On the Capital/Output Ratio

A post on the capital output ratio was perhaps inevitable given my teaching and research engagements with macroeconomics, growth theory, and capital theory. This blog post seeks to critically discuss some of the manifestations of the capital-output ratio (K/Y ratio henceforth) in economics. 

K/Y ratio in Macroeconomics

The K/Y ratio captures a technological characteristic of the economy as a whole. It conveys to us the amount of capital required to produce one unit of output. A reduction in it therefore implies we require less capital to produce one unit of output. 

Since capital refers to the stock of produced means of production, which are of a heterogenous nature, K for the economy as a whole requires aggregation via prices: k1p1+k2p2+…+knpn=K. That is, K refers to, as H. G. Jones puts it (p. 17) in his 1975 book An Introduction to Modern Theories of Growth, “an index of aggregate capital.” Of course, Y too requires aggregation via prices.

Roy Harrod, in the chapter ‘Capital Output Ratio’ in Economic Dynamics (1973) treats K/Y ratio as a “kindred concept of the capital-labour ratio” (p. 46). Subsequently, he outlines the scope of the capital-labour ratio in economic studies. 

“It is to be stressed that the capital-labour ratio is a useful weapon for comparing alternative methods of producing a given object, for comparing methods of producing different objects or for comparing the changes through time of methods of producing a given object. It is on the whole an unserviceable tool in relation to national income as a whole, but it can be employed in a very rough sort of way for comparing different countries” (p. 48, emphasis added). 

Similarly, Harrod writes that “the concept of the capital labour ratio is not very helpful, if applied to the economy as a whole, owing to the difficulty of assessing the value of K, namely capital as a whole” (p. 50). 

Additionally, I think that such an aggregate conceptualization conceals more than it reveals. For instance, it conceals the nature of interdependence of production in an economy. What if K/Y changes because of a change in the nature of structural interdependence? Or, what if it changes because of a change in the volume and composition of aggregate consumption demand? After all, the volume of investment influenced by consumption. As Keynes rightly writes in Chapter 8 of The General Theory, “capital is not a self-subsistent entity existing apart from consumption”. 

K/Y ratio in Growth Theories

The K/Y ratio is used as an argument in Kaldor’s (1957) stylized facts: ‘steady capital-output ratios over long periods’. Here too, what is it saying about the structural nature of production and consumption in the economy? 

While Kaldor is talking about ex-post K/Y ratios, the ex-ante K/Y ratio plays a crucial role in Harrod’s growth equation g=s/v. Here, s refers to the marginal propensity to save and v refers to the desired or normal K/Y ratio. A decrease in v raises g, or more accurately, the ‘warranted rate of growth’. 

In the super abstract setup of the corn model (as in Ricardo) or the single-commodity model (as in Solow), since the input and the output are the same commodity, aggregate K is a homogenous set. This assumption allows us to sidestep the problems associated with the measurement and aggregation of ex-ante K. 

One cannot help but wonder how Solow’s single-commodity growth model (expressed via the aggregate production function) continues to be applied in growth accounting exercises on actual multi-commodity economies. We had noted some of the theoretical and empirical problems with one such exercise on the Indian economy in a short note in Economic & Political Weekly.  

K/Y ratio and Capital Theories

Capital theories are concerned with the conceptualization, measurement, valuation, determination, and aggregation of capital. Owing to the central role capital plays in production, the choice of the capital theory has a significant impact on both microeconomics and macroeconomics. Moreover, since capital accumulation is central to growth theory, the choice of the capital theory has a significant impact on development theories too. Similarly, on international trade theories; on this subject, you can consult the 1979 book Fundamental Issues in Trade Theory edited by Ian Steedman. 

In sum, while mathematization of the growth models gives us a better sense of its grammar, capital theory helps us understand its epistemology. And it is the latter which can better guide the use of K/Y ratio in economic theories, empirics, and policies.  

Cheryl Misak’s Ramsey: Notes on his association with Harrod, Dobb, and Sraffa

Frank Ramsey was in Cambridge at the same time as John Maynard Keynes, Arthur Pigou, and Piero Sraffa, some of the most influential economists of the twentieth century. Ramsey died on 19th’January 1930, six years before The General Theory of Employment, Interest and Money’(1936), ten years after The Economics of Welfare(1920), and around the same time as the central propositions in Production of Commodities by Means of Commodities’(PCMC) was worked out. While an earlier blog post had examined Ramsey’s views on the rate of interest, the present one narrates his intellectual association with Maurice Dobb, Roy Harrod, and Sraffa, and a forthcoming one will focus on his intellectual association with Pigou and Keynes. The present and future posts are primarily based on Cheryl Misak’s new biography of Ramsey (2020, Oxford University Press). This post supplements the observations found in Misak’s Ramseywith those found in the books on Harrod and Sraffa published as part of the Palgrave Macmillan ‘Great Thinkers in Economics’ series by Esteban P’rez Caldentey (2019) and Alessandro Roncaglia (2009) respectively and the book on Dobb by Timothy Shenk (2013) published as part of the ‘Palgrave Studies in the History of Economic Thought’ series.


While Harrod today is probably most well-known for his contributions to growth theory, he made important contributions to the fields of trade cycle theory, imperfect competition, and international economics. While there are 14 references to Harrod in Misak’s Ramsey, there are only eight references to Ramsey in Caldentey’s Harrod’(2019). [If there are two or more mentions of Harrod in a single page, I treat that as one reference.]

Ramsey and Harrod were friends (p. xxxi). Ramsey had known him ‘since 1922, when Harrod spent part of the year at King’s. Frank had taken Harrod under his wing then, introducing him to [G. E.] Moore and others’ (p. 195). After Ramsey was elected a fellow of King’s College, Cambridge in 1924, he renewed his friendship with Harrod, ‘a young left-leaning economics don at Oxford ‘ and they travelled between Oxford and Cambridge for intellectually rich weekends’ (p. 195). Caldentey mentions Harrod experiencing ”tremendous stimuli” after meeting Ramsey in Cambridge as opposed to his ‘frustrating Oxford experience’ (p. 10).

Although Harrod’s paper on the concept of marginal revenue curve was eventually published in the Economic Journal’as ‘Notes on Supply‘ (1930), on Ramsey’s advice, its editor, Keynes, had initially rejected the article in 1928 and had asked for revisions on the treatment of cartels (p. 305). In the meantime, according to Harrod, others had ‘discovered’ his concept and therefore he failed to receive credit for inventing it. Caldentey informs us that Harrod’s initial paper submitted in 1928 was titled ‘Notes on Monopoly and Quasi-competition’ wherein ‘he derived the increment of aggregate demand curve which was later re-baptized, the marginal revenue curve by Joan Robinson’ (p. 18). Moreover, Caldentey notes that in the foreword to the first edition ofThe Economics of Imperfect Competition’(1933), Robinson acknowledges the following individuals for teaching her about the marginal revenue curve: C. H. P. Gifford, P. S. Sloan, and T. O. Yntema (p. 101, n. 30). Also see Caldentey (pp. 18-19, 100-1) for a recounting of the refereeing episode between Ramsey and Harrod, which also makes reference to the three-volume work, The Collected Interwar Papers and Correspondence of Roy Harrod’published by Edward Elgar in 2003 under the editorship of Daniele Besomi.


Dobb’s contributions to Marxist economics are well established. I was introduced to his work during my Master’s in Economics at the University of Hyderabad where we read selected parts from Theories of Value and Distribution Since Adam Smith: Ideology and Economic Theory’(1973). His collaboration with Sraffa in editing and producing The Works and Correspondence of David Ricardo’has also been noteworthy. In Shenk’s Dobb, surprisingly, there is not even a single reference to Ramsey while there are 21 references to Dobb in Misak’s Ramsey.

Dobb was Ramsey’s friend from their undergraduate days (1920-3) at Cambridge (p. 94). They had started their degrees at the same time (p. 79); Ramsey enrolled for mathematics at Trinity College and Dobb for economics at Pembroke College. And during this time, ‘Dobb had considerable influence on Ramsey, both by engaging with him about the kind of socialism that would be best, and by introducing him to workers’ meetings’ (p. 299). While Ramsey was finishing his secondary education at Winchester in 1920, in addition to reading the economics books by Alfred Marshall and Keynes, he also read works by Karl Marx and V. I. Lenin (p. 47). However, according to Misak, it isn’t clear how much they associated with each other after completing their undergraduate studies (p. 87).

In his 1925 doctoral thesis, Dobb tried to bring Marx and Marshall together (p. 300). Shenk points out that Dobb had been trying to synthesize Marx and Marshall even before he started his PhD at the London School of Economics (LSE): ‘Dobb, too, sought to integrate marginalism with classical political economy, but with Marx substituting for Ricardo as the standard-bearer for political economy. ‘ In Dobb’s vision, Marx appears as a theorist of the social, Marshall of the economic’ (p. 36). Dobb’s PhD thesis was published in 1925 as Capitalist Enterprise and Social Progress, and Shenk provides us with its outline: ‘Dobb dedicated the first section to economic theory, the second to economic history, and the third to evaluating contemporary economic practices from the perspective developed over the course of the book’ (p. 38). Since Ramsey ‘was considered (and considered himself) a socialist’ (p. 301), Misak argues that Ramsey’s use of utility theory in his paper on optimal saving needs to be seen in the light of the synthesis Dobb had attempted between Marxism and marginalism (p. 302).

Ramsey’s view of the use of mathematics in economics was similar in spirit to that of Dobb (and Keynes): ‘Like Dobb, he thought that one ignores mathematics at one’s peril, for the mathematics has to be right in order for progress in the real world to be made. And some real-world issues are going to be solvable by doing the maths’witness Ramsey’s response to the Douglas Proposals. But he did not think that the mathematician could step in and solve all problems. He agreed with Keynes that we mustn’t be so taken with the precision of mathematics that we erase the outlines of the very thing we are examining. As Ramsey so often put it, one mustn’t be woolly, but one mustn’t be scholastic either’ (p. 326).


Sraffa has made significant contributions to price theory and capital theory and deserves high praise for his editorship of the collected works and correspondence of Ricardo. I have written on Sraffa earlier.’ While there are only two references to Ramsey in Roncaglia’s Sraffa, there are 18 references to Sraffa in Misak’s Ramsey. Given this scant attention to Ramsey in Roncaglia’s Sraffa, I make use of Heinz Kurz and Neri Salvadori’s essay ‘Sraffa and the Mathematicians: Frank Ramsey and Alister Watson’ first published in 2000 in Piero Sraffa’s Political Economy: A Centenary Estimate, a volume edited by Terenzio Cozzi and Roberto Marchionatti (as republished in Classical Economics and Modern Theory: Studies in Long-Period Analysis, an edited volume by Kurz and Salvadori in 2003).

As Sraffa writes in the preface to his 1960 classic, ‘the central propositions had taken shape in the late 1920’s’ (p. vi). In the following paragraphs, he expresses his gratitude to Ramsey (along with Alister Watson) for ‘invaluable mathematical help’at different periods’, and his greatest debt is reserved for A. S. Besicovitch. Kurz and Salvadori examine Sraffa’s diaries to identify the number of his meetings with Ramsey; according to the dairy entries, they met twice in 1928 (28 June and 11 November) and thrice in 1929 (10 May, 30 May, and 29 November) (p. 190).

The main outcome of their first meeting is capably captured by the following excerpt from Kurz and Salvadori: ‘At first Sraffa appears not to have explicitly distinguished between the quantity and the price or value of a commodity, a fact to which Ramsey immediately seems to have objected. Sraffa then appears to have introduced the distinction during the conversation with Ramsey’. Ramsey then reformulated the system first by putting the system of homogeneous linear equations in its canonical form, then by setting the determinant of coefficients equal to zero in order to get a non-trivial solution’ (p. 197). The key aspects of this meeting are not as ably captured in Misak and it is also incorrectly stated that Sraffa’s famous work related to ‘the determination of prices and’outputs’ (p. 305; emphasis added) whereas the size and composition of output is a given in PCMC.

Ramsey died in the middle of writing his book on truth and probability. Misak draws attention to the fact that after his death the philosopher R. B. Braithwaite published some of Ramsey’s essays in 1931 under the title The Foundations of Mathematics and Other Logical Essays’(p. 273). According to Misak, John von Neumann and Oskar Morgenstern had reached very similar conclusions in their 1944 Theory of Games and Economic Behaviour’(p. 274). And Misak further notes that, the similarity was so striking that John Hicks went to the extent of writing to Sraffa on 3rd’September 1960 asking if Ramsey’s ideas were transmitted to von Neumann through him (and his ‘mathematical friends’) but Sraffa didn’t reply (p. 274; although a draft of Sraffa’s response is available, it is not clear whether he actually sent it to Hicks). However, after consulting the letter (available here), it is clear that Hicks is actually asking Sraffa how von Neumann arrived at a similar theoretical outlook as Sraffa; and it is not about the similarities between Ramsey and von Neumann as Misak claims.


This blog post ends with some critical observations on Ramsey’s engagement with value theory. According to Misak, Ramsey ‘blended neo-classical economics and socialism’ (p. 303). Despite his ‘scepticism about the utility theory of value’, as Misak notes, ‘his two famous papers were written in the neo-classical framework of individuals maximizing utility’ (p. 302). The two important pieces of evidence Misak provides for the former are given in the following excerpt: ‘In his 1924 Apostles paper, he castigated Mill for putting all his eggs in the utilitarian basket. During 1927’28, when his two important papers in economics were written, he was also working on a book in which he hoped to carve out a subtle, naturalist theory of value’ (p. 302). Since this book was not completed, it is difficult to state whether Ramsey would have stood closer to the neoclassical or the classical theory of value. However, Sraffa’s position on the marginalist (or neoclassical) value theory is clear: it is futile. Therefore, unlike Misak, who writes that ‘It’s clear that Ramsey,’like’Dobb and Sraffa, had a complex, pluralistic, view of value’ (p. 302; emphasis added), I would be very reluctant to conjecture a similarity between Ramsey and Sraffa on the question of value theory.


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’

Source: meritnation.com

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.


A Case for Pluralism in ‘Microeconomics’

[My return to blogging is motivated by the extremely warm response I’ve received in person – in the last 6 months – from several people who have been readers of this blog. I’m also happy to announce the publication of my co-edited book on the history of economic thought.]

The subject matter of microeconomics is enshrined in the economics curriculum at all levels – school, undergraduate, postgraduate, and doctoral. The central objective of microeconomic theory is to provide a solution for equilibrium price and quantity in both the commodity (say, apples or coconuts) and factor (wage and ‘capital’) markets. Indeed, questions of what is the source of value and what is the exchange value of two commodities have been posed much earlier. You can find answers in Kautilya, Aquinas, Petty, and Cantillon – all of them writing prior to Adam Smith’s foundational treatise on political economy.


Kautilya’s Arthashastra contains discussions of a fair price. Aquinas, drawing inspiration from Aristotle and Christianity, tries to arrive at the notion of a just price. One of the founders of political economy, William Petty, derives the distinction between necessary price and political price and possesses a rudimentary labour theory of value. Following Petty, Cantillon distinguishes between ‘intrinsic value’ and ‘market price’ based on a land-cum-labour theory of value. The contributions of Smith, Ricardo, Marx, and Sraffa to value theory follow this tradition of objectively determining value.


The dominant theory of value in contemporary economics is not the objective theories of value found in Ricardo, Marx, or Sraffa but the subjective theories of value whose pioneers are Jeremy Bentham, William Stanley Jevons (whose son taught at Allahabad University), Alfred Marshall, AC Pigou, and Paul Samuelson. The value theory (or microeconomic theory, as it is now called more fashionably) found in the textbooks of Hal Varian or Gregory Mankiw take the following as data when solving for equilibrium prices and quantity: (i) preferences, (ii) technology, and (iii) endowments. On the other hand, Piero Sraffa’s value theory, found in his Production of Commodities by Means of Commodities (1960), takes the following as given when arriving at a solution for prices and one distributive variable: (i) size and composition of output, (ii) technology, (iii) the real wage or rate of profit.


How do you measure the data listed above’ While technology, endowments, and real wage can be measured in terms of the commodity-mix, the rate of profit is a pure number. However, how are preferences measured (or ordered)’ They are measured in a subjective manner. This is one of the core differences between the dominant marginalist theory of value and the Classical/Sraffian objective theory of value. Given this core difference, it is incorrect to treat the objective theory of value found in Ricardo or Marx as a precursor or rudimentary version of modern subjective theory of value. And therefore, it is important that students of economics learn about different value theories in microeconomics.


I shall end by drawing your attention to the practical implications of believing in the marginalist conception of the labour market vis-a-vis that of the classical economists (see an earlier post on wages). Under conditions of perfect competition, the equilibrium real wage is determined by the marginal product of labour. Any intervention, such as a minimum wage legislation or collective bargaining by the workers, results in imperfections and consequently leads to unemployment. However, in classical economics, real wage is exogenously determined though historical and social factors. If you believe in the marginalist conception, the logical policy recommendation is to eliminate any intervention/imperfection (such as minimum wage legislation or collective wage bargaining) whereas if you believe in the classical conception, you would treat collective wage bargaining and minimum legislation as legitimate ways of improving workers’ conditions.


This post argues that value theory matters for both contemporary politics and policy. And consequently, the teaching of microeconomics needs to become pluralistic. Moreover, as pointed out earlier, the politics of microeconomics ought to be made explicit. It is, as Keynes, said that we are the ‘usually the slaves of some defunct economist.”