Value – Undergraduate Economist

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.]

Alfred Marshall (1842 ‘ 1924)

Alfred Marshall made lasting contributions to economics. No economist will question that. However, his precise contributions to economics are often forgotten. In a way, the microeconomics that we learn and apply today has strong Marshallian foundations. This post draws on Peter Groenewegen’s excellent (concise) biography of Alfred Marshall (2007) which has been published as part of the Great Thinkers in Economics Series published by Palgrave Macmillan.

Marshall is most famous for his Principles of Economics first published in 1890; the definitive eighth edition was published in 1920. In addition, he wrote Industry and Trade (1919), Money, Credit and Commerce (1923) and Economics of Industry (1879) which he wrote along with his wife, Mary Paley Marshall. Besides these, he also printed and privately circulated his work entitled The Pure Theory of Foreign Trade. The Pure Theory of Domestic Values (1879). Overall, he taught for more than forty years in Bristol, Oxford and Cambridge. The most notable among his students are John Maynard Keynes and Arthur Cecil Pigou.

He took German lessons in order to read Kant in the original. Hegel’s Philosophy of History had a strong influence on his thought. Marshall commenced his study about economics with a close reading of John Stuart Mill’s Principles of Political Economy. He also read the methodological works of Mill on logic and particularly criticised Mill’s conception of the individual as a ‘self-seeking, wealth-maximising homo economicus‘. His other economics readings included Smith’s Wealth of Nations, Ricardo’s Principles and Marx’s Capital. Other important influences were Cournot’s Mathematical Investigations in the Theory of Wealth and von Thunen’s The Isolated State; they motivated Marshall’s use of diagrams.

For Marshall, ‘the proper work of economic science’was solving economic problems’. ‘The necessity of economic theory, the importance of facts and continual striving to keep economic analysis relevant and practical were all crucial parts of Marshall’s promise to devote his professional life to the improvement of economic science’ (p. 74). It is also quite well known now that, for Marshall, the ‘mecca of the Economist lies in Economic Biology rather than in Economic Dynamics’ (p. 106).

Groenewegen informs us that Marshall had a personal dislike of the use of textbooks in university teaching (p. 77). Not surprisingly, ‘[t]he Principles of Economics remained a leading textbook on the foundations of economics not only during the life of its author, that is, from 1890 to 1924, but for the next quarter century as well, that is, until the early 1950s’ (p. 111).

The use of mathematics in the Principles has garnered lot of attention since he ‘banished’ all equations to the appendix. In any case, Marshall considered economics as ‘form of reasoning’. Perhaps, given the use of mathematics during his time, his relegation of equations to the appendix might have been appropriate. I quote an interesting letter Marshall wrote to his student Bowley: ‘(1) Use mathematics as a shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples which are important in real life. (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This last I did often’ (p. 114).

Marshall identified time to play an important role in the theory of value. He developed the concepts of the short and long period. He paid particular attention to ‘elasticity’. Besides these, he laid the foundations for the theory of the firm, use of offer curves or reciprocal demand curves in international trade and distinguished internal and external economies.

This post has only very briefly touched upon the way Marshall viewed economics, especially his use of mathematics and his evolutionary notion. We have not detailed his precise contributions to economics. This post serves the purpose of being a very short introduction to Marshall. As students of (micro)economics, it will be fascinating to read Marshall’s works, especially his Principles.

Labour, Scarcity and Techniques of Production

Value ‘ is of utmost importance to all paradigms in Economics (Neo-classical, Classical Political Economy, Austrian Economics, Marxian Economics, etc) because the theory of value is the fundamental proposition or the foundation on which subsequent theories are built. Therefore, it is crucial to understand the various theories of value.

The problem of value has different features. The aim could be to find the source of value, a standard of value for inter-temporal comparisons between and across countries and determination of exchange values in theoretical problems.

Through an example pertaining to ‘value’, this post tries to bring out the distinction between the Neo-classical and Classical paradigm in terms of the source of value. As students of economics, all of us have come across the Diamond-Water paradox. This paradox is a commonplace in economic literature, even before Adam Smith. This is how Smith refers to the paradox:

‘The things which have the greatest value in use have frequently little or no value in exchange; and, on the contrary, those which have the greatest value in exchange have frequently little or no value in use. Nothing is more useful than water: but it will purchase scarce anything; scarce anything can be held in exchange for it. A diamond, on the contrary, has scarce any value in use; but a very great quantity of other goods may frequently be had in exchange for it.‘

For the classical economists, value of a commodity means the value in exchange. And prices of commodities are believed to reflect its ‘value’. Value in exchange is determined by the conditions of reproduction of the economic system. The economic system is one where a number of firms using labour, land and capital (machinery, tools, etc), produce commodities (goods produced with the intention of selling them) by using commodities produced by the economic system (the firms within it). The conditions of reproduction would include the technology available (which would tells us in what proportions the labour and capital need to be mixed; in neo classical terminology, it would give a fixed proportions production function) Moreover, the classical economists did not consider value in use as a measurable quantity.

Before the ‘marginalist revolution’, utility had an objective sense as the capacity of a good to satisfy some need, and not as the subjective evaluation on the part of one or more individuals. It is worth noting that, in a capitalist economy a good or service is produced only because it can be sold. According to Marx, it is commodity production which forms the fundamental tenet of Capitalism. So, any commodity in a capitalistic economy does have utility. To clarify my argument, let me modify the definition of a commodity. A commodity is a good or service which is produced or offered only because it has a use value. Rather, it can be put for sale only if it has utility for someone or the other. The market does not produce commodities which has no demand or that which has no use/utility for any one.

Thus, it is clear that in a capitalistic economy (all economics theories, namely neoclassical, classical and Marxian tried to understand the working of a capitalist mode of production) the proposition that a commodity has a use value is a truism. So, because all commodities had a use value which they believed could not be measured, the value of a commodity was seen as the exchange value of it.

Since, labour was considered to occupy a central position in the economy, Adam Smith put forth the view that ‘labour commanded’ could be used as a standard to measure exchange value. In Marx, it takes the form of ‘labour embodied’ which then gives rise to the labour theory of value. For Marx, it is labour which provides value to the commodity by engaging in the production of that particular commodity.

Thus when the paradox is viewed through the classical and Marxian lens, it seems as if the paradox is only an illusion. The production of diamond is a costly affair and thereby requires a lot of labour (in today’s world, a lot of capital as well) due to which the value (exchange value) of diamond is high and thereby it commands a high price. More the labour needed for producing a commodity, more will be its value. So, because of the higher production costs, diamond is priced high.

For the neoclassical economists, the price of a commodity is determined by its marginal utility. Marginal utility is based on a subjective theory of value. Let me put forth two snippets from neoclassical economics as to how the paradox is resolved.

‘The more there is of a commodity, the less the relative desirability of its last little unit becomes, even though its total usefulness grows as we get more of the commodity. So, it is obvious why a large amount of water has a low price.‘ ‘ Paul Samuleson, the first American to receive a Nobel Prize in Economics.

In the blogosphere, I came across this piece from Michael Stastny, who blogs at Mahalnobis.

‘A better answer to the paradox why diamonds are more expensive than water would be that since water is so plentyful, the marginal utility (= the derivative of U(x) with respect to x, i.e. (approx.) the extra satisfaction of wants and needs obtained from consuming one additional unit of good) of water is is relatively low. An extra liter of water provides very little additional satisfaction. To the contrast, diamonds are very scarce and the marginal utility is therefor relatively high.‘

The study of economics is aimed at discovering the laws prevailing in the economic sphere. This helps in understanding the inter relationships within an economy. This further helps in policy purposes, by trying to increase investment rates, saving rates, GDP, etc.

The reasons provided for the paradox above assume that prices of commodities arise from their scarcity. Capitalism ensures a constant supply of the commodities which have utility (objective or subjective). It is to understand how prices come about, that economists theorize on values. For neoclassical economics, prices are indices of scarcity.

Let me illustrate the ignorance of neoclassical economics with an example. In a functioning economy, suppose an inventor discovers/invents a new product/commodity ‘ say a vehicle that runs on air. So, at this point of time, there is only one firm supplying this commodity. It is extremely scarce and according to neoclassical theory, it is rational for the producer to sell the first vehicle at any price because it has the highest value by being the sole product in the market.

So, when the first vehicle is on sale, the demand outstrips the supply. According to the neoclassical theories, the capitalist can ask for a higher price in such circumstances. I conclude by asking: is that how commodities are priced’ Are such prices ethical’ Isn’t it the techniques of production along with the wage rate and profit rate that governs the prices of commodities’

References

1) The Wealth of Ideas: A History of Economic Thought, Alessandro Roncaglia, 2005.

2) Das Kapital, Volume 1, Karl Marx.

3) Economics, 11th edition, Paul A Samuelson, 1980.