Category: Marginalist economics

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.  

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.

REFERENCES

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.

Acknowledgement

I thank Mohib Ali for his helpful comments.

 

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’

REFERENCES

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.’ 893‘903.

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.]

 

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.”