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.  

Frank Ramsey and the Rate of Interest

I first came across Frank Ramsey in the preface to Piero Sraffa’s classic Production of Commodities by the Means of Commodities: Prelude to a Critique of Economic Theory (1960). My recent interest in Ramsey is primarily motivated by the following news. Cheryl Misak, a philosopher based at the University of Toronto has recently completed a biography of Ramsey. This blog post provides an introduction to Ramsey’s life and his contribution to the growth theory literature. [It was reassuring to notice that I first blogged about History of Economic Thought (HET) explicitly more than 10 years ago.]

Ramsey was born in 1903. In the year 1920, he read around 45 books, which included Karl Marx’s Capital, Sidney Webb and Beatrice Webb’s The History of Trade Unionism, J. A. Hobson’s The Industrial System, J. S. MiIl, and Alfred Marshall’s Industry and Trade. At the age of 19, he was commissioned to review Ludwig Wittgenstein’s Tractacus Logico-Philosophicus (1922), a significant treatise in philosophy, for the journal Mind; the review was published in 1923. Subsequently, he was commissioned to translate Wittgenstein’s work into English. In Wittgenstein’s later work, Philosophical Investigations, there is an explicit acknowledgement of Ramsey. He was acknowledged for his critique/interventions of Bertrand Russell’s and Alfred Whitehead’s Principia Mathematica in a new introduction by the authors. Sraffa, in his PCMC, had acknowledged Ramsey for mathematical help. In 1929-30, Ramsey met with J. M. Keynes, Sraffa, and Wittgenstein to discuss the theory of probability advanced by Keynes and Ramsey and also to discuss Freidrich Hayek’s theory of business cycles. Ramsey also had a close engagement with AC Pigou, a leading marginalist economist who was also the target of criticism in Keynes’s General Theory. Ramsey died in 1930.’

Under the patronage of Keynes, who was the editor of the’ Economic Journal, Ramsey published in it articles on the ‘theory of taxation’ (1927) and the ‘theory of saving’ (1928). In my 2019 article which critically evaluated the Nobel contributions of Paul Romer and Nordhaus, I had highlighted that Nordhaus employs a marginalist growth model drawing from Ramsey (without further comment). Ramsey’s question was the following: how much should a nation save today for future consumption tomorrow so as to maximise consumption across generations’ Nordhaus employs the optimal growth model with environmental protection as an important constraint. And, the rate of interest is seen as a price which equilibrates the society’s time preference. In other words, the rate of interest equilibrates the society’s preference for the future with that of the present. The policy implication when marginalist economists have a significant say in practical matters is as follows. Since the (actual) rate of interest captures the time preference of the society, this rate can be used to decide how much of current gross domestic product (GDP) should be devoted to environmental protection. In effect, not enough resources are being allocated to mitigate climate change and undertake environmental protection.’

Ramsey’s optimal growth theory also underlies Thomas Piketty’s position on economic growth. In his 2015 article in the American Economic Review, he writes that in the standard model ‘where each individual behaves as an infinitely lived family, the steady-state rate of return is well known to be given by the modified ‘golden rule’ r = + ‘ g (where is the rate of time preference and is the curvature of the utility function)’ (p. 2). The reciprocal of is the intertemporal elasticity of substitution which captures how much the representative family wishes to smoothen consumption over time. He uses this to point out that in general (marginalist) economic theory, we arrive at the r>g result–the focal argument in his book Capital in the Twenty First Century (2015; for a critical assessment see Thomas 2017). Furthermore, ‘in steady-state each family only needs to reinvest a fraction g/r of its capital income in order to ensure that its capital stock will grow at the same rate g as the size of the economy, and the family can then consume a fraction 1 ‘ g/r‘ (p. 3). To a marginalist (or neoclassical) economist, as Joseph Stiglitz wrote in an article in 1974, ‘interest rates are just intertemporal prices’ (p. 901).’

Therefore, for both Nordhaus and Piketty, interest rates are ‘intertemporal prices’ which allocate today’s income between today’s consumption and tomorrow’s consumption (today’s saving). As Ramsey (1928) writes, ‘The more we save the sooner we shall reach bliss, but the less enjoyment we shall have now, and we have to set the one against the other’ (p. 545). It is also interesting to note that their use of optimal growth models yields vastly different policy suggestions. While Nordhaus is conservative in his proposals for environmental protection, Piketty is progressive in his proposals to tax wealth.’

The rate of interest in Ramsey, as in Alfred Marshall, is a reward for waiting. Therefore, inequality in Ramsey necessarily arises from the heterogeneity of tastes or preferences; if a family is (relatively) more patient, it saves more than the (relatively) impatient one, and ends up owning all the capital stock (Attanasio 2015). How does this conception differ from the notions of interest rate found in Marx and Keynes’ For Marx, the rate of interest is the part of surplus value which is expropriated by the financial capitalist; the source of it is from the value added by labour. Keynes views the rate of interest as an expression of the preference for liquidity. To conclude, is the conception of the rate of interest found in Ramsey satisfactory for understanding a competitive economy’


Attanasio, Orazio P.’ (2015), ‘Frank Ramsey’s Mathematical Theory of Saving’, The Economic Journal, 125 (March), pp. 269’294. https://doi.org/10.1111/ecoj.12229

Duarte, Pedro (2017), ‘Frank Ramsey’, In: Robert Cord (ed.) The Palgrave Companion to Cambridge Economics, Palgrave Macmillan, vol. 2, pp. 649’671.

Monk, Ray (1990), Ludwig Wittgenstein: The Duty of Genius, London: Vintage Books.’

Stiglitz, Joseph E. (1974), ‘The Cambridge-Cambridge Controversy in the Theory of Capital; A View from New Haven: A Review Article,’ Journal of Political Economy, vol. 82, no. 4, pp.’ 893903.

Further reading

Collard, David (2011), ‘Ramsey, saving and the generations’, Generations of Economists, London: Routledge.’

[Most of the contents of this post was informally discussed with my Economics colleagues at Azim Premji University on 19th February 2020.]


Understanding India’s Economic Growth and Development

This post is a review of the recent book by Jean Dr’ze and Amartya Sen titled An Uncertain Glory: India and Its Contradictions. An earlier post in this blog has dealt with the vexed relation between economic growth and development and elsewhere, I have discussed the need to focus on the structure of economic growth. Dr’ze and Sen’s book contains 10 chapters including the introduction (‘A New India”) and the conclusion (‘The Need for Impatience’); the main text spreads across 287 pages. Their argument is buttressed with comparative exercises between Indian states, international comparisons, historical facts, surveys, published data sources and contemporary events apart from ample secondary literature. However, this review does not engage with their empirical findings.

For Dr’ze and Sen, the aim of any society should be the expansion of human capabilities. And, institutions such as markets and democracy are a means to that end. Similarly, economic growth ‘generates resources’ which can be used to improve human capabilities. As they write in the preface, ‘the achievement of high growth must ultimately be judged in terms of the impact of that economic growth on the lives and freedoms of the people’ (p. viii). Human capabilities, as is to be expected, refer to a spectrum of endowments and the ability to access all of them. For instance, it includes, in no particular order, nutrition (pp. 157-162), education (see ch. 5), health (see ch. 6), clean environment (pp. 41-44), access to energy (pp. 84-87), transportation, communication and banking infrastructure. The ability to access them, however, is severely constrained by caste (pp. 218-223). And some of them are also constrained by gender (pp. 224-239) besides other power relations.

Given India’s high growth rate, the authors pose one major question: why has the ‘pace of change ‘ been excruciatingly slow’ for majority of the Indian populace (p. 29)’ According to Dr’ze and Sen, the major cause for this is the abysmal situation of public education and health in India. (There are some Indian states which have done relatively better.) This is because of issues relating to accountability and also due to insufficient public spending. Moreover, the authors harshly criticize the Indian media for their ‘excessive focus on a relatively small part of the population whose lives and problems are much discussed’ (p. 261; see also pp. 262-267). This wide gap in public discourse provides their motivation in writing the book. Hence, they point out the ‘importance of enlightened public reasoning’ as ‘a central part of the general thesis of this book’ (p. 239). Furthermore, they state that ‘this book is aimed much more as an attempted contribution to public reasoning, including discussion in the media, than at giving professional advice to the government in office’ (p. 253).

Is their account of economic growth and development entirely satisfactory’ Their second chapter is about ‘Integrating Growth with Development’. First, what determines economic growth’ According to mainstream (neoclassical) economics, a growth in physical capital, human capital (educated and healthy workforce) and technological progress causes economic growth. This is known as the supply-side view of economic growth. If we accept this growth account, then clearly an improvement in the quality of life directly contributes to faster economic growth. Dr’ze and Sen do not have theoretical dissatisfactions with mainstream economics, as is made very clear in the following passage written in the context of a discussion on markets.

Relying solely on the market has become a strongly advocated theme in India on the basis on highly exaggerated expectations, often based on a misreading of the conclusions of mainstream economics, which includes much scepticism of the performance of markets in the presence of externalities, public goods, asymmetric information and distributional disparities. We do not have to look for any ‘alternative economic paradigm’ to see what the market cannot do, in addition to what it can do ‘ and do very well. (p. 184; emphasis added)

They also approvingly cite Joel Mokyr and Elhanan Helpman who emphasize the importance of ‘accumulation of knowledge’ and ‘total-factor productivity’ through education in economic growth respectively (p. 35). This is the supply-side production function approach in understanding the growth determinants. No one denies their significance. However, if one is convinced by such a theory/view of economic growth, the popular version of it being the Cobb-Douglas production function in various clothes, then, theoretically, physical capital can be substituted with human capital. And, this would entail a very different method of attaining economic development from that mentioned in the book. Moreover, aggregate demand does not play a role in this growth account; as the authors write in the preface, the ‘expansion of human capability, in turn, allows a faster expansion of resources and production, on which economic growth ultimately depends’ (p. x). That is, economic growth is entirely determined by the growth of aggregate supply, without considering the problems which can arise from aggregate demand deficiency (such as a fall in wage income or decrease in government spending). Without getting into the details of the argument, it appears that their conception of economic growth and development sits more comfortably with the economics of the classical economists (such as Adam Smith, David Ricardo and Karl Marx) combined with the effective demand theories of Michal Kalecki and John Maynard Keynes.

The surplus generated from economic growth can be utilized for societal needs which is further determined through socio-political movements and economic considerations of the entrepreneurs as well as the state. To put it differently, ‘the fruits of growth’ need to be allocated intelligently ‘ based on our physical, economic, environmental, social and cultural needs (p. 9; cf. p. 14, p. 18, p. 38). There are two very different kinds of distribution that takes place ‘ income distribution between wage-earners and profit-earners and the expenditure of the government from the revenue they collect as taxes and duties. They also observe,

The impact of economic growth on the lives of the people is partly a matter of income distribution, but it also depends greatly on the use that is made of the public revenue generated by economic expansion. (p. 37)

They mention the importance of collective bargaining (p. 141) and point out that the NREGA ‘strengthened the bargaining power of rural workers’ (p. 201). But their focus in the book is how to utilize public revenue in improving the quality of life (p. 269). Since this public revenue can be utilized in a variety of ways, Dr’ze and Sen assert ‘the constructive role of the state for growth and development’ (p. 39; italics in original). Hence, the organs of the state need to be made more accountable (ch. 4).

Since democracy offers ‘significant opportunities’ for improving the quality of life as well as its pace, the authors are ‘contingently optimistic’ (p. xii). In fact, the issues addressed by the authors are intended to be a contribution to a wider debate on how to construct a better society. Thus, the book aims to provide ‘reasoned solutions to the problems’ (p. 3). They also write that ‘economic reforms, even when appropriate, require informed public debate’ (p. 28). In sum, there ought to be a ‘greater use of informed reasoning in the practice of democracy’ (p. 181). As they observe, and correctly, I think, that daily troubles are ‘less spectacular and less immediate ‘ [and hence] provide a much harder challenge’ to politicize (p. 14). The book is primarily about these issues and since they cover a vast terrain, there have been some omissions. Two very varied issues come to my mind: the influence of public debt on economic growth is only addressed briefly (p. 18) and the gap between English and non-English speakers get barely one paragraph (pp. 215-6). In addition, there is no mention of freedoms relating to sexuality. To conclude, the book is an excellent contribution in so far as it provides an accessible introduction to several social concerns such as armed conflicts, child mortality, corporate power, corruption, land ownership, minimum wages, nutrition, open defecation, pollution and sanitation.