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.”

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

This post is second in the two-part commemoration of Capital‘s 150^th 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 Marxists.org), 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 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)

The Union Budget 2018-19 in 5 charts

The Union Budget is a key document which informs the public about the Government’s socio-economic plans and priorities. It is important to critically evaluate this document because of our collective ‘failure to provide for full employment’ and the ‘arbitrary and inequitable distribution of wealth and incomes’; Keynes wrote this in 1936 and it continues to remain the same. Moreover, it is our collective right and responsibility to decide how the government should obtain its revenue and how it must be spent. No formula or algorithm exists for this. As Piketty wrote in his Capital in the Twenty-First Century, ‘Taxation is not a technical matter. It is preeminently a political and philosophical issue, perhaps the most important of all political issues. Without taxes, society has no common destiny, and collective action is impossible.

This blog post aims to outline the priorities of the current central government by examining the expenditure on physical and social infrastructure and the nature of taxes. This is done in 5 charts.

(1) Physical Infrastructure

Defence is significantly more important than roads, housing, food, and farmers’ welfare.

Capital Expenditure of Select Central Ministries (in Rs. Crore)

Source: Expenditure Budget Vol. 1, 2016-17, Statement 2, pp 4-9

All values are rounded off to the nearest crore.

(2) Social Infrastructure

Physical infrastructure creation is more important than social infrastructure creation.

Have the negative effects of physical infrastructure creation been accounted for’

‘Total Allocations of Select Ministries (Rs. 112753 Crore)

Source: BS, p 36, Annex No. III-A to Part A

RE refers to revised estimates which include supplementary demands for funds made by the ministries during the financial year.

BE refers to budget estimates.

(3) Direct & Indirect Taxes

Our taxation policy is regressive due to the high proportion of indirect taxes.

Select Direct and Indirect Taxes (in Rs. Crore)

Source: Receipts Budget, 2018-2019, pp. 2-4

(4) Corporate Tax Concessions

Our tax concessions could approximately fund 75% of the social infrastructure spending estimate.

(5) Corporate Tax Structure

Our corporate taxes are regressive.

Effective tax rate paid by sample companies across range of PBT (FY 2016-17)

Source: Statement of Revenue Impact of Tax Incentives under the Central Tax System: Financial Years 2014-15 and 2015-16, p 30 of the Receipts Budget, 2016-2017, Annex-15.

¹ Values rounded off to the nearest integer; hence the total adds up to 101 and not 100. Financial year 2012-13. The number of companies whose PBT is zero is 17,912 and their share in total income is around 9 per cent.

Concluding comments

Our government prioritises defence over agriculture. Our government prioritises physical infrastructure over social infrastructure and does not take into account ecological damage and the displacement caused due to physical infrastructure creation. And our taxation policy is regressive. We must use our collective rights and responsibilities to decide how the government should obtain its revenue and how it must be spent.

Acknowledgement

I thank Rahul Lahoti for inviting me to be a part of the panel which discussed the Union Budget at Azim Premji University-Undergraduate Campus on 14th February 2018, from which this post originated.