Training Workshop The Political Economy of Value and Price

Wednesday 5 November 2014

School of Oriental and African Studies, London

SESSION 1: A HISTORY OF THE LABOUR-THEORY OF VALUE*

by Marco Veronese Passarella

* Loosely based on Giorgio Gattei’s ‘History of Economic Analysis’ module at the University of Bologna

and David Spencer’s ‘Theories of Growth, Value and Distribution’ module at the University of Leeds

Updated: October 31st, 2014

IIPPE

Download this presentation from:

http://www.marcopassarella.it/en/ (under Next Events)

PLAN / CONTENTS

1. Introduction (to Classical Political Economy)

2. Adam Smith and the emergence of the labour-theory of value

3. David Ricardo and the pure labour-theory of value

Break

3. David Ricardo and the pure labour-theory of value (cont.)

4. Karl Marx: surplus-value as surplus-labour and the transformation

problem

Discussion

Part I

10:00-11:10

Part II

11:30-12:40

12:40-13:00

11:10-11:30

Introduction

(to Classical Political Economy) 1

1.1 WHAT IS CLASSICAL POLITICAL ECONOMY (CPE)?

o CPE had its heyday in the period from late 18th to late 19th century in England. It is

usually said to begin with the writings of Adam Smith. What is the main subject? Many

answers are possible, depending on the specific component one wishes to focus on.

o There is an ambiguity that comes from the two main components or souls of Adam

Smith’s economic thought:

● Micro (or individual): natural laws, competitive equilibrium, harmony or

spontaneous order, invisible hand, market price, laissez-faire, etc.

● Macro (or social): social relations, surplus theory, class struggle, growth and

distribution, intrinsic value, etc.

o CPE is a Marx’s definition, who identifies it with Ricardo’s (macro) approach. The

‘marginalist revolution’ was mainly a (micro) rebellion against the Ricardian approach

and its possible socialist use. While CPE is no longer dominant, its legacy survives in

some heterodox schools (Sraffians, Marxists, Post Keynesians, Institutionalists,

Evolutionarists, etc.).

1.2 CPE AND THE INTRINSIC THEORY OF VALUE

o CPE aims to disclose the natural (?) laws underpinning production, distribution, and

growth, in a capitalist economy.

o It relies on three main concepts: social class (landlords or rentiers, industrial

capitalists, and workers); cost of production (labour cost); and surplus (deduction

from the product of labour).

o The intrinsic theory of value (pioneered by William Petty, Richard Cantillon, and

François Quesnay, and further developed by Adam Smith and David Ricardo) is at the

heart of the analysis.

o As the quantity of labour expended in the production process is regarded as the

primary source of value, Smith-Ricardo’s view about value is usually referred to as

the labour-theory of value.

Adam Smith and the emergence of the

labour-theory of value 2 Name: Adam Smith.

Born: 5 June 1723, Kirkcaldy, Scotland.

Died: 17 July 1790 (aged 67), Edinburgh,

Scotland.

Main work: An Inquiry into the Nature and

Causes of the Wealth of Nations (1776).

2.1 THE WEALTH OF NATIONS

o The research question underpinning Smith’s ‘inquiry’ is: what is the cause, and the

proper measure, of the real wealth of a certain nation or region?

The annual labour of every nation is the fund which originally supplies it with all the necessaries and

conveniences of life which it annually consumes, and which consist always, either in the immediate

produce of that labour, or in what is purchased with that produce from other nations. […] But this […] must

in every nation be regulated by two different circumstances; first, by the skill, dexterity, and judgment with

which labour is generally applied; and, secondly, by the proportion between the number of those who are

employed in useful labour, and that of those who are not so employed. (Smith 1776, Intro.)

o Labour is the cause or source of value. The higher the capital invested in productive

labour-power (tangible output, surplus), and the higher labour productivity (via

division of labour, market extension), the higher will be the real wealth.

o The wellbeing of the society corresponds to that of the ‘industrial’ capitalist class. But

how to measure it? Wealth and income are heterogeneous aggregates. A money

measure is unreliable, because of the change in the real value of money. Labour

quantity is a natural deflator, but what labour?

2.2 VALUE IN USE VS. VALUE IN EXCHANGE

o The value in use (or use-value) of a given commodity is its want-satisfying power. It

roughly corresponds to the individual utility.

o The value in exchange (or exchange-value) of a commodity, call it 𝑖, is defined as

the quantity of other commodities that a unit of 𝑖 can be exchanged for.

o A positive use-value is a necessary prerequisite for a commodity to have a positive

value in exchange. However, the use-value is not the cause of value of commodities.

Neither is it a good measure of value.

The word value, it is to be observed, has two different meanings, and sometimes expresses the utility of

some particular object, and sometimes the power of purchasing other goods which the possession of that

object conveys. The one may be called ‘value in use;’ the other, ‘value in exchange.’ 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. (Smith 1776, Ch. 4)

o It is usually claimed that Smith did not get that he should have looked at the ‘marginal

utility’, instead of the ‘total utility’ (as marginalists successfully argued). But the point

is that he took a different path to solve the paradox: production (labour) costs.

2.3 VALUE AND THE MARKET PRICE

o A commodity has an intrinsic value because it is produced by human labour. Value is

expressed by (embodied) labour. In formal terms:

𝜆𝑖𝑥𝑖 = 𝐿𝑖 ∀ 𝑖 = 1,2, … , 𝑁

where 𝜆𝑖 is the unit value of commodities, 𝑥𝑖 is their quantity, and 𝐿𝑖 is the direct

labour expended in the production process.

o The total value of commodities produced in the 𝑖-th sector is given by the total

quantity of labour time expended in the production process.

o Yet, commodities are exchanged one another on the market according to their

(volatile) market prices. These prices depend on demand and supply forces.

The market price of every particular commodity is regulated by the proportion between the quantity which is

actually brought to market, and the demand of those who are willing to pay the natural price of the

commodity, or the whole value of the rent, labour, and profit, which must be paid in order to bring it thither.

(Smith 1776, Ch. 7)

2.4 THE NATURAL PRICE

o Due to competition, market prices will gravitate around a natural price. The latter is

realised on the market, but determined by conditions (i.e. costs) of production.

When the price of any commodity is neither more nor less than what is sufficient to pay the rent of the land,

the wages of the labour, and the profits of the stock employed in raising, preparing, and bringing it to

market, according to their natural rates, the commodity is then sold for what may be called its natural price.

[…] The natural price […] is […] the central price, to which the prices of all commodities are continually

gravitating. Different accidents may sometimes keep them suspended a good deal above it […]. But

whatever may be the obstacles which hinder them from settling in this center of repose and continuance,

they are constantly tending towards it. (Smith 1776, Ch. 7)

o In a pure-labour capitalist production (no means of production, advanced capital

equal to wage-bill), the natural price of the 𝑖-th commodity is:

𝑝𝑖 = 𝑤 ∙ 𝑙𝑖 + 𝑤 ∙ 𝑙𝑖 ∙ 𝑟𝑖

= 𝑤𝑙𝑖(1 + 𝑟𝑖)

where 𝑙𝑖 = 𝐿𝑖/𝑥𝑖 is the labour coefficient, 𝑤 is the natural unit nominal wage, and 𝑟𝑖

is the natural rate of return (or profit) on capital. (Notice that rent is neglected)

2.5 THE EXCHANGE RATIO

o The relative price between two commodities, call them ‘1’ and ‘2’, is:

𝑝1

𝑝2=

𝑤𝑙1(1 + 𝑟1)

𝑤𝑙2(1 + 𝑟2)

o Does this ratio reflect embodied labours? According to Smith, two cases are possible:

a. In an ideal cooperative economy (𝑟1,2 = 0), the exchange ratio does express the

relative embodied labour time. For, if individuals are free to allocate their labour time,

there would be a shift from under- to over-remunerated activities.

In that early and rude state of society which precedes both the accumulation of stock and the

appropriation of land, the proportion between the quantities of labour necessary for acquiring different

objects seems to be the only circumstance which can afford any rule for exchanging them for one another.

(Smith 1776, Ch. 6)

In algebraic, terms: 𝑝1

𝑝2=

𝑤𝑙1(1+0)

𝑤𝑙2(1+0)=

𝑙1

𝑙2=

𝜆1

𝜆2.

2.6 COMMANDED LABOUR

b. Under a capitalist society (in which workers no longer control the productive

process, and 𝑟1 > 𝑟2 > 0) exchange ratios are defined by the amounts of labour

commanded by commodities:

𝑝1

𝑝2=

𝑤𝑙1(1 + 𝑟1)

𝑤𝑙2(1 + 𝑟2)=

𝑙1(1 + 𝑟1)

𝑙2(1 + 𝑟2)>

𝑙1

𝑙2

As soon as stock has accumulated in the hands of particular persons […] the whole produce of labour

does not always belong to the labourer. […] Neither is the quantity of labour commonly employed in […]

producing any commodity, the only circumstance which can regulate the quantity which it ought commonly

to […] exchange for. […] The real value of all the different component parts of price […] is measured by

the quantity of labour which they can, each of them, purchase or command. (Smith 1776, Ch. 6)

o In algebraic terms: 𝑝𝑖

𝑤= 𝑙𝑖 1 + 𝑟𝑖 = 𝑙𝑖

𝑐𝑜𝑚 > 𝑙𝑖

o The labour commanded is a relative price (in terms of labour). If the profit rate is

positive, then the labour a commodity can buy is greater than the labour expended to

produce it.

2.7 THE ‘ADDING-UP’ APPROACH

o Command over labour is the precondition for capital accumulation and growth. The

higher the amount of labour that the annual product of a certain nation can command

(compared to the labour necessary to produce it), the wealthier is that nation.

o The price of the commodity can be expressed as the summation of incomes paid to

produce it (i.e. wages, profit, and rent). Abstracting from rent, it is:

𝑝𝑖𝑥𝑖 = 𝑤𝑙𝑖𝑥𝑖 + 𝑤𝑙𝑖𝑥𝑖𝑟𝑖

= 𝑉𝑖 + Π𝑖

o Sometimes Smith claims that payments made to the owners of inputs are the primary

sources of value. The natural rates of wages and profit would be determined by the

forces of supply and demand on the market.

o As a result, the natural price of the commodity would be determined by adding-up 𝑉𝑖

and Π𝑖. However, this is a misleading position, as it is at odd with the labour

commanded theory (if the real wage is set at the subsistence level).

FOCUS WHAT THEORY OF PRICE AND DISTRIBUTION?

As is known, in CPE it is usually assumed that workers’ wage is defined in real terms by

the level of subsistence.

However, the labour commanded by consumption goods is known once the real wage

is known. The rate of profit is determined residually. In formal terms, it is:

𝑝𝑐

𝑤=

1

𝑤𝑟= 𝑙𝑐 1 + 𝑟𝑐

𝑟𝑐 =1

𝑙𝑐 ∙ 𝑤𝑟− 1

where subscript ‘c’ defines the consumption good industry and 𝑤𝑟 is the real wage.

Corollary: the theory of value based on labour commanded is correct as a price theory if

and only if it relies on a theory of profit as a ‘residue’.

2.8 TO SUM UP

o The cause of value is labour, i.e. it is the quantity of labour embodied in commodities

produced that makes them valuable for the individuals and the society.

o The best measure of the relative value is not the embodied labour, but the labour

commanded by commodities, i.e. the quantity of labour that a certain commodity can

purchase on a competitive market.

o The market price of a certain commodity gravitates around a natural price. This is

defined by the conditions of production, but can also be expressed as the sum of the

natural incomes (wages, profits, and rents) paid to produce the commodity (adding-up

theory?).

o The labour commanded by the domestic output of a certain country provides the

measure of the real wealth (defined as «the annual produce of the land and the

labour») of that country.

David Ricardo and the pure labour-

theory of value 3 Name: David Ricardo.

Born: 18 April 1772, London, England.

Died: 11 September 1823 (aged 51).

Main work: Principles of Political Economy

and Taxation (1817).

3.1 EPISTEMOLOGICAL DEFINITION OF POLITICAL ECONOMY

The produce of the earth […] is divided among three classes […]; namely, the proprietor of the land, the

owner of the stock or capital necessary for its cultivation, and the labourers by whose industry it is

cultivated. But in different stages of society, the proportions of the whole produce of the earth which will be

allotted to each of these classes, under the names of rent, profit, and wages, will be essentially different;

depending mainly on the actual fertility of the soil, on the accumulation of capital and population, and on the

skill, ingenuity, and instruments employed in agriculture. To determine the laws which regulate this

distribution, is the principal problem in Political Economy. (Ricardo 1817, Preface)

o The natural price of a certain commodity is calculated on the marginal land, thereby

including the natural profit rate and the natural wage rate only. The rent of the

landlord is a deduction from the profit of the capitalist due to differences in fertility

of soils.

o The real wage is exogenous. It is defined by the subsistence level of consumption of

workers (Malthus’s Law of Population). Profit is a residue. Natural prices can

certainly be ‘expressed’ as the sum of natural wages and natural profits, but any

adding-up theory of price is at odd with the theory of profit as a residual income.

3.2 THE EQUALISATION OF RATES OF PROFIT

o If the competition between capitalists is fully developed, the rate of profit tends to be

uniform across different sectors (equalisation of profit rates).

This restless desire on the part of all the employers of stock, to quit a less profitable for a more

advantageous business, has a strong tendency to equalize the rate of profits of all, or to fix them in such

proportions, as may in the estimation of the parties, compensate for any advantage which one may have, or

may appear to have over the other. (Ricardo 1817, Ch. 4)

o The natural price ratio expresses nothing but the embodied labour ratio:

𝑝1

𝑝2=

𝑤𝑙1(1 + 𝑟)

𝑤𝑙2(1 + 𝑟)=

𝑙1

𝑙2=

𝜆1

𝜆2

It cannot then be correct, to say with Adam Smith, “that as labour may sometimes purchase a greater, and

sometimes a smaller quantity of goods, it is their value which varies, not that of the labour which purchases

them;” […] but it is correct to say, as Adam Smith had previously said, “that the proportion between the

quantities of labour necessary for acquiring different objects seems to be the only circumstance which can

afford any rule for exchanging them for one another”. (Ricardo 1817, Ch. 1)

3.3 PROFIT RATE AND WAGE RATE IN A ‘CORN MODEL’

o Consider a single-industry economy. The natural unit price of output (say, corn) is:

𝑝𝑐 = 𝑤𝑙𝑐 1 + 𝑟 . Dividing each side by 𝑝𝑐 and solving by 𝑟, one obtains:

𝑟 =𝑎𝑐

𝑤𝑟− 1

where 𝑎𝑐 is labour productivity, i.e. the inverse of 𝑙𝑐. The rate of profit decreases as

the real wage increases and/or labour productivity (in agriculture) decreases.

[C]an any point be more clearly established than that profits must fall, with a rise of wages? (Ricardo 1817,

Ch. 6)

o Notice that the rate of profit can be calculated in real terms as the ratio between the

surplus of corn and the quantity of corn used as input (i.e. to pay workers):

𝑟 =surplus corn

wages=

𝑥𝑐 − 𝑤𝑟𝐿𝑐

𝑤𝑟𝐿𝑐= ⋯ =

𝑎𝑐

𝑤𝑟− 1

where 𝐿𝑐 = 𝑙𝑐𝑥𝑐 and 𝑎𝑐 = 𝑥𝑐/𝐿𝑐 = 1/𝑙𝑐.

3.4 DISTRIBUTION AND LABOUR-THEORY OF VALUE

o What happens when considering 𝑧 > 1 goods? If corn is the main component of

wage bundle, a raise in corn price (due to either a fall in productivity or a raise in real

wage rate) entails a fall in the profit rate of the economy.

o The higher the price of corn (𝑝𝑐) the higher must be the nominal wage (𝑤) paid to

workers of every industry, given the subsistence threshold (𝑤𝑟 = 𝑤/𝑝𝑐). Thanks to

this simple mechanism, the rate of profit of the whole economy is anchored to the rate

of profit of the corn sector. The former decreases as the latter decreases.

o Finally notice that if goods are exchanged according to their embodied labours (and 𝑣

is the share of labour embodied in workers’ subsistence) then:

𝑟 =surplus labour

labour embodied in wages=

∑𝐿𝑖 − 𝑣∑𝐿𝑖

𝑣∑𝐿𝑖=

1

𝑣− 1

The rate of profit can still be determined irrespective of prices. It is sufficient to look at

quantities of labour embodied in (net) output and wages, respectively.

3.5 A 93% LABOUR-THEORY OF VALUE

o Ricardo implicitly adopted a pure-labour production function. However, as Torrens pointed out, the use of machineries and other fixed components of capital could not be neglected. Their value concurs to define the (relative) price of commodities produced. And so does the time of production.

After capitalists become a distinct class from labourers, competition turns, not upon the quantity of labour, but on the amount of capital expended in production; and the results obtained after the employment of equal capitals, will always tend to an equality of value in the market. (Torrens 1821, Essay)

I would ask what means you have of ascertaining the equal value of capitals? [...] These capitals are not the same in kind […] and if they themselves are produced in unequal times they are subject to the same fluctuations as other commodities. Till you have fixed the criterion by which we are to ascertain value, you can say nothing of equal capitals. (Ricardo 1823, Letter to McCulloch)

Suppose then, that owing to a rise of wages, profits fall […] [T]he manufactured goods in which more fixed capital was employed, would fall relatively to corn or to any other goods in which a less portion of fixed capital entered. The degree of alteration in the relative value of goods, on account of a rise or fall of labour, would depend on the proportion which the fixed capital bore to the whole capital employed. All commodities which are produced by very valuable machinery […] or which require a great length of time before they can be brought to market, would fall in relative value, while all those which were chiefly produced by labour, or which would be speedily brought to market would rise in relative value. The reader, however, should remark, that this cause of the variation of commodities is comparatively slight in its effects. […] The greatest effects which could be produced on the relative prices of these goods from a rise of wages, could not exceed 6 or 7 per cent. (Ricardo 1817, Ch. 1)

3.6 DIFFERENT TECHNIQUES OF PRODUCTION

o In algebraic terms, the natural price of the 𝑖-th commodity should be redefined as:

𝑝𝑖 = 𝑤𝑙𝑖 + 𝑝𝑘𝑘𝑖 1 + 𝑟

where 𝑘𝑖 and 𝑝𝑘 stand for the capital good coefficient and its price. If the capital good

is produced by labour only – i.e. 𝑝𝑘 = 𝑤𝑙𝑘 1 + 𝑟 – then the relative price of two

commodities, call them ‘1’ and ‘2’, becomes:

𝑝1

𝑝2=

𝑤𝑙1 + 𝑤𝑙𝑘(1 + 𝑟)𝑘1 1 + 𝑟

𝑤𝑙2 + 𝑤𝑙𝑘(1 + 𝑟)𝑘2 1 + 𝑟=

𝑙1 + 𝑙𝑘(1 + 𝑟)𝑘1

𝑙2 + 𝑙𝑘(1 + 𝑟)𝑘2

o But this corresponds to the embodied labour time ratio (𝑙1/𝑙2) if and only if the same

technique (labour/capital ratio) is used in the two sectors (i.e. 𝑙1/𝑘1= 𝑙2/𝑘2).

I sometimes think that if I were to write the chapter on value again which is in my book, I should

acknowledge that the relative value of commodities was regulated by two causes instead of by one,

namely, by the relative quantity of labour necessary to produce the commodities in question, and by the

rate of profit for the time that the capital remained dormant. (Ricardo 1820, Letter to McCulloch)

3.7 TO SUM UP

o The cause of value is labour, i.e. it is labour embodied in commodities produced that

makes them valuable for individuals and the society.

o Under a competitive equilibrium, the relative amount of embodied labours is also an

excellent empirical measure of relative prices of commodities.

o However, the analytical soundness of the labour-theory of value is weakened by the

presence of different techniques of production (marked by different compositions

of capitals).

o Income distribution is a by-product of class-struggle: the profit of the capitalist class

is a residue, depending on both labour productivity (in the consumption or agricultural

industries) and the historically-given subsistence threshold. This inter alia means that

the rate of profit is doomed to decrease in the long run, due to decreasing returns

in agricultural sectors.

Karl Marx: surplus-value as surplus-

labour and the transformation problem 4 Name: Karl Marx.

Born: 5 May 1818, Trier, Kingdom of

Prussia.

Died: 14 March 1883 (aged 64), London,

England.

Main work: Capital (1867).

4.1 A CRITIQUE OF CLASSICAL POLITICAL ECONOMY

o CPE was the theoretical expression of the bourgeoisie in a period in which it was struggling for political hegemony (till 1830s). When it came to power, the view of the new economic order as an harmonic cosmos (vulgar economics) gained momentum.

o The task of the working movement was/is to further develop the analytical tools of CPE in order to turn them into instruments to change the reality (establish a new order).

o Three were/are the chief criticisms of CPE:

1. CPE (especially Smith’s version) is contaminated by vulgar economics, referring to individuals as atoms whose behaviours are driven by their self-interest only. By contrast, an ontology of the social being is necessary.

2. In CPE an attempt is made to provide a measure of profit, but the origin of such surplus-value is unexplained. To address this point, it is necessary to go deeper into the production sphere.

3. Capitalism is anything but an eternal and self-regulating natural order. It is an historical (transient) mode of production, prone to conflict, instability and crisis. Capital is a social relationship.

4.2 THE CAPITALIST CIRCULATION

o What is capital? Capital is neither a set of means of production nor a sum of money. Rather, it is a dynamic process, i.e. the never-ending movement of capital self-valorisation. Under that movement lies a social (class power) relation.

o While the form of the simple circulation is C - M - C (commodity-money-commodity), in which money acts as a simple means of exchange, the capitalist circulation form is M - C - M’ or M - C - (M + ∆M), in which money acts as capital.

o But where does that surplus-value, ∆M = S, come from (for capitalists as a whole)? To unveil the origin of the surplus value, it is necessary to go under the surface of capitalism in which it looks like a market exchange between peers.

Accompanied by Mr. Moneybags and by the possessor of labour-power, we therefore take leave for a time of this noisy sphere, where everything takes place on the surface and in view of all men, and follow them both into the hidden abode of production, on whose threshold there stares us in the face “No admittance except on business.” […] On leaving this sphere of simple circulation […] we can perceive a change in the physiognomy of our dramatis personae. He, who before was the money-owner, now strides in front as capitalist; the possessor of labour-power follows as his labourer. The one with an air of importance, smirking, intent on business; the other, timid and holding back, like one who is bringing his own hide to market and has nothing to expect but – a hiding. (Marx 1867, Ch. 6)

4.3 THE ORIGIN OF THE SURPLUS-VALUE

[O]ur friend, Moneybags, must be so lucky as to find, within the sphere of circulation, in the market, a commodity, whose use-value possesses the peculiar property of being a source of value, whose actual consumption, therefore, is itself an embodiment of labour, and, consequently, a creation of value. The possessor of money does find on the market such a special commodity in capacity for labour or labour-power. (Marx 1867, Ch. 6)

o In the production, the use-value of the labour-power is given by the total amount of working hours, whereas its (exchange-)value is only defined by the labour time required by the production of commodities workers need to survive and reproduce as a class. The difference between the two is a surplus-labour. It is the source of S.

o The surplus-value does not (necessarily) come from underpayment of workers. On the market, the value of labour-power is set by its conditions of re-production. Capitalists can be assumed to pay a ‘fair’ wage corresponding to that (exchange-)value. Yet, they are still shown to realise a profit.

o Exploitation is about production, not about circulation. Labour market and the labour contract are the two fundamental institutions of capitalism, as they enable the production of the social surplus to take the (capitalist) form of a surplus-value created by capital investment.

4.4 VALUE AND PRICE OF COMMODITIES

o Value (of a certain commodity) is a social substance (corresponding to the socially necessary labour time required by its production), whereas price is the (monetary) form that value takes in market relations.

o The total value of commodities produced in the 𝑖-th industry (expressed in labour units) is defined as:

Λ𝑖 = 𝐶𝑖 + 𝑉𝑖 + 𝑆𝑖

where:

• Λ𝑖 = 𝜆𝑖𝑥𝑖, in which 𝑥𝑖 is the quantity of commodities and 𝜆𝑖 is their unit value;

• 𝐶𝑖 is the constant capital, i.e. the value of both fixed and circulating capital (net of wages) invested by capitalists in the 𝑖-th industry;

• 𝑉𝑖 is the variable capital, i.e. the overall value of labour-power employed in the 𝑖-th industry (corresponding to the wage-bill);

• 𝑆𝑖 is the (single-period mass of) surplus-value created in the 𝑖-th industry.

4.5 EXPLOITATION AND THE RATE OF SURPLUS-VALUE

o It is only the variable capital that valorises in the production process (creating a 𝑆𝑖).

By contrast, 𝐶𝑖 can only transfer its own value to output. 𝑉𝑖 corresponds to the part of

the working day (𝐿𝑖) in which the working class works for itself (necessary labour).

𝑆𝑖 mirrors the part in which workers produce for the capitalist class (surplus labour).

o The rate of exploitation of the working class is given by the rate of surplus value:

𝑒 =𝑆𝑖

𝑉𝑖 𝑜𝑟 𝑒 =

𝐿𝑖 − 𝑉𝑖

𝑉𝑖=

1 − 𝑣 𝐿𝑖

𝑣𝐿𝑖=

1

𝑣− 1

where 𝑣 is the uniform unit value of labour-power (and 𝐿𝑖 = 𝑙𝑖𝑥𝑖).

o The expression of the value of commodities produced in the 𝑖-th industry becomes:

Λ𝑖 = 𝐶𝑖 + 𝑉𝑖 1 + 𝑒 𝑜𝑟 Λ𝑖 = 𝐶𝑖 + 𝐿𝑖

The value of commodities is the sum of the value of constant capital (i.e. the indirect

labour) and the direct labour expended in their production (law of value).

4.6 THE PRICE OF PRODUCTION

o Under a competitive equilibrium, commodities are exchange according to their prices

of production (capitalist law of exchange):

𝑃𝑖 = 𝑚 ∙ 𝐶𝑖 + 𝑉𝑖 (1 + 𝑟)

where 𝑟 is the general rate of profit (equalisation), 𝑚 is the monetary expression of

the labour time (but we assume 𝑚 = 1 hereafter), and 𝑃𝑖 = 𝑝𝑖𝑥𝑖.

o Prices of commodities usually diverge from their values. However, the deviations of

the prices of production from the labour-values offset one another. It is about a zero-

sum game. For the system as a whole, two aggregate equations hold:

1. ∑𝑃𝑖 = ∑Λ𝑖, i.e. the overall price of output equals (or is proportional to) the

overall value of output.

2. 𝑟 ∙ 𝐶 + 𝑉 = 𝑒 ∙ 𝑉, with 𝐶 = ∑𝐶𝑖 and 𝑉 = ∑𝑉𝑖, i.e. the overall profit equals

(or is proportional to) the overall surplus-value.

4.7 THE RATE OF PROFIT AND THE ‘TRANSFORMATION’

o The (single-period) general rate of profit is:

𝑟 =𝑆

𝐶 + 𝑉=

𝑒𝑉

𝐶 + 𝑉=

𝑒

𝐶𝑉

+ 1=

𝑒

𝑞 + 1

where q is the average organic composition of capital. The higher the rate of

exploitation of the working class and the lower the organic composition of capital, the

higher will be the general rate of profit for the capitalist class.

o The equation of the price of production of the 𝑖-th commodity becomes:

𝑃𝑖 = 𝐶𝑖 + 𝑉𝑖 1 +𝑒

𝑞 + 1

o The price of production depends on labour-value magnitudes only. Prices are nothing

but phenomenical (transformed) forms of labour-values. Profit is the monetary form

of social surplus labour. It stems from the exploitation of the working class.

4.8 THE TENDENCY OF THE PROFIT RATE TO FALL

In order to increase labour productivity (relative surplus-labour) and to weaken the

bargaining power of the working class, capitalists introduce (labour-saving) technical

innovations. Fallacy of composition: while this raises the profit rate of the individual

capitalist, the profit rate for the capitalist class as a whole tends to decline.

↓ 𝑟 ⇐𝑒

↑ 𝑞 + 1, with: 𝑞 = 𝐶/𝑉

However, some counteracting factors have to be accounted for, such as:

1. The increase in labour productivity (leading to ↑ 𝑒 and ↓ 𝑞).

2. The reduction in wages below the value of labour-power (leading to ↑ 𝑒).

3. The cheapening of constant capital via foreign trade or ‘imperialism’ (leading to ↓ 𝑞).

The reduction in the rate of profit is a (long-run) stylised fact. It should be regarded as a

the economic equivalent of the law of gravity. The MEGA2 sheds a new light on this.

LUBS 2040 - Appendix 4

FOCUS 1 THE MAXIMUM RATE OF PROFIT

The maximum general rate of profit is obtained by using 𝑣 = 0 in the standard

equation. This is the rate that would prevail «if the workers could live on air» (Marx 1894,

Ch. 15, quoted by Sraffa 1960). In algebraic terms:

𝑟 =S

C + 𝑉=

(1 − 𝑣)L

C + 𝑣𝐿 with: 𝐿 = Σ𝐿𝑖

𝑅 = max 𝑟 =(1 − 0)L

C + 0 ∙ 𝐿=

L

C

The maximum general rate of profit decreases as the ‘constant capital’ to labour ratio

(𝐶/𝐿) raises.

𝑅 is the ceiling of the actual rate of profit, 𝑟. If the former decreases, then the latter will

decrease too.

To sum up, the general rate of profit is expected to decrease in the long run, due to

technical innovation (which, in turn, is fostered by the class struggle).

4.9 MARX VS. RICARDO: SOCIAL VS. EMBODIED LABOUR

o Surplus value is created in proportion to direct labour expended, but realised in

proportion to capital invested. There is no contradiction between the law of value

(exploitation) and the law of exchange (equalisation and other market forces).

o Unlike Ricardo, Marx understands that the source of value (for the capitalist class) is

not individual concrete labour (micro), but socially-necessary abstract labour

(macro). The former creates use-values. The latter is what creates value, and hence

value in exchange (for capitalists).

o Individual labour turns into socially necessary labour to the extent that output is

validated (or exchanged) against money on the market. In other words, value is

created (in potentia) in the production sphere, but it has to be socially validated (i.e.

it turns into value in acto) in the circulation sphere.

o Ricardo’s theory relies on an individual-real take. Marx’s theory relies on a macro-

monetary conception of value (under a capitalist system).

4.10 THE TRANSFORMATION PROBLEM

o We have simply transferred the values of inputs (𝐶𝑖 and 𝑉𝑖) to the price of production

of output-commodities. However, inputs should have been estimated at their prices of

production, not at prices proportional to values. Marx was aware of this problem.

We had originally assumed that the cost-price of a commodity equalled the value of the commodities

consumed in its production. But for the buyer the price of production of a specific commodity is its cost-

price, and may thus pass as cost-price into the prices of other commodities. Since the price of production

may differ from the value of a commodity, it follows that the cost-price of a commodity containing this price

of production of another commodity may also stand above or below that portion of its total value derived

from the value of the means of production consumed by it. (Marx 1894, Ch. 9)

As for the variable capital, the average daily wage is indeed always equal to the value produced in the

number of hours the labourer must work to produce the necessities of life. But this number of hours is in its

turn obscured by the deviation of the prices of production of the necessities of life from their values. (Marx

1894, Ch. 9)

o Unfortunately, Marx claimed that:

Our present analysis does not necessitate a closer examination of this point. (Marx 1894, Ch. 9)

FOCUS 2 ONGOING CONTROVERSY ON TRANSFORMATION

Consider an economy in which 𝑁 output-commodities are produced by means of labour

and the same commodities used as inputs (in the form of circulating capital). The right

(matrix) formulation for the system of prices of production would be:

𝑝𝑖𝑥𝑖 = 𝐩𝐓𝐚𝐢𝑥𝑖 + 𝑤𝑙𝑖𝑥𝑖 1 + 𝑟

𝐩𝐓𝐱 = 𝐩𝐓𝐀𝐱 + 𝑤𝐥𝐓𝐱 1 + 𝑟

No labour-value accounting is necessary to define prices (redundancy). The system can

be solved by defining a numeraire and then setting either 𝑟 or 𝑤 (Sraffa 1960). The

transformation would be simply a ‘complicating detour’ (Samuelson 1957).

(But was Marx’s objective to show that prices cannot be computed without values?!)

In addition, once capital is revaluated at prices of production, the sum of profits will in

general differ from the sum of surplus-values. The equation defining Marx’s theory of

value and exploitation does not hold anymore. Labour-values could be even negative

when joint productions are considered (Steedman 1977) (inconsistency).

i-th commodity or industry

economy as a whole

FOCUS 3 A NEW (SINGLE-SYSTEM) INTERPRETATION?

Another interpretation of Marxian thought is possible: it is the price of the net product of

the economy that accounts for the expression in prices of the total direct labour expended

during the period considered (Foley and Duménil 2008):

price form of output = m∙(direct labour + value transferred from C-inputs)

price form of output – price form of C-inputs = m∙direct labour

price form of net product = m∙direct labour

where m is the (correct) monetary expression of the labour time. In algebraic terms:

𝑚 =price form of net product

direct labour=

𝐩𝐓 𝐈 − 𝐀 𝐱

𝐥𝐓𝐱

In this take, total profits are shown to be the price form of surplus-value. The value of

the labour-power is defined by the (unallocated) purchasing power on the portion of the

net product that workers can buy with their money wages.

4.11 TO SUM UP

o To unveil the origin of surplus value, it is necessary to go under the surface of the

reality (the circulation sphere) and to get in the production sphere. It turns out that the

only possible source of surplus-value is the exploitation of living labour.

o Values of commodities are usually not proportional to prices. This is due to both the

competition among capitalists (profit rate equalisation) and market forces. However,

prices are transformed forms of values. At the macroeconomic level, the overall

price of output mirrors its overall value. Profit is the price form of surplus-labour.

o When calculating prices of production, Marx implicitly assumes that prices of inputs

are proportional to their values. But this not satisfactory.

o To the extent that the equation of the price of production is amended, Marx’s theory

becomes redundant or even logically inconsistent (though class exploitation, as

conflict over distribution, can be still invoked). However, a different interpretation is

possible, recovering the main insights of the Marxian Critique.

TO SUM UP: SMITH, RICARDO AND MARX

o According to Smith, the direct labour expended in is the process of production is the

cause of value. However, relative prices are better measured by the amounts of

labour that commodities can command.

o Ricardo shows that, under a competitive equilibrium, relative prices mirror embodied

labours. Value is labour. As a result, the distribution of net income (or product)

originates from the class struggle. The introduction of fixed capital sullies the

analytical pureness of this law, but does not affect its empirical robustness.

o Marx understands that prices usually do not match labour-values. However, for the

economy as a whole, a law of conservation of value holds: total profit is the price

form of social surplus-labour. The standard formulation of Marx’s transformation is

rather controversial, though alternative interpretations have been provided which

could validate Marx’s original insights.

“We no longer have the learning of the

ancients, the age of giants is past!” Nicholas of

Morimondo

William of

Baskerville

From: Umberto Eco, The Name of the Rose, 1980.

“We are dwarfs, but dwarfs who stand on

the shoulders of those giants, and small

though we are, we sometimes manage to

see farther on the horizon than they.”

ABOUT GIANTS’ SHOULDERS…

• Duménil G. and Foley D. 2008. The Marxian transformation problem, in Durlauf S. N. and Blume L. E. (eds.), The

New Palgrave Dictionary of Economics (Second Edition), Basingstoke: Palgrave Macmillan.

• Marx K. 1857-58. Grundrisse Foundations of the Critique of Political Economy (Rough Draft), UK, Penguin Books

Ltd/New Left Review, 1993.

• Marx K. 1867. Capital. A critique of Political Economy, Volume One, UK, Penguin Books Ltd/New Left Review,

1976.

• Marx K. 1885. Capital. A critique of Political Economy, Volume Two, UK, Penguin Books Ltd/New Left Review,

1978.

• Marx K. 1894. Capital. A critique of Political Economy, Volume Three, UK, Penguin Books Ltd/New Left Review,

1981.

• Screpanti E. And Zamagni S. 2005. An outline of the history of economic thought, Oxford, Oxford University Press.

• Smith A. 1776. An Inquiry into the Nature and Causes of the Wealth of Nations, Chicago, University of Chicago

Press, 1977.

• Sraffa P. and M.H. Dobb (eds.) 1951-1973. The works and correspondence of David Ricardo, Vol. I, VII-IX,

Cambridge, Cambridge University Press.

• Sraffa P. 1960. Production of Commodities by Means of Commodities. Prelude to a Critique of Economic Theory.

Cambridge: Cambridge UP.