’s1922 classic paper ‘Of Empty Economic Boxes‘ published in The Economic Journal, and raises some critical questions about the continued use of constant returns to scale (CRS hereafter) assumption in marginalist (or neoclassical) microeconomics and macroeconomics. In 1926, Piero Sraffa took Clapham’s 1922 paper as a starting point to mount a more devastating logical critique of Marshallian notions of increasing returns and the representative firm; this was published as part of a symposium in the Economic Journal.

What is returns to scale’ According to marginalist economics, the technique of producing a commodity may be represented by a functional relationship between inputs (say, k’and l) and output (say, y): y’= f(k,l). If all the inputs are multiplied by a positive scalar m, and the resultant output is expressed as mr’y, then r’represents the magnitude of the returns to scale. If r = 1, the technique exhibits CRS, if r < 1, it exhibits diminishing returns to scale (DRS), and if r’> 1, it exhibits increasing returns to scale (IRS).

Despite the ‘advances’ in mainstream economics research, the marginalist theory of value and distribution still requires the CRS assumption (and the diminishing returns to a factor assumption) to make several key claims. The aggregate production function employed in the Solow growth model is assumed to exhibit CRS. And the Solow growth model forms the core of supply-sidegrowth accounting exercises which are used to make policy prescriptions (for a critique of one such exercise for the Indian economy, see Joshi & Thomas 2013).

The central argument in Clapham’s article is that the categories of diminishing returns, constant returns, and increasing returns industries are ’empty economic boxes’. In other words, from the standpoint of actual economies, these categories lack empirical and historical content. Consequently, industries cannot be classified into one or the other box a priori.

Clapham asks: what does AC Pigou (in his Economics of Welfare) mean when he writes ‘when conditions of diminishing returns prevail’ (p. 305)’ According to Clapham ‘constant returns…must always remain a mathematical point, their box an empty one’ (p. 310). He acknowledges that different kinds of returns have a ‘logical’ and ‘pedagogic value’ which ‘goes so prettily into graphs and equations’ (p. 312). How can we then use this framework to draw policy conclusions given the inability to classify industries a priori into constant, diminishing, and increasing returns’

The following observation by Clapham is insightful and worth thinking about further. He writes that diminishing returns must be balanced with increasing returns to arrive at constant returns (p. 309). Surely, this makes no conceptual sense and neither does it have any basis in empirical reality. As Clapham puts it, with CRS ‘the conception of the balance of forces, man’s organization versusNature’s reluctance, was worked out’ (p. 309). In other words, is CRS an expression of the balancing of the symmetrical forces of IRS (‘man’s organization’) and DRS (‘Nature’s reluctance’)’ For a visual representation, see the images below. If so, it would add to the symmetrical concepts found in the marginalist toolbox, most notably that of supply and demand. However, beyond the ease of exposition symmetry provides us, is it really how the actual world works’


CRS, DRS, and IRS posit an a priori functional relationship between labour (L) and capital (K), the ‘factors of production’ and output (Y) for an individual firm and for an economy: Y=f(L,K). While the idea underlying the production function, whether industry-level or aggregate-level, that outputs are produced by inputs is commonsensical and intuitive, its expression as a mathematical function isn’t as benign. Since marginalist economics requires continuous functions (often, of a monotonic nature) to ensure the existence of equilibrium, the ‘f’ is able to map infinitesimal combinations of Land Kto a unique Y. This ‘one-way street’, to use Sraffa’s phrase in his 1960 classic Production of Commodities by Means of Commodities(see my blog post Sraffa), between ‘factors of production’ and output is conceptually unsatisfactory because it misses a fundamental aspect about modern economies: the structural interdependence between inputs and outputs. In addition, it assumes that capital goods (K) are infinitely divisible, a very difficult assumption to uphold.

John Eatwell (2008; first published in 1987), in his entry on ‘returns to scale’ published in The New Palgrave Dictionary of Economics, also notes the apparent symmetry between IRS and DRS but points out its spuriousness. While there is no evidence of functional relationships in Adam Smith and David Ricardo, Smith’s discussion of division of labour, capital accumulation, and economic growth indicates that he recognised scale-enabled technological progress and Ricardo recognised diminishing returns to land, a non-reproducible input in production. Subsequently, Alfred Marshall, in his Principles of Economics, ‘attempted to formulate a unified, symmetric, analysis of returns to scale which would provide the rationale for the construction of the supply curve of a competitive industry, derived in turn from the equilibria of the firms within the industry’ (Eatwell 2008, p. 140). This point was initially noted by Sraffa 1926, and later much more thoroughly investigated also by Krishna Bharadwaj (1978).

It is well understood that the question of returns to scale is important in the construction of the supply curves which are integral for the marginalist price theory. Therefore, a thorough critical study of mainstream price theory and a renewal in the interest in rival price theories (found in Ricardo, Marx, Sraffa, and Kalecki, among others) are warranted. This is crucial because it is value or price theory which provides us with the economic possibilities a competitive economy generates. If it generates unemployment and worsens inequality, we know that intervention of a particular kind is necessary. However, if it generates full employment and reduces inequality, then it supports the idea of making markets more competitive and reducing government intervention.


Clapham, J. H. (1922), “Of Empty Economic Boxes.”‘The Economic Journal,’vol. 32, no. 127, pp. 305-14.

Eatwell, John (2008), ‘Returns to Scale’. In: Durlauf S.N., Blume L.E. (eds.) The New Palgrave Dictionary of Economics. London: Palgrave Macmillan.

Sraffa, Piero (1926), “The Laws of Returns under Competitive Conditions.”‘The Economic Journal,’vol. 36, no. 144, pp. 535-50.


I thank Mohib Ali for his helpful comments.


Bernard Mandeville and his Unorthodox Economics

mandevilleI first came across Bernard Mandeville (1670-1733) while reading Keynes’s General Theory as a student at the University of Hyderabad. Mandeville’s Fable of the Bess: or, Private Vices, Publick Benefits was published in two parts in different times. This work has its origins in an earlier work of his: The Crumbling Hive: or Knaves Turn’s Honest (1705). I recently read the Fable of the Bees edition published by Oxford University Press in 1924 with a commentary by F. B Kaye; interestingly, this work is an expanded version of Kaye’s PhD dissertation submitted at Yale University in 1917. On looking up the Yale University Library Catalogue, I found out his complete name and the years he lived – Frederick Benjamin Kaye (1892-1930).

Mandeville was born into a family of city governors, physicians, scholars, and naval officers. He studied medicine and philosophy. The other notable ‘physician-economists‘, as Peter Groenewegen, the emeritus historian of economic thought at University of Sydney, labels them, are William Petty and Fran’ois Quesnay (for a short account of the ‘natural’ origins of economics, read this). Mandeville also published a book entitled A Treatise of the Hypochondriack and Hysterick Passions (1711). Kaye informs us that his books sold very well.

The Root of evil Avarice,

That damn’d ill-natur’d baneful Vice,

Was Slave to Prodigality,

That Noble Sin; whilst Luxury.

Employ’d a Million of the Poor,

And odious Pride a Million more

Envy it self, and Vanity

Were Ministers of Industry;

Their darling Folly, Fickleness

In Diet, Furniture, and Dress,

That strange, ridic’lous Vice, was made

The very Wheel, that turn’d the Trade.

(p. 25; or see the online source)

In the above passage, Mandeville is arguing that prodigality, considered a virtue, is actually a public vice and luxury, considered a vice, is a public virtue. The importance of consumption in the growth of the economy is also to be found in Sismondi, Malthus, Marx, and Keynes. As Kaye puts it, this is Mandeville’s thesis: ‘vice is the foundation of national prosperity and happiness’ (p. xlvii). In other words, public benefits are a consequence of private vices ‘ ‘pride’ and ‘luxury’.

According to Mandeville, all actions were influenced in part by selfishness. If all people behaved selflessly, Mandeville argued that trade and crafts would be abandoned.

As Pride and Luxury decrease,

So by degrees they leave the Seas.

Not Merchants now, but Companies

Remove whole Manufactories.

All Arts and Crafts neglected lie;

Content, the Bane of Industry.

(p. 34; or see the online source)

How can vice become a virtue’ This is the paradox, much like Keynes’s paradox of thrift where increase in saving, while good for the individual, is bad for the economy as a whole.

THUS every Part was full of Vice,

Yet the whole Mass a Paradise;

(p. 24; or see the online source)

Mandeville thus argues that private vices have public benefits. What is ‘good’ or ‘virtuous’ for an individual need not be beneficial to the public or society. In the General Theory, Keynes approvingly cites Mandeville’s The Fable of the Bees before articulating his fundamental point: ‘capital is not a self-subsistent entity existing apart from consumption’ (p. 106). And, again on p. 371, he places Mandeville among ‘the brave army of heretics’ alongside Malthus, Gesell and Hobson (see Keynes’s short commentary on Mandeville on pp. 359-362 in ch. 23).

It must be noted that Mandeville favoured virtuous vice and not vicious vice (such as crime and theft). Moreover, his thesis is not that all private vices have public benefits. The Fable of The Bees, Kayes cautions us, ought not to be taken literally. As Kaye elaborates, ‘it is not ascetic virtues, such as hoarding frugality, which make a nation prosperous’ (p. lxviii).

Let me now summarise Mandeville’s position on luxury spending. First, he disagreed with the extant view that frugality is a virtue. Second, he disagreed with the dominant view that luxury is bad for the economy. We must also remember the context in which he is writing ‘ luxury was condemned by Christianity. Indeed, Mandeville was challenging the extant religious and economic orthodoxy with his arguments favouring luxury.

Mandeville argued for freer trade both domestically and internationally (pp. xcviii ff.). His argument was anticipated by mercantilists such as Charles D’Avenant, Dudley North, and Josiah Child. According to Kaye, it is in Mandeville’s work that ‘individualism became an economic philosophy’ (p. ciii). In fact, F. A. Hayek labels Mandeville ‘an advocate of laissez-faire as Adam Smith’ (p. 135) in his 1966 lecture at the British Academy (published in 1967; this lecture is publicly available). And, as is to be expected, he thinks that Keynes’s enthusiastic approval of Mandeville is unfounded (p. 133). Moreover, Hayek finds Mandeville’s ‘understanding of human nature’ noteworthy but not his economics ‘ of division of labour and luxury consumption (pp. 125-6). Karl Marx notes that Smith’s ideas on division of labour were strongly influenced by Mandeville’s work but that there is no mention of Mandeville in the Wealth of Nations. However, Smith discusses Mandeville’s views on vice and virtue in his Theory of Moral Sentiments.

Perhaps, it is befitting to conclude this essay by summarising Marx’s views regarding Mandeville. After all, Marx is one of the greatest unorthodox economist whose political economy is of enduring value.

Originally, Political Economy was studied by philosophers like Hobbes, Locke, Hume; by businessmen and statesmen, like Thomas More, Temple, Sully, De Witt, North, Law, Vanderlint, Cantillon, Franklin; and especially, and with the greatest success, by medical men like Petty, Barbon, Mandeville, Quesnay.

(Capital, vol. 1, Ch. 25: The General Law of Capitalist Accumulation)

Marx describes Mandeville as ‘an honest, clear-headed man’ in volume 1 of Capital and writes in part 1 of Theories of Surplus-Value that ‘Only Mandeville was of course infinitely bolder and more honest than the philistine apologists of bourgeois society.’




A Foreword to Sraffa’s Production of Commodities by Means of Commodities

Piero Sraffa’s classic Production of Commodities by Means of Commodities (PCMC) was published in 1960. It runs into 87 pages of main text (inclusive of the content list), 6 pages of appendices, less than 3 pages of Preface and a 3-page index. As we pointed out in A Foreword to Keynes’s General Theory, by foreword, we mean the following: ‘The introduction to a literary work, usually stating its subject, purpose, scope, method, etc.’ (Oxford English Dictionary).

The book is subtitled ‘Prelude to a Critique of Political Economy’. This slim book is divided into 3 parts: (1) ‘single-product industries and circulating capital’; (2) ‘multi-product industries and fixed capital’; and an untitled third part containing a single chapter titled ‘Switch in Methods of Production’. In the Preface, Sraffa acknowledges Keynes, A. S. Besicovitch (‘for invaluable mathematical help’), Frank Ramsey and Alister Watson. Sraffa was friends with Gramsci and Wittgenstein. [Ramsey, a friend of Keynes, supervised the 40-year old Wittgenstein’s PhD thesis at the age of 26 (source).] Appendix D contains the ‘references to the literature’ wherein works by Quesnay, Smith, Ricardo, Torrens, Malthus and Marx are mentioned. As Sraffa writes in the appendix, ‘[t]he connection of this work with the theories of the old classical economists have been alluded to in the Preface. A few references to special points, the source of which may not be obvious, are added here’ (p. 93). The orthodox economists mentioned by Sraffa are Marshall and Wicksteed.

With respect to method, Sraffa adopts the standpoint of the old classical economists ‘ the surplus approach to value and distribution. This is contrast to the orthodox marginalist scarcity approach to value and distribution. In the surplus approach, one distributive variable is exogenously determined. This is in fact a realistic assumption because the rate of interest is set by monetary authorities and the rate of profit can be conceptualised as a sum of the riskless rate of interest (on government securities) and a pure rate of return on capital.

The conception of the ‘system of production and consumption as a circular process’, Sraffa notes in Appendix D, is to be found in Quesnay which ‘stands in striking contrast to the view presented by modern theory [marginalist], of a one-way avenue that leads from ‘Factors of production’ to ‘Consumption goods” (p. 93) [cf. Kurz & Salvadori 2005]. The subject matter of PCMC is the theory of value and distribution ‘ how are relative prices and distributive variables determined’ More specifically, in an economy where the production of commodities is undertaken by means of commodities, how are prices and distributive variables determined’ Sraffa’s correct solution is that ‘the distribution of the surplus must be determined through the same mechanism and at the same time as are the prices of commodities’ (p. 6). What are the data or givens’ (1) size and composition of output; (2) methods of production; and (3) one distributive variable (either the wage rate or profit rate). The first two givens are mentioned in the Preface when Sraffa writes that his ‘investigation is concerned exclusively with such properties of an economic system as do not depend on changes in the scale of production or in the proportions of ‘factors” (p. v). The rationale for the third given is as follows: ”the practice, followed from outset, of treating the wage rather than the rate of profits as the independent variable or ‘given’ quantity’ has been reversed because the ‘rate of profits, as a ratio, has a significance which is independent of any prices, and can well be ‘given’ before the prices are fixed ‘ in particular by the level of the money rates of interest’ (p. 33).

While the scope of PCMC is limited to the subject matter, its implications on general economic theory are far reaching; for instance, his work has implications for the theory of value and distribution (capital theory forms an important part of this). Therefore, his work has positively contributed to the theorising of economic growth and environmental economics. Also, Sraffa’s work is to be a ‘basis for a critique of’ ‘the marginal theory of value and distribution’ (p. vi). Sraffa’s work is a coherent articulation of the theory of value and distribution the classical economists attempted to solve. At the same time, it also forms the basis for a critique of the marginalist theory of value and distribution by underscoring the logical fallacy in treating capital as a quantity independent of prices.

In a sense, the purpose of Sraffa’s work depends on the use that is made of it and there is a growing body of literature emanating from PCMC (a useful survey is Aspromourgos’s 2004 paper titled ‘Sraffian Research Programmes and Unorthodox Economics’). The classical approach to economics has been made more articulate and coherent. By marrying the classical or ‘surplus’ approach to value and distribution with the principle of effective demand, an alternative explanation for the determination of activity levels and economic growth has been developed. Work is also going on in the areas of environmental economics, public debt, monetary economics and history of economic thought, all of which draws upon and/or are inspired by Sraffa’s work.

The Indian readers would be interested to know that an Indian edition of PCMC was published by Vora & Co. Publishers, Bombay (available online). ‘However, PCMC is out of print since 1996 according to Cambridge University Press.

Those of us who are dissatisfied with mainstream neoclassical economics will find valuable insights and an economically superior but modest basis in Sraffa’s work to develop a coherent alternative to the mainstream approach to economic thinking. Particularly fruitful is this research programme when combined with the rich insights of the classical economists and Marx as well as the principle of effective demand of Kalecki and Keynes.

A Very Brief Introduction to Adam Smith’s Wealth of Nations

The Inquiry into the Nature and Causes of the Wealth of Nations (WoN hereafter) was published on 9th March, 1776. It was advertised in the concluding paragraph of Theory of Moral Sentiments (1759). This blog post is a very brief introduction to Adam Smith’s theory of political economy as presented in the WoN. According to John Rae, the biographer of Smith, the WoN ‘took twelve years to write, and was in contemplation for probably twelve years before that.’ Smith never engaged in any commercial activity unlike his predecessor, Richard Cantillon or his successor, David Ricardo, yet his insights into the working of the competitive economy is intellectually deep and of enduring relevance. His intellectual acquaintances include David Hume, Francois Quesnay, Jacques Turgot and Voltaire.

WoN is divided into 5 books: Book I presents a detailed examination of how labour becomes productive, and contains a theory of supply (of output). On what factors does the annual supply of commodities depend’ Book II builds on this and contains a theory of accumulation (of capital stock). The growth policies undertaken by various nations form the content of Book III. The existing theories of political economy are critically appraised in Book IV; this book also includes the policy effects of these theories. Finally, in Book V, a theory of public finance ‘ the theory of the revenue, expenditure and borrowing of the government ‘ is outlined. Given the recurring themes of economic growth and development in this blog, the title of books I and II deserve to be quoted in full.

Book I: Of the Causes of Improvement in the productive Powers of Labour, and of the Order according to which its Produce is naturally distributed among the different Ranks of the People

Book II: Of the Nature, Accumulation, and Employment of Stock

In other words, the first book contains a theory of income distribution and the second contains a theory of economic growth. Recent research has noted the similarities between Smith’s theory of economic growth and neoclassical ‘new economic growth theory’ of Romer; in fact, Smith’s theory clearly emerges as a superior one.

The ‘necessaries and conveniences of life’, according to Smith, are produced by labour. That is, labour produces the annual aggregate supply of commodities and services. The nation is considered better supplied if the proportion between the annual aggregate supply and annual population is high. To expand this definition and adopting modern terminology, we can say that this idea of Smith corresponds to that of output per capita (for example, a high GDP per capita is favoured over a low GDP per capita). Further, Smith asks: what determines the output per capita’ According to Smith, there are two factors which determine this proportion. (1) The productivity of labour, and (2) the ratio of workers employed in physical and human capital generation to other workers. Smith uses a different terminology: the ratio of productive to unproductive labour. The number of workers employed in physical and human capital formation is necessarily in proportion to the capital advanced in these sectors. And, labour productivity depends on the capital advanced. But, what is there in Smith’s theory of economic growth which ensures that the growth in aggregate supply is validated by an equivalent growth in aggregate demand’

Smith’s WoN, particularly the first 2 books, is of much contemporary relevance in understanding the socio-cultural idea of ‘subsistence wage’. Also, it contains a rich exposition of productivity unlike the ‘blackbox’ of productivity commonly found in the Solow-type growth theory. Smith’s WoN contains both logical rigour as well as rich prose, and together they vastly enrich our understanding of economic phenomena.