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 In other words, from the standpoint of actual economies, these categories lack empirical and historical content.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.


150th Anniversary of Capital: Reading Wage-Labour and Capital (Part II)

This post is second in the two-part commemoration of Capital‘s 150th anniversary (last year); part I was a commentary on Francis Wheen’s biography of Capital and Part II undertakes a critical engagement with Wage-Labour and Capital (available freely at, which were originally lectures, and later published as a set of articles in 1849 in the Neue Rheinische Zeitung (which roughly translates into the ‘New Rhenish Newspaper’). Marx had delivered the lectures at the German Working Men’s Club of Brussels in 1847, a year before the publication of the Communist Manifesto and twenty years before the publication of Das Kapital.

wage labour capitalWage-Labour and Capital is made up of 9 short chapters, with the largest chapter containing 5 pages, and a total of 48 pages. In the introduction, F. Engels provides his reasons for altering the original text of Marx, and writes ‘this pamphlet is not as Marx wrote it in 1849, but approximately as Marx would have written it in 1891’ (p. 6). To assess the merits of Engel’s editorial intervention, one needs to compare it with Marx’s original. Marx intended his writings to be understood by the workers and therefore they do not ‘presuppose a knowledge of even the most elementary notions of political economy’ (p. 16).

In capitalism, according to Marx, ‘it appears that the capitalist buys their labour with money, and that for money they sell him their labour. But this is merely an illusion. What they actually sell to the capitalist for money is their labour-power’ (p. 17). Therefore, labour-power ‘is a commodity, no more, no less so than is the sugar. The first is measured by the clock, the other by the scales’ (p. 17). And wages is the ‘special name for the price of labour-power’, a ‘peculiar commodity’. The wage-workers, who owns labour-power, does not really have a choice in deciding whether to sell it to the capitalist or not, but is forced to ‘in order to live’ (p. 19). While it appears that the worker has a choice, in essence, she does not (this idea can help transform the dominant labour-leisure trade-off story). Then Marx points out that this feature ‘ the idea of free labour ‘ is particular to capitalism, and not found in slave or feudal societies. While the worker owns labour-power, the capitalist owns ‘raw materials, tools, and means of life’ (p. 20). The following description of work (and life) deserves to be quoted in full.

‘Life for him begins where this activity [work] ceases, at the table, at the tavern, in bed. The 12 hours’ work, on the other hand, has no meaning for him as weaving, spinning, boring, and so on, but only as earnings, which enable him to sit down at a table, to take his seat in the tavern, and to lie down in a bed.’ (p. 19)

Subsequently, Marx discusses the determination of commodity prices, which contains an account of competition. The latter is studied in three parts: ‘among the sellers’, ‘among the buyers’, and ‘between the buyers and the sellers’ (p. 21). It is this competition which seeks the highest ‘customary profits’ among the different sectors, and this constant ‘immigration’ (p. 23) tends to equalise the rate of profits across sectors. This force of competition also tends to bring the actual price of a commodity close to its ‘cost of production’ (p. 24). The ‘fluctuations’ occasioned by competition is not an ‘accident’ or exception but the ‘law’ contrary to the accounts of the ‘bourgeois economists’ (p. 24). Thus, ‘In the totality of this disorderly movement is to be found its order’ (p. 24).

Wages are regulated by the cost of production of labour-power, which ‘is the cost required for the maintenance of the labourer as a labourer, and for his education and training as a labourer’ (p. 26). In other words, it is ‘the cost of the existence and propagation of the worker’ (p. 27). Here, Marx is referring to the wages for the entire class of workers and not of an individual worker because ‘millions of workers, do not receive enough to be able to exist and to propagate themselves’ (p. 27).

Most economists define capital as produced means of production, and this is the starting point of their analysis. But Marx pushes the starting point further and rightly labels capital as ‘accumulated labour’, as the raw materials, instruments, and machines were also created by labour. Capital is also a ‘social relation of production’ (p. 29). As noted earlier, the existence of wage labour is a characteristic of capitalism where workers are forced to sell their labour power to the capitalist in order to live. And as Marx writes, ‘The existence of a class which possesses nothing but the ability to work is a necessary presupposition of capital’ (p. 30). Furthermore, capital, or accumulated labour dominates living labour.

Mainstream (marginalist) economics is built on the marginal productivity theory of distribution which states that under conditions of perfect competition, in equilibrium, workers are paid the marginal product of capital and capitalists get the marginal product of capital ‘ a harmonious explanation of income distribution. In contrast, Marx argues that wages are profit are inversely related pointing to the fundamental conflict characterising income distribution in a capitalist society (p. 37). In the same chapter (VII), Marx outlines two major routes through which profits increase: (1) increase in aggregate demand and (2) technological improvements (see an earlier post on the link between demand, profits, and employment). In the following chapter, Marx reiterates the distributional conflict: ‘the interests of capitals and the interests of wage-labour are diametrically opposed to each other’ (p. 39). And ‘If capital grows rapidly, wages may rise, but the profit of capital rises disproportionately faster. The material position of the worker has improved, but at the cost of his social position. The social chasm that separates him from the capitalist has widened’ (p. 40). This underscores the social nature of economic relations, an aspect which marginalist economics has eschewed with its assumption of the independence of individual preferences.

The following remark about economists by Marx is appropriate for our current times: ‘The economists tell us, to be sure, that those labourers who have been rendered superfluous by machinery find new venues of employment’ (p. 45). I shall end this post by quoting Marx on capitalist accumulation, crises, and exploitation of markets, since it continues to remain relevant today.

”capitalists are compelled ‘ to exploit the already existing gigantic means of production on an ever-increasing scale, and for this purpose to set in motion all the mainsprings of credit, in the same measure do they increase the industrial earthquakes, in the midst of which the commercial world can preserve itself only by sacrificing a portion of its wealth, its products, and even its forces of production, to the gods of the lower world ‘ in short, the crises increase. They become more frequent and more violent, if for no other reason, than for this alone, that in the same measure in which the mass of products grows, and therefore the needs for extensive markets, in the same measure does the world market shrink ever more, and ever fewer markets remain to be exploited, since every previous crisis has subjected to the commerce of the world a hitherto unconquered or but superficially exploited market’ (pp. 47-8)




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.