Category: Neoclassical Economics

Sraffa: The Origins of ‘Marginal’ Analysis

Since the advent of the ‘marginal’ method, the doctrines of the old classical economists have been submerged and forgotten. It is this standpoint that Sraffa revives in his 1960 book Production of Commodities by Means of Commodities. Being third in the series of posts [Post 1; Post 2] on Sraffa, this post examines the origin of the ‘marginal’ method and its subsequent (mis)use by the neoclassical economists. The posts concludes with a brief mention of how history of economic thought is important so as to place theories in a proper context.

In the preface of his book, Sraffa points out that in a system of production where the scale of an industry or proportions of factors of production remained unchanged, one would not be able to locate marginal product and marginal cost. To put it differently, marginal analysis is done by considering ‘potential change’. That is, we try to find out variations in equilibrium quantities and prices with respect to infinitesimal changes in the neighbourhood. [Bharadwaj 1986, p 39]

What we do not pay adequate attention to, is that the most familiar case of ‘marginal analysis’ is that of the product of marginal land (also known as no rent land) in agriculture, when lands of different qualities are cultivated side by side. This refers to the well known differential rent theory of David Ricardo. In fact, it is the case of diminishing marginal returns on land which is at the junction of the ‘fundamental methodological shift from classical to equilibrium theory’. [Bharadwaj 1986, p 40] This can be understood only through a discussion of ‘extensive’ and ‘intensive’ margins.

Cultivation on lands of different qualities is visualised as the outcome of a process of ‘extensive’ diminishing returns. On the other hand, successive use of more output producing techniques refers to the process of ‘intensive’ diminishing returns. [Sraffa 1960, p 76] In the case of ‘extensive’ margins in cultivation, ‘the rents can directly worked out on the basis of the single observed situation.’ [Bharadwaj 1986, p 41] Whereas, in the case of ‘intensive’ margins, the calculation of rent requires a quantitative change in the situation. That is, successive doses of labour and ‘capital’ need to be added to the land. And, a further assumption is made on the nature of these ‘doses’. These ‘doses’ are considered to be homogeneous. As Krishna Bharwadwaj explains: ‘At any moment of observation, no dose is distinguishable from each other. No ‘marginal product’ can, therefore, exist in this case without introducing potential change.’ [Bharadwaj 1986, p 42]

Thus, it is the Ricardian theory of rent which provided the basis for the neoclassical theory of distribution by providing an inverse relationship between successive doses of labour and ‘capital’ and their remuneration. This theory of Ricardo was intended to explain the origin of rents. In the hands of later authors, this was generalised to labour and ‘capital’. Hence, we see the inverse relation between ‘capital intensity’ and rate of profit in microeconomics textbooks of today.

From this excursion into the Ricardian theory of rent, two aspects are very clear. First, the concept of ‘marginal’ or ‘margins’ was used exclusively in the domain of cultivation. In ‘intensive’ cultivation, it is obvious that the output would increase only until a certain point, owing to the quality of that piece of land. Whereas, in the case of ‘extensive’ cultivation, the output would increase till all the acres of land are cultivated- notice the scarcity element here. What is not clear is the rationale of extending such an analysis into the area of manufacturing! Also, it is well accepted that land is scarce; but, is ‘capital’ or produced commodities scarce in a similar way’

No book of microeconomics mentions the origins of the famous ‘marginal’ analysis. And this method is so entrenched in the profession, that it is almost impossible to throw it away. It is in this context that other conceptual frameworks, that pay more attention to the changing historical conditions, assume importance. Probably, we need to revisit earlier theories and theorists not just for their own sake but for our sake as well in throwing light on contemporary issues. Sraffa’s work has inspired a lot of work on the history of economic thought, which will be summarised in a later post.

References

Bharadwaj, Krishna (1986), ‘Classical Political Economy and Rise to Dominance of Supply and Demand Theories‘, Universities Press: Calcutta.

Sraffa, Piero (1960), ‘Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory‘, Cambridge University Press: Cambridge.

Knut Wicksell: Some Aspects of his Work

This post is different from the others because it deals with the contributions of a single economist. Knut Wicksell was a Swedish economist who made significant contributions to capital theory, monetary economics and fiscal policy. Despite being grouped under the neoclassical or the Austrian school because of his affinities to ‘marginal’ analyst, Wicksell was a socialist and a radical. He advocated policies which involved the government in a big way. And owing to his varied interests in poetry, mathematics, feminism, mathematics, politics, etc he became a Professor of Economics and Fiscal Law at Lund University only when he was fifty. A few of his well known students are Erik Lindahl, Gunnar Myrdal and Bertil Ohlin. They are considered to be part of Stockholm or Swedish school of economic thought.

In the passages below, only a few of his contributions will be elaborated. He has also made lasting contributions to the theory of interest, revitalised quantity theory of money, introduced mechanisms linking the real and monetary sector, etc.

Wicksell demonstrated that problems could arise if capital is treated just like other ‘factors of production’ ‘ land and labour. Cambridge capital controversies dealt with many of these problems. ‘Knut Wicksell (1851’1926) himself casts doubt on the specification of the value of capital, along with the physical quantities of labour and land, as part of the data of the system. ‘Capital’ is but a set of heterogeneous capital goods. Therefore, unlike labour and land, which ‘are measured each in terms of its own technical unit . . . capital . . . is reckoned . . . as a sum of exchange value’ (Wicksell, 1901, 1934, p. 49). But capital goods are themselves produced commodities and, as such, their ‘costs of production include capital and interest’; thus, ‘to derive the value of capital goods from their own cost of production or reproduction’ would imply ‘arguing in a circle’ (ibid., p. 149).’ [Segura and Braun 2004]

Like other contemporaries of his, Wicksell did not write about unemployment. This was because the existence of unemployment was considered to be a paradox, an anomaly for neoclassical economists. As they could not comprehend why resources (here, labour) would be left idle! The central problem in (neoclassical) economics was not to provide or create uses for factors, but only to allocate the factors among various uses. As Bo Sandelin, editor of Wicksell’s papers and the author of A History of Swedish Economic Thought writes in the introduction that ‘the fundamental question in economics was how to manage an economy with scarce resources.’ Strange indeed!

Wicksell was a strong proponent of the marginal productivity theory of distribution. A corollary of this theory is the the sum of all the marginal products of the factors should be equal to the total product, known as the product exhaustion theorem. However Wicksell demonstrated that the operation of this theory depends on the returns to the scale. That is, only under constant returns to scale will the marginal products exactly add up to the total product. And that for both decreasing returns and increasing returns, the product will not be completely exhausted.

The Swedish school made another important contribution to economic theory. They introduced the categories of ex ante and ex post. These categories, we know are used widely today and were the result of the School’s dissatisfaction with the equilibrium analysis. Apart from these ways of thinking, Myrdal has provided us with the concept of circular and cumulative causation as well. These categories provide us with alternative modes of conceptualising or thinking about economic problems.

Relying solely on textbooks reduces our extent of reach. We often fail to come across interesting and heterodox economists. But, history of economic thought provides us with ample personalities to look into. Wicksell is one among them. Also, some of their categories provide us with alternatives, which remain unfinished. For instance, after going through some of the secondary and primary works on/by Wicksell, he appears exceedingly interesting and aware of the implications of certain simplifying assumptions. He pointed out the ‘necessity’ of the constant returns to scale assumption, which economics faithfully aligned with for a considerable period. This was challenged within the mainstream only with the entry of the endogenous growth theories, which emphasised increasing returns.

References

Pressman, Steven (2004), Fifty Great Economists, Routledge: India.

Groenewegen, P and Vaggi, G (2006), A Concise History of Economic Thought: From Mercantilism to Monetarism, Palgrave Macmillan.

De Marchi, N and Blaug, M (1991), Appraising Economic Theories: Studies in the Methodology of Scientific Research Programmes, Edward Elgar.

Segura, J and Braun, C (2004), An Eponymous Dictionary of Economics: A Guide to Laws and Theorems Named After Economists, Edward Elgar.

Sraffa: Production as a Circular Process

This is the second in the series of posts on Sraffa. The objective of this post is to clarify the assumption of scarce resources made frequently in neoclassical economics. This is then contrasted with the notion of mass-production in capitalist economies. This facet of capitalism is understood by concepts such as ‘circular production’ and ‘production of commodities by means of commodities’ in Classical Economics.

A brief look at the history of micro and macroeconomics becomes essential. Elements of Marshall and Walras are found in modern microeconomics. Specifically, partial equilibrium analysis comes from Marshall; whereas, Walras contributed ‘general equilibrium analysis’ to economics. Usually, emergence of macroeconomics is considered to have originated with the work of Keynes. This has been contested and it has been shown with considerable evidence that William Petty (1623-1687) was the first macroeconomist. [See Murphy 2009] And that economists like Adam Smith, David Ricardo and Karl Marx were talking about macroeconomics when they discussed production, distribution and accumulation. Neoclassical macroeconomics can be loosely said to comprise New Classical Economics, Neo-Keynesian Economics, variants of Computable General Equilibrium Models (CGE), etc. One of the unifying features of the above mentioned neoclassical schools/models is the assumption of ‘scarce factors’. It is owing to the assumption that factors are scare, that optimization is carried out.

Lionel Robbins defined economics as ‘the science which studies human behaviour as the relationship between ends and scarce means which have alternative uses.’ Here, scarce means refers to scarce factors of production ‘ land, labour and capital. Yes, land can be considered scarce in an economy where the pressure of population is high (or for environmental reasons). But, wouldn’t labour be scarce in some countries and abundant in others’ Now for the tricky ‘capital’. Capital is understood as produced means of production. That is, tools, machinery, plants, conveyor belts, electrical appliances, tractors, etc are ‘capital goods’. Are they scarce’ They would be scarce if nobody produced them. Usually, in a capitalist or quasi-capitalist economy, capital goods are produced by the private sector, the government and often, imported from abroad. Therefore, a priori, we have no reason to maintain that capital is a scarce factor. Or for that matter, even labour.

Marshall provided a theoretical partition through which one could say that factors are scarce. He introduced the concept of ‘short period analysis’. Till Marshall, the early classicals and neoclassicals analysed economies using the ‘long period method’. Through the short period, Marshall introduced an imaginary period wherein one factor is fixed (usually, capital) and the other factor (labour) is variable. In this period, it is as if one factor is scarce. In a later post, it will be shown that this sort of analysis is an improper generalisation of Ricardo’s theory of rent.

Sraffa’s Production of Commodities by Means of Commodities deals with ‘value and distribution’. That is, he focuses on the relationship between relative prices, wages/profits and technique of production. Throughout the whole analysis, output/quantity is treated as given. This is in tune with the ‘sequential analysis’ of classical economics. Value & distribution is one level of analysis or the ‘core’, as was popularised by Garegnani. Once, the foundation is well-established, the next level is growth & accumulation. In the first level, quantities are treated as given and in the second level, prices are assumed to be given. This is done keeping in view the complexity of the economic processes. Whereas, as we know, in neoclassical theory of general equilibrium, there is a simultaneous determination of quantity, price, wage rate, employment, rate of interest and quantity of capital. That is, all kinds of prices and quantities are simultaneously determined.

A set of equations from classical and neoclassical production theory is given below. This is so as to bring out the differences in a clear way.

Production function: Ya = f(La, Ka)

Sraffa’s equations:
(AaPa + BaPb + … + KaPk) (1 + r) + LaW = APa
(AbPa + BbPb + … + KbPk) (1 + r) + LbW = BPb
. . . . . .
(AkPa + BkPb + … + KkPk) (1 + r) + LkW = KPk

where A, B …. K are the output produced in various industries, L is the labour employed in each industry, Pa refers to price/value of output A and Pk refers to value of output K, r is the rate of profit. [As these are for purposes of illustration alone, some conditions have not been mentioned]

In the first case, it represents the transformation of inputs ‘ labour and capital into an output Y. Let me reproduce what Sraffa writes about his particular conception of production: ‘It is of course in Quesnay’s Tableau Economique that is found the original picture of the system of production and consumption as a circular process, and it stands in striking contrast to the view presented by modern theory, of a one-way avenue that leads for ‘Factors of production’ to ‘Consumption goods’.’ [Sraffa 1960, 93]

The concept of circular production also brings to the fore the web of connections between different production structures. Both classical and neoclassical economics attempts at reducing the complexity of economic phenomena. Neoclassical economics, at the outset abstracts away from interrelated production structures through the concept of ‘representative firm’ in microeconomics. In a similar way, in the area of consumption, man as a social being is reduced to man as an individual whose utility does not depend on that of others. Classical economics carries out its analysis by taking prices as given so as to analyse interrelated production structures.

References

Sraffa, P (1960), Production of Commodities by Means of Commodities, Cambridge: Cambridge University Press.

Murphy, A (2009), The Genesis of Macroeconomics: New Ideas from Sir William Petty to Henry Thornton, New York: Oxford University Press.

Paul Samuelson: The Father of 'Modern Economics' Dies

All those who have studied economics for the past 50 years or so have heard about Samuelson – Foundations of Economic Analysis, Samuelson-Stopler theorem, Factor-price equalisation theorem, revealed preference theory, Bergson-Samuelson social welfare functions, non-substitution theorem, linear programming in economics, etc. The first one is his 1947 book which dominates economics teaching even today, directly or indirectly. Samuelson transformed economics into some sort of science (pseudo-science, as some call it)-social physics. [For more on this, go here]

Robert Lucas on Samuelson:

‘Samuelson was the Julia Child of economics, somehow teaching you the basics and giving you the feeling of becoming an insider in a complex culture all at the same time. I loved the Foundations. Like so many others in my cohort, I internalized its view that if I couldn’t formulate a problem in economic theory mathematically, I didn’t know what I was doing. I came to the position that mathematical analysis is not one of many ways of doing economic theory: It is the only way. Economic theory is mathematical analysis. Everything else is just pictures and talk.’ [Marginal Revolution and here]

SCARY!

In his Foundations, he is supposed to have popularised the views of Keynes. In fact, what he popularised is the neo-classical synthesis (IS-LM curves, which were created by Hicks). Hence, what we learn in most macroeconomics texts is not what Keynes said. Post-Keynesian economics is more closer to what Keynes said.

Despite his ‘ideas of good economics’, one needs to appreciate the works he carried out in different areas in economics – macroeconomics, public finance, international trade, consumer theory, capital theory and general equilibrium, etc.

In his initial editions of the Foundations, one could find a few pages devoted to the 1960 capital theory debates. However, with passage of time, the debate was relegated to footnotes. Now, in mainstream textbooks, capital theory is entirely omitted. In fact, Samuelson admitted the problems neoclassical microeconomics and general equilibrium run into because of their notion of capital. [More here]

I end with two questions.
Is mathematics the only way of studying economics and analysing economies’ [We mostly use calculus and game theory. Should we employ other kinds of mathematics’]

How reliable are textbooks’ It makes learning easy, but probably, a bit too easy.