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Marxian epistemology and the transformation problemGeoff HodgsonPublished online: 28 Jul 2006.

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Marxian epistemology and the transformation problem Geoff Hodgson

Abstract A discussion and statement of Marx's solution to the problem of deriving prices from embodied labour values, i.e. the transformation problem. A critique of the inconsistencies inherent in Marx's solution, and a citation of some of Marx's own doubts about the adequacy of his solution. A consideration of Bortkiewicz's solution and certain objections to it. Presentation of a modified Bortkiewicz-type solution. Extension of the problem from formal economics to epistemology. Discussion of the epistemological status of such concepts as value, price of production, and the general rate of profit. An interpretation of Marx's epistemology and its relation to the transformation problem. Discussion of the labour theory of value in the light of the previous results.

'The good Christian should beware of mathematicians.'-St. Augustine

No controversy has racked the Marxian school of political economy more than its dispute with orthodox economic theory on the question of values and prices1 Associated with this dispute is the well known 'transformation problem' which deals with the derivation of relative prices from values (i.e. quantities of embodied socially necessary labour time). I t is well known that in the first volume of Capital Marx assumes that prices are proportional to values, in other words com- modities of equal value exchange at the same price on the market. Often this assumption is mistaken for the labour theory of value itself, but Marx himself was aware that this proportionality is not present under general capitalist conditions.

I t is clear from his correspondence with Engels that Marx had already formed some thoughts on the more complex relation between values and prices before the publication of the first volume of Capital in 1867 (Marx and Engels, S.C., pp. 157-62). Marx's solution to the transformation problem was to be presented in the third volume. However, he did not live to prepare this volume for the publisher, and Engels was left to edit the manuscript. It was eventually published in 1894.

Ever since that date, debate on the issue has periodically erupted, but significantly no consensus of opinion on this question has been achieved, even among Marxists. There have been various formulations of the law of value and the labour theory of value, and controversy over

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358 Geoff Hodgson

the very meaning of the Marxian concepts of value, price of production, and the general rate of profit. A serious examination of the problem is now necessary, particularly if Marxian political economy is to develop in response to Sraffa's rehabilitation of classical economic theory (Sraffa, 1960).

We shall commence with Marx's solution to the problem of trans- forming values into prices, and some criticisms of his approach. An alternative solution will be presented within a minimum of mathematics, but the discussion does not end there. The matter will not be resolved until the wider methodological and theoretical issues are clarified. One aim of this essay is to interpret Marx's epistemology, and to outline the relevance of this to the concepts of price, value, and the general rate of profit.

Marx's solution

It is not until the third volume of Capital that Marx discusses the formation of a general rate of profit. Capitalists, Marx explained, tend to invest in those industries with a higher profit rate until there is a relative overproduction of goods, some prices and profits fall, and the economy gravitates towards some sort of equilibrium. From the point of view of the ebb and flow of investment funds, the only equilibrium solution, in a perfectly competitive environment, is where the rate of profit in each firm is equal to a single general rate of profit which pertains to the economy as a whole. Of course, in the real world, the rates of profit are never exactly equalised. But as a tendency exists towards their equalisation we must consider the abstract equilibrium case, with a general rate of profit, before more realistic and dynamic cases are examined. Any solution to the transformation problem must cover the equilibrium situation, at least as a special case.

At this stage it is necessary to define some basic variables:

y = net output in value terms.

This is the magnitude of the socially necessary living labour time ex- pended in the economy in a given time period, say one year. I t corre- sponds to the value of the gross output minus the dead labour time embodied in it.

v = variable capital.

The working class receives a number of wage goods in a year. The amount of socially necessary labour time embodied in these goods is the variable capital.

S = surplus value.

The workers are compelled to produce an amount of surplus value over

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Marxian epistemology and the transformation problem 359

and above the value of the wage goods they receive in return for the sale of their labour power. Obviously, by definition: v + s = y.

c = constant capital flow (i.e. circulating capital).

This is the value of the raw materials used up, plus the depreciation of the means of production, in value terms. Like v and S, c is a flow variable.

k = constant capital stock (i.e. fixed capital).

This is the value of the means of production that remain at the end of the production period, after depreciation. I t does not enter into the gross value of the social product; it remains for use in the next period. Evidently :

value of gross output = c + v + s = c + y.

Many Marxists have a strange and unacceptable habit of always ignoring fixed capital (K), especially in the formulation of the rate of profit. Marx, however, was insistent that the latter is the ratio between surplus value realised and total capital invested, including constant capital stock (Marx, 1962, pp. 47, 70-6, 111, 222,224). ~ e n c e , accord- ing to Marx:

where p is the rate of profit in value terms. I t is a ratio between values, as k, c, v, and s are all in value terms. I t is assumed, for simplicity, that the turnover period, or time period of production, is one year. Other- wise this additional variable must be included in the formula for the general rate of p r ~ f i t . ~

Marx's approach will be explained by means of an example of an economy which consists of just three firms. Here the letters k , c, v, and s have numerical subscripts to denote the particular firm:

Firm I: k, = 60 c , = 30 v , = 10 S , = 10

Firm 2: k z = 40 cz = 30 vz = 30 sz = 30

Firm 3: k, = 30 c, = 50 v , = 20 S, = 20

(In order to simplify the arithmetic ki f ci + vi = IOO in each case.) The above data have two important characteristics. Firstly, the rate of surplus value (i.e. slv) is the same in every firm. Secondly, in contrast, the ratios klv and c / v change from firm to firm. Consequently, the rates of profit in value terms are different in each firm:

Firm I :

Firm 2 :

I0

= 60 + 30 + 10 = 10 per cent.

30 = 40 -/- 30 + 30

= 30 per cent.

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20 Firm 3 :

= 30 + 50 + 20 = 20 per cent.

Geoff Hodgson

Where p,, p, and p, are the rates of profit in value terms in each firm, calculated with Marx's formula.

The transformation problem applies to the situation, illustrated by the above example, where the rate of surplus value is equalised throughout the economy, but where the ratios klv and c/v are not consistent between firms. The problem is to form the general rate of profit and determine what Marx calls 'prices of production'. In short the transformation problem expresses the essential unity of the antag- onistic capitalist phenomena of a competitive labour market, and competitive capital movements subject to the influence of the rate of profit.

In order to determine the magnitude of the general rate of profit for the economy as a whole Marx makes a crucial assumption; he treats the whole economy as it was one giant firm, to use his words: 'a single capital' (Marx, 1962, p. 153). In our example

60 p = - - - 20 per cent. 300

The assumption is equivalent to the assertion that this average rate of profit is identical to the general rate of profit. In all of Marx's writings, however, no argument to support this assertion may be found. I t is evident that Marx used such concepts as 'capital in general', but these do not yield the notion that the general rate of profit is the average, or more precisely, the arithmetic mean of all the other constituent rates of profit. After all there are other different types of 'average', such as the geometric mean and the harmonic mean, which could, for example, give greater weight to the larger firms than the arithmetic mean.

According to Marx the aggregate amount of surplus value is some- how distributed amongst the firms in proportion to the size of their capitals (i.e. ki + ci + vi) to form their profits. These amounts of profit, plus the value of the capital used up in production (i.e. ci + vi), constitute the prices of production. In our example total surplus value is 60, and the profit distributed to each firm is 20 units, as all three capitals are of the same size. Hence the prices of production are as follows :

Firm I : 30 + 10 + 20 = 60

Firm 2: 30 + 30 f 20 = 80

Firm 3: 50 + 20 + 20 = 90

Note that in the first two firms the price of production deviates from the value of the gross output. We shall define the price coejicient as the

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Marxian epistemology and the transformation problem 36 1

price of a unit value output, in each firm. It is price of production divided by the value of the gross output:

60 Firm I : - = 1-2

50 80

Firm 2: - = 0.889 approx. 90

90 Firm 3: -= 1.0 90

In addition, note that, as a result of Marx's assumptions, total price of production equals total value, and total profit equals total surplus value.

Marx's doubts

Close consideration of Marx's solutions reveals an inconsistency. The price coefficients are not necessarily unity, yet the rate of profit is computed on the basis that the cost or supply prices of the various elements of the aggregate capital (i.e. K , c, and v ) are proportional to their values. There is a difference between the rate of profit calculated in terms of values and the rate of profit calculated in terms of prices of production. If the prices of production of the various commodities are used to calculate the rates of profit in each firm then these rates of profit will no longer be equal. Marx seemed aware of the difficulty, for he raised the problem in several places in Capital. For instance he wrote :

Aside from the fact that the price of a particular product, let us say capital B, differs from its value because the surplus value realized in B may be greater or smaller than the profit added to the price of the products of B, the same circumstance applies also to those commodities which form the constant part of capital B, and indirectly also its variable part, as the labourers' necessities of life. So far as the constant portion is concerned, it is itself equal to the cost price plus the surplus value, here therefore equal to the cost price plus profit, and this profit may again be greater or smaller than the surplus value for which it stands. As for the variable capital, the average daily wage is not 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 price of production of the necessities of life from their values. However, this always resolves itself into one commodity receving too little of the surplus value while another receives too much, so that the deviations from the value which are embodied in the prices of production compensate one another.

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362 Geoff Hodgson

Under capitalist production, the general law acts as the prevailing tendency only in a very complicated and approximate manner, as a never ascertainable average of ceaseless fluctuations. (Marx, 1962, p. 159, our emphasis)

I t is clear from this quotation that Marx thought that the values of the constant and variable capital, in the expression for the rate of profit, must themselves be transformed into prices before the true general rate of profit is formed. In the penultimate sentence he evades the problem by asserting, without proof, that the various deviations of price from value will cancel each other out when they are aggregated in the total capital, and the total result will be the same. But this does not banish the nagging doubt in his mind, for in the final sentence he states that this cancellation will only work in an 'approximate manner', and after all the rate of profit is never really stable in the real world. This evades the problem of constructing a consistent equilibrium solution.

There are many other passages in Capital where Marx argues that the values of the inputs used to produce a given commodity must themselves be transformed into prices, in order to determine the price of production of that commodity. For example see Marx (1962, pp. 157-8, 162, 202-3). It is amazing that some Marxists still attribute to Marx the idea that it is wrong to transform these input values.

There is no basis to suggest, as Marx does, that the fluctuations of price from value tend to cancel each other out when aggregate prices are considered in one particular firm. Prices can deviate from values in an irregular and disproportionate manner in different industries. Even if we accept Marx's solution it is easy to conceive of a situation where the price coefficients in the wage and capital goods industries are both greater than unity, and the price coefficients for luxury goods are less than one. In this case the prices of constant and variable capital are both greater than their value, and deviations of price from value in the denominator of the expression for the rate of profit do not cancel each other out. Hence the true general rate of profit which takes account of deviations of price from value is not

k + c + v '

This expression does not yield an equalised equilibrium profit rate.

The basic flaw in Marx's solution

I t must be remembered that the capitalists are primarily concerned to increase their profit in money terms. This the essential meaning of Marx's well-known diagram

M - C - M ' .

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Marxian epistemology and the transformation problem 363

Money capital M is invested in constant and variable capital, production takes place, commodities C are produced, and finally these are sold on the market to reap an enlarged money revenue M'. It was Marx's aim to explain the source of the profit: the difference between M and M'.

The capitalists will calculate their rate of profit in terms of prices, not values. Money capital movements between firms will be in equilibrium when the rate of profit in price terms is equal in each firm. Interest rates, dividends, and so on are not calculated in terms of values. The value of a given commodity is hardly easily obtainable everyday information. Capitalists are not aware of, or disposed towards, any calculation in terms of embodied labour values. Hence the rate of profit that tends to be equalised to form a general rate of profit is in terms of prices, not values.

Neither Marx, nor any of the adherents of his solution, have given any reason why we should expect the rate of profit in terms of values to be equalised. The adherents have never attempted a direct reply to the criticism in the previous paragraph. Perhaps the reason for this is quite simple; the criticism is sound and cannot be answered.

Marx's error is connected with his arbitrary assumption that we may treat the social capital as a whole, as if it was one giant firm. Hence this avoids the main problem: to determine the general rate of profit that pertains to separate firms. The interaction of different capitals is a fundamental feature of capitalism. Without separate capitals, capital itself ceases to be a commodity, it is no longer bought and sold on the market, and it no longer exists as capital. Marx, himself, was aware of this when he wrote in the Grundrisse: 'Capital exists and can only exist as many capitals, and its self-determination therefore appears as their reciprocal interaction with one another' (Marx, 1973, p. 414).

The inability of Marx to formulate a correct solution to the trans- formation problem is at least partly explained by his lack of expertise in mathematics. Engels gave a different assessment of Marx's mathe- matical abilities, but none of Marx's available writings give testimony to support Engels' view. The absence of functional notation, a crude and unsubstantiated disposition towards averages, and the clumsy handling of reproduction schemes in the second volume of Capital, are all symptomatic of a lack of mathematical experience and knowledge. An examination of Marx's treatment of the transformation problem will show that he was trying to determine the prices of production after the determination of the general rate of profit (Marx, 1962, pp. 155-9). Had he analysed the problem mathematically it would have been evident that only a simultaneous determination of these magnitudes was possible.

Marx's arbitrary use of overall averages in his treatment of the problem led to an implicit methodological error. I t must not be over- looked, however, that Marx's general methodological capabilities have been hardly surpassed in generations.

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364 Geoff Hodgson

Bortkiewicz's solution

Thirteen years after the publication of the third volume of Capital one L. von Bortkiewicz, an experienced mathematician, produced his alternative solution to the transformation problem (Bortkiewicz, 1949 and 1952). He considered an economy in simple reproduction, and assumed that all the constant capital was used up in one production period, i.e. constant capital stock was non-existent. These assumptions are not at all necessary and they are not adopted here, However, the basic approach is the same.

The rate of profit in the Bortkiewicz solution is in price terms. I t is the amount of profit divided by the price of the total capital outlay. We shall assume that the economy produces three types of good: capital goods, wage goods consumed by the workers, and luxury goods consumed by the capitalists. Consequently we have taken the rather severe assumption that capital goods are homogeneous, but this does not invalidate the approach, as it can easily be generalised to include heterogeneous capital goods, as in the work of Sraffa (1960). We shall adopt the common notation of calling the capital goods industry Department I, the wage goods industry Department 2, and the luxury goods industry Department 3. We shall let the price coefficients of the three types of good be X,, X, and X, respectively, and the rate of profit in price terms be p". The solution will be illustrated with the following numerical example :

Dept. I : k, = 3000 cl = 999 vl = 500 sl = 500

Dept. 3 : k, = IOO c, = 102 v, = 51 S, = 51

For simplicity we shall assume that the time taken to produce, transport and sell each good is one year. It can be shown that the above figures will allow a 10 per cent per annum growth rate in each depart- ment. This is demonstratated in Appendix I, and it rests upon the further assumption that constant capital stock is fully utilised.

The unknown quantities that have to be found are X,, X,, X, and p*. I t is not necessary to follow all the arithmetic and algebra. At first we shall show the crucial steps with Department I only. The price of the total capital outlay in this department is the price of the constant plus the variable capital :

Dept. I : total capital outlay = klxl + clx, + v,x,

Note that the price coefficient X, applies to both constant capital stock and constant capital flow. All values that appear in the denominator of

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Marxian epistemology and the transformation problem 365

Marx's expression for the rate of profit have been transformed into prices by multiplying them by the appropriate price coefficient.

The revenue received from the sale of the gross product in Depart- ment I is as follows:

Dept. I : gross revenue = (c, + v , + s,)x, = ~gggx,

The cost of producing this product, i.e. the price of the constant capital flow plus variable capital, is as follows:

Dept. I : costs = clxl + v,x2 = 999x1 + 5 0 0 ~ ~

Note that both the gross revenue and the costs have once again been found by transforming the appropriate values into prices by means of the price coefficients.

The profit is found by subtracting the latter costs from the gross revenue :

Dept. I : profit = ~gggx, - (gggx, + 5 0 0 ~ ~ ) = IOOOX, - 5 0 0 ~ ~

Note that if the price coefficients X, and X, were unity then profit would be equal to surplus value. But generally this is not the case.

Now the rate of profit in price terms is defined as follows:

gross revenue - costs p* = - - profit

total capital outlay total capital outlay'

where both numerator and denominator are measured in price terms. This gives us an expression for the rate of profit in Department I :

1000xl - 500x2 Dept. I : p* =

3999x1 + 500x2

The same procedure can be followed in the other two departments to produce two more experessions for the rate of profit:

Dept. 2: p* = -319x1 f 638x2 1589x1 f 319%

-I02X1 - 51x2 + 204X3 Dept. 3 : p* =

202x1 + 51x2

These three expressions for the rate of profit must, of course, be equal. We have three equations with four unknown quantities. The general solution of these equations is shown in Appendix 2. However, it must be noted here that these equations are not sufficient to determine the absolute magnitude of the price coefficients; we can only find the ratios between them. But the three equations are sufficient to find the actual magnitude of the rate of profit. The approximate numerical solutions are as follows :

p*= 0.127 and X, : X , : X , = I : 0.872 :o-go8

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366 Geoff Hodgson

The reader may wish to verify that the above rate of profit and price coefficient ratios satisfy the three expressions for the rate of profit and thus ensure that the price accounts balance.

In the Bortkiewicz solution the prices themselves depend upon the choice of unit in which they are measured. Hence, in general, and in contrast to Marx's solution, total price does not equal total value and total profit does not equal total surplus value. Even if the price unit is chosen so that one of these pairs are equal, then in general the other pair will be unequal.

Nevertheless it has been argued that the Bortkiewicz-type solution does not contradict Marx's theory of the origin of profit. I t can be demonstrated that with certain assumptions, such as those that have been made in the numerical example above, total profit is positive if and only if total surplus value is p~si t ive .~ More precisely, in mathe- matical terms, profit is an increasing monotonic function of surplus value, passing through the origin, according to Bortkiewicz. In Marx's view profit is an increasing linear function of surplus value, passing through the origin. In a recent and stimulating article, E. Wolfstetter argues from a rigorous presentation of a Bortkiewicz-type solution that profit is 'the phenomenal form of surplus value' (Wolfstetter, 1973, p. 802). Hence the adoption of a Bortkiewicz-type solution does not necessarily mean a relapse in bourgeois value theory, or a break with the spirit of Marx's theory of value and exploitation. In addition it does not mean the automatic adoption of the remainder of von Bortkiewicz's views on the theory of value.

The Bortkiewicz corollary

A logical result follows from Bortkiewicz's solution that has been the subject of considerable controversy. I t is usually known as the Bortkiewicz corollary. We shall attempt to explain it here by referring to the previous numerical example. We noted that there were three expressions for the rate of profit, one for each department. Now X,

does not appear in the first two equations. Hence these two equations contain just three unknowns: X,, X, and p*. It is possible, therefore, to solve these equations and find the solution for p* and the ratio between X, and X,. It must be concluded that the conditions of production in the third department do not enter into the determination of the general rate of profit. I t is solely determined by the conditions of production in those industries which directly or indirectly produce wage goods, i.e. the first two departments. This conclusion is not exactly the same as Ricardo's, as he thought that the wage goods industry alone determined the rate of profit. Unlike Marx and Bortkiewicz he did not directly consider constant capital, and Marx was quite right to criticise him for this omission.

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Mamian epistemology and the transformation problem 367

One important feature of Bortkiewicz's solution is that we must consider the physical structure of the economy in order to determine prices and the rate of profit. The values in Marx's solution could be regarded as aggregates pertaining to a number of commodities, and the physical nature of the product of any firm is irrelevant when forming the general rate of profit. All firms, whatever their type, and including the luxury goods sector, play the same role in determin- ing the overall average rate of profit. The contrasting character of Bortkiewicz's solution is the source of the important corollary. It is easy to understand if we consider the physical elements in the rate of profit. The total capital outlay which appears in the denominator consists of capital goods, and indirectly, wage goods. Luxury goods, and arma- ments, do not appear as they are not used in production. Neither do they appear as costs in the numerator of the expression, nor as the surplus product in the wage and capital goods sectors. Hence the conditions of production in the arms and luxury goods sectors do not enter into the determination of the rate of profit.

Objections have been raised to the proof of this corollary on the grounds that the component values of the reproduction scheme must, in some sense, be dependent on each other, and hence the values in Department 3 are related to the values in the other two departments. Consequently it is asserted that all the formulae for the rate of profit could be re-written so that they included some of the variables from the third department. Hence it is argued that the rate of profit is partly dependent on the conditions of production in the luxury goods and arms sector. There are at least two reasons why this argument is false. Firstly it rests on the assumption that there is no constant capital stock; if that is included then there is no determinate relationship between the size of the constant capital stock and the values in the first two departments. To illustrate this let us consider another numerical example :

Dept. I : k1 = 3000 cl = 999 v l = 500 sl = 500

Dept. 2: k , = 1270 c , = 319 v z = 319 sz = 319

Dept. 3: k , = 650 C , = 52 v , = 51 S , = 51

The values in the first two departments are exactly the same as in the previous numerical example. The only differences are found in the third department; K, is over six times larger, and c, is about half its former size, but v , and S, are the same. Clearly the organic composition of capital in the third department is much larger than before. In Appendix I it is verified that this second example will also allow a growth rate of exactly 10 per cent cent. The point of the Bortkiewicz corollary is that these differences in the third department make no difference to the rate of pro$t, or to the ratio between X , and X,. The only thing that needs to be changed is X, . In the example

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368 Geoff Hodgson

X , : X , : X , = I : 0.872 : 1.243

The reader may wish to verify that these price coefficient ratios, with the same rate of profit as before, satisfy the price and profit accounts in the latter example. This example is not just a fluke. There are an infinite number of possible values of k, and c, that yield the same rate of profit and growth rate.

A second situation where the conditions in the third department have no determinate relation to the remainder of the economy is when the third department itself consists of at least two industries. In that case there are again an infinite number of possible combinations of size in the third department, even if the economy is in simple reproduction, or constant capital stock is zero. We must conclude that the Bortkiewicz corollary is correct.4

The logico-historical objection

One objection to the Bortkiewicz solution centres on a consideration of an approach to analysis often attributed to Marx. I t is argued that Marx often develops a logical argument in the same form and sequence that real life processes develop and unfold. For instance, in Capital, he discusses pre-capitalist commodity production before he develops the concept of capital. In this case it seems to be both a necessary and an historical order of exposition. In Volume One Marx did not deal with the formation of a general rate of profit, and this allows him to assume that prices are proportional to values. This has led some economists to assert that in the early stages of capitalist development a general rate of profit was not formed, and prices were more or less proportional to values. Capital existed, but the exchange ratios and relative prices of simple commodity production prevailed. Marx's presentation of the transformation problem is meant to illustrate the real process of formation of a general rate of profit, at a later stage of capitalist development.

There is no historical basis for this argument. Feudal relations of production did not allow perfect commodity competition to prevail. The vast bulk of produced goods were not offered for sale at all; they were consumed directly. This does not mean that accounting in terms of labour time was unimportant in production. But in exchange, on the limited feudal market, prices did not exactly reflect amounts of embodied labour. The fact that rent, in many forms, was so significant adds weight to this assertion. The elements of simple commodity production that existed in the pre-capitalist period were subject to the distorting influences of land rent and vestiges of the feudal mode of production. I t is highly unlikely that perfect competition in the commodity market has ever existed within simple commodity pro- duction at least before the rise of capitalism. Consequently, there is

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Marxian epistemology and the transformation problem 369

very little evidence that prices were proportional to values in the pre- capitalist period.

When capitalist production began to emerge there was already a rate of profit in price terms in existence: it was the merchant's rate of return from investment. Sufficient competition existed in the mercantile era to create a tendency for the general rate of profit to form. As a result the early industrial and finance capitalists had to compete against mercantile capital and reap a similar, or slightly greater, rate of profit. This created a strong tendency for prices to diverge from values in industries with varied methods of production, and different organic compositions of capital.

It is clear that Marx's method was historical in character: he studied definite historical modes of production. But that does not mean that he generally develops categories in the order that they appeared on the historical stage. There are important didactic and methodological reasons why Marx did not deal with the formation of the general rate of profit in the first two volumes of Capital. These volumes deal with the production and circulation of value and surplus value under capitalism. The question of the formation of prices and the general rate of profit is conveniently left to the third volume when the system is discussed as a whole. Capital is historical, but it is not history.

Althusser has noted the theoretical dangers, especially that of empiricism, in the confusion of the object of knowledge with the real object, and the related confusion of logical time with real historical time (Althusser, 1970, pp. 119-44). From a different point of view Colletti comes to a similar conclusion. He attacks Mandel and others for 'mistaking the logical process for the process of reality' (Colletti, 1973, pp. 131-2). Both Colletti and Althusser agree that this type of mistaken interpretation of Marxism is essentially Hegelian: science rests exclusively within the domain of consciousness. In our view the logico- historical objection to Bortkiewicz's solution rests upon the same misinterpretation of Marxism.

Process and equilibrium

Another version of the logico-historical objection to Bortkiewicz's solution is that it does not illustrate the actual short term process by which prices and profits are formed. Marx's solution, in contrast, is regarded as the actual process by which these amounts are formed. We start in production with values, and Marx's solution shows the actual process which ends up with prices of production: which relate to exchange. Objection is raised to the prices in the Bortkiewicz solution because they are not derived ex post; they appear at the start of the 'process' as well as at the end. This view is mistaken for a number of additional reasons.

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At first let us suppose that Marx's solution really did represent the actual process by which prices and profits were formed. At the end of one period surplus values would be 'redistributed' according to Marx's conception, and prices of production would be formed. Now if these prices of production had any economic meaning at all, then, either they would enter as modified values into the next period, or they would have some direct effect on prices. In the former case the adherents of Marx's solution must admit that these modified values would appear in the expression for the rate of profit. Consequently, the elements in the rate of profit have been transformed in one sense, but not into prices. It so happens that these modified values do not yield an equalised profit rate in the next period. But if the same process is carried out several times over, then these 'modified values' and the rates of profit will gravitate towards a stable solution. This solution is precisely the same as in the Bortkiewicx solution. This has also been pointed out by Morishima (1973, p. 77).

If the adherents of Marx's solution accept the second interpretation : that prices of production have some direct effect on prices, then it seems reasonable to argue that these prices of production should again transform the input values in the next period. In which case a successive repetition of this process will again iterate towards the same results as in Bortkiewicz's solution. If the prices of production are not used to transform the input values in the next period then the process is no longer regarded as iterative or successive; it starts anew in every production period. In this case our previous objections hold; an equalised rate of profit in price terms is not formed, and this approach takes no account of Marx's recognition that the input values must be transformed.

It should be obvious to the reader that we have no objective criteria to use when choosing between these various interpretations, other than the word of Marx himself. This seems to indicate that Marx's solution is on shaky theoretical ground. It is only the assertion of Marx which can be used to back up the notion that Marx's solution represents a real process of price formation in the capitalist economy. In fact we can invent many other faulty 'solutions'-they are equally arbitrary.

It is, of course, necessary for political economists to examine the dynamic formation of prices. But the equilibrium solution has to be derived first. Marx's solution fails to provide a situation of economic equilibrium, and we have no reason to suppose that it represents the real dynamic process in the economy. In fact there are many indications in Capital that Marx intended to construct an equilibrium solution. For instance he writes: 'capital withdraws from a sphere with a low rate of profit and invades others, which yield a higher profit. Through this incessant outflow and influx, or, briefly, through its distribution among the various spheres, which depends on how the the rate of profit falls here and rises there, it creates such a ration of supply to demand that

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the average profit in the various spheres of production becomes the same, and values are, therefore, converted into prices of production' (Marx, 1962, p. 192, our emphasis). Further vindication of our view that Marx intended to construct an equilibrium solution is found in the following discussion on prices of production.

Price and price of production

It has been argued that the Bortkiewicz solution is at fault because it deals with daily market prices. Mandel, for instance, has implied that the Bortkiewicz solution has something to do with 'price fluctuations on the market' (Mandel, 1973, p. 63). This is simply not so, and it exhibits some confusion. Everyday fluctuations in price result from variations of supply and demand, and they are not the concern of any equilibrium solution to the transformation problem. Prices in the Bortkiewicz solution are not everyday market prices ; they are theoretical equilibrium prices. These prices are not observable on the market unless supply and demand are in equilibrium. Prices in the Bortkiewicz solution are as much a theoretical concept as they are in Marx's solution.

Furthermore, there is overwhelming evidence in Capital that Marx intended his prices of production to be market equilibrium prices: not purely theoretical prices which never appear in view. He wrote: 'The price of production is regulated in each sphere, and likewise regulated by special circumstances. And this price of production is, in its turn, the centre around which the daily market prices jluctuate and tend to equalise one another within definite periods' (Marx, 1962, p. 176, our emphasis). Later in the same work he writes: 'If supply and demand coincide, the market price of commodities corresponds to their price of production, . . . since the fluctuations of supply and demand explain nothing but deviations of market price from price of production' (Marx, 1962, p. 349). In an important letter to Engels, written in 1868, Marx gives a concise summary of his solution to the transformation problem. It is significant that even in this short letter he chooses to explain prices of production as follows : 'The price thus equalised, which divides up the social surplus value equally among the individual capitals in proportion to their sizes, is the price of production of com- modities, the centre around which the oscillation of the market prices move' (Marx and Engels, S.C., p. 249).

However, it is important to emphasise that neither Marx nor Bortkiewicz dejne prices of production from the empirical phenomenon. Unlike the vulgar economists, they both attempt to explain surface appearances, such as prices, by probing beneath; and showing the determination of prices by embodied labour values. But the theoretically constructed concept of price of production is not numerically different B

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to the prices of other economists: 'The price of production includes the average profit. We call it price of production. I t is really what Adam Smith calls natural price, Ricardo calls price of production, or cost of production, and the physiocrats call prix nhcessaire . . .' (Marx, 1962, P. 194)-

In conclusion, therefore, Marx's prices of production were intended to be theoretical equilibrium prices. But we have shown that Marx's solution fails to produce equilibrium ; at most it is an iterative approach. Marx aimed to explain the empirically given equilibrium prices, but he failed to do so. The works of Bortkiewicz and Sraffa are logically consistent attempts to show the derivation of prices from underlying relations in the economy. They succeed in providing an equilibrium solution when Marx failed. But their work is not to be confused with the approach of the vulgar economists who try to 'explain' empirical prices from supply and demand curves, which, in turn, are derived from empirical prices and quantities. That approach is clearly tauto- logical, circular, and empiricist.

The rate of profit

In a similar way we can show that Marx's intentional conception of the rate of profit differs from the implicit conception in his faulty solution to the transformation problem. We have shown that Marx's formulation of the rate of profit, in value terms, does not correspond to the equalised equilibrium rate of profit in price terms, i.e. to the rate of profit that the capitalists themselves 'perceive' in an equilibrium situation. Yet Marx could write: 'Surplus value and rate of surplus value are, relatively, the invisible and unknown essence that wants investigating, while rate of profit and therefore the appearance of surplus value in the form of profit are revealed on the surface of the phenomenon' (Marx, 1962, p. 43, our emphasis). Again in the same work he writes: 'The average profit figures practically, in the mind and calculation of the capitalist himself . . .' (Marx, 1962, p. 849). Clearly Marx's conception of the rate of profit was the real operative rate of profit in the capitalist economy. But no capitalist calculates the rate of profit in value terms, according to Marx's formula. Hence the inconsistency between Marx's solution to the transformation problem and his own epistemological conception of prices of production and the rate of profit.

The mystification of Marx's political economy

It follows, therefore, that those Marxists who cling to Marx's solution have to mystify and distort Marx's epistemological conception of prices of production and the rate of profit, in the face of the correct criticisms

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of those who accept a Bortkiewicz-type solution. This epistemological distortion has done immense harm to Marxism. We argue that it has resulted in the virtual supremacy of a Hegelian, rationalistic, type of 'Marxism' which has no contact with empirical data and real develop- ments in the modern capitalist economy.

The writings of Mandel, perhaps the leading and most influential populariser of Marx's political economy apart from Sweezy, often display this distortion. In an important pamphlet he asserts that Marxists cannot use bourgeois statistics for the rate of profit (Mandel, 1969, pp. 7-8). In another article he states: 'In Marx's theory "prices of production" are not "prices" in the current sense of the word at all.. .' (Mandel, 1973, P. 63).

In a work of empirical research (a type of work that is rare in the Marxian movement and is commendable for that reason) Gillman produces some figures which show only a slight and unimpressive fall in the real rate of profit in the United States since the 1920's (Gillman, 1957). This does not lead him to question Marx's faulty theory of the falling rate of profit, as Sweezy, and others, including myself (Hodgson, 1974), have done. Instead he arbitrarily re-defines the rate of profit, in such a way that it has no phenomenal form, in order to escape from the problem.

Both Gillman and Mandel cannot decide if the 'Marxian' 'rate of profit' should be calculated including or excluding constant capital stock. (See Gillman (1957); Mandel (1968), p. 159n.; Mandel (1969), p. 7.) But both writers are aware that the real operative rate of profit in a capitalist economy is calculated on a stock basis. In fact Marx repeatedly asserted that constant capital stock must be included in his definition of the rate of profit.

The mystification of Marxian economic categories is often accom- panied with the assertion that Marx was attempting to analyse real underlying forces. Hence the mystified 'rate of profit' is regarded as the 'real' driving force, which does not appear in view. This sort of position allows empirical data to be rejected, if, for instance, they do not show the falling tendency of the rate of profit. Quite clearly we are now discussing an epistemological and methodological evaluation of appearances and essences, and the relation between the theoretical and the empirical in Marxian political economy. We must deal with these questions in some detail.

Epistemology and method

The assertion that theoretical prices of production should be observable, more or less, in an equilibrium situation, and the assertion that the operative rate of profit is the empirically given rate of profit in price terms, have both led to the accusation that the Bortkiewicz-type

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transformation is empiricist in character. In contrast, it is argued, Marx insisted that a minimum necessary condition of a scientific analysis was to probe beneath outward appearances and find the essential laws of motion. This latter point, of course, is true. As Marx put it: 'all science would be superfluous if the outward appearance and the essence of things directly coincided' (Marx, 1962, p. 797).

But this is not a sufficient characterisation of scientific method in political economy. The need to shatter the obviousness of immediate experiences is a rule that must be common to all forms of scientific enquiry, regardless of the subject matter under investigation. This leads us to suggest that the Marxian method in political economy must be enriched with additional methodological injunctions of crucial and particular significance.

Several writers have pointed out that the selection of the concept of the commodity as the starting point of Capital is of vital methodological importance. Marx takes the 'form of value', the 'commodity form' as the starting point because it is the most abstract and highly generalised form taken by the social product in the specific object of investigation- the capitalist mode of production. There is nothing in a pure capitalist economy that does not present itself in the form of a commodity.

From this point Capital proceeds in a deductive manner. From the commodity in general we proceed to money as a particular commodity, then labour power, and capital itself. All the links in this logical chain appear to be suspended from the initial concept of the commodity in general. As Marx himself remarks: 'it may appear that we had before us a merely a priori construction'. In other words Marx's analysis of capitalism can appear to be purely a product of thought, contained within thought itself, without congruence with empirical reality. In actual fact the logical starting point of Capital is grasped in relation to the particular historical object from which it was abstracted. Hence the theoretical results in the work are not derived in a purely a priori manner; they are not completely contained within thought. In a sense, therefore, the concrete reality of capitalism, i.e. generalised commodity production, is the starting point of Capital.

In a different sense the end point of capital is the concrete; we have 'capitalist production as a whole'. In our thought, however, the argument seems to remain within the realm of the abstract conceptual system; simply because no theoretical system can completely embrace all the heterogeneous elements of reality. Marx makes this point in the following manner :

The concrete is concrete because it is the concentration of many determinations, hence unity of the diverse. I t appears in the process of thinking, therefore, as a process of concentration, as a result, not as a point of departure, even though it is the point of departure in reality and hence also the point of departure for

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observation and conception. . . . the abstract determinations lead towards a reproduction of the concrete by way of thought. (Marx, 1973, P. 10')

This passage is rich in theoretical insights which pass beyond the limitations of this essay. Colletti (1973, pp. 123-38) has provided an important and plausible interpretation of this and other passages. We simply need to make the point here that the empirically given concrete has a vital and central place in Marx's method of analysis. In contrast, Hegel's method operates exclusively within thought:

Hegel fell into the illusion of conceiving the real as the product of thought concentrating itself, probing its own depths, and unfolding itself out of itself, by itself, whereas the method of rising from the abstract to the concrete is only the way in which thought appropriates the concrete, reproduces it as concrete in the mind. But this is by no means the process by which the concrete itself comes into being. (Marx, 1973, p. 101)

If we accord the empirically given concrete a central position, how then does our method differ from that of empiricism? The character of modern empiricist vulgar economy provides a useful reference point in our attempt to answer this question.

The empiricism of modern vulgar Economy

Today, even some macroeconomic textbooks start with the theory of 'consumer behaviour'. The current fashion is to extend the subjectivist value theory into this sphere. Individual consumption levels are seen as the result of persons each maximising their own satisfaction or 'utility'. Hence subjectivist, or neoclassical, vulgar economy sees utility maximisation as the 'essence' that lies behind empirical con- sumer behaviour. Marxists have correctly criticised the atomistic conception of the individual that is implicit in this analysis. In addition it is argued that it is incorrect to pose consumer demand as the starting point of analysis. Demand does not originate primarily from the subjective wishes of the individual: it is socially determined in produc- tion.

Theprofessedabilityof atheoryto make correct predictions is regarded as an adequate verification of the analysis, by neoclassical economists. But the concept of utility is not established in a scientific manner; it is an arbitrary and ahistorical construct that bears no particular relation to any given historically determined system of production. I t is purely an idea. Alternatively a whole multitude of theories could be con- structed and invoked to 'explain' consumer behaviour, just as the early physicists developed many theories, which were later rejected, to explain such phenomena as fire, heat and light. But none of these

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theories were disproved or rejected by recourse to the empirical data alone. A concept cannot be either validated or rejected by a mere appeal to a given body of facts.

The empiricist method of vulgar economy is clearly illustrated by the manner in which modern econometric techniques are employed. Vulgar econometrics attempts to explain economic data by constructing mathematical functions that can reproduce the same data by means of algebraic processes. The accepted criterion of validity is the degree of correspondence or 'fit' between the observed data and that produced by the mathematical function. What is wrong with this approach is not the use of mathematical or econometric techniques in themselves. The error is epistemological: the degree of correspondence between the ideal and the real sets of data is regarded as the sole criterion of validity. An arbitrary model is constructed solely within thought, so this model collapses uncritically onto the empirical data in order to appeal for objective validity.

But it is wrong to suppose that modern vulgar economy does not attempt to find a kind of essential reality behind outward appearances. Empiricism is not just the assertion of facts. Vulgar economy also attempts to discover laws located in the 'essence' of reality. A crucial difference with scientific Marxism lies in the method of validation of the essence. Vulgar economy uncovers a false, mystical, unscientific essence that really explains nothing. For this reason vulgar economy actually remains trapped within outward appearances; its attempted excursions toward the real essence fail to cross the threshold of scientific validation. They tour in tautological circles on the surface of things. Vulgar economy does not synthesise and reproduce the concrete as an understandable whole. It is not anchored by a conceptual structure that derives from a materially determined real object-capitalist society. Hence the 'essence' it produces is purely an idealistic abstraction.

The empiricist method of validating this 'essence' is based on the notion of an immediate hard crust of facts in which all truth is embodied. This notion has been exploded by criticism from several angles, e.g. historiography, psychology, and even physics. Before facts are recog- nised, selected, arranged and imbued with meaning the observer must utilise a conscious or unconscious system of concepts. There is no vision of the world that is free from an implicit conceptual structure. The belief in a given body of facts from which truth can be distilled, independently of the concepts and theories used to provide a meaning is one of the most preposterous fallacies of empiricism.

An idealist reaction against empiricism

It has been suggested above that empiricism is a form of idealism. But the rejection of such a philosophy based upon immediate appearances

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has led to an equally idealistic reaction against empiricism. In recent years this reaction has taken sophisticated forms, such as in the philosophy of Marcuse. In Reason and Revolution Marcuse gives a useful account of the Hegelian dialectic. But to be found in this book is the type of theoretical attitude that characterises all of his works. I t consists of the statement that 'the facts' possess no authority. For example, he writes: '. . . the given facts that appear to common sense as the positive index of truth are in reality the negation of truth, so that truth can only be established by their destruction' (Marcuse, 1963, P. 27).

This negativist attitude to empirical research frequently appears in the Marxian movement. Consider the example of a well known British revolutionary grouping that still refuses to accept that capitalism has passed through an unprecedented twenty year boom. If an objection to this blindness is raised on the basis of the available data then it is dismissed as 'empiricism'. This may be an extreme example but the attitude is still rampant elsewhere. There has been a complete failure to produce suitable data to support the theory of the falling rate of profit in a convincing manner. I n fact most of the available data seems to contradict the theory (Hodgson, 1974, pp. 70-5). The 'anti-empiricists' then exclaim that Marxists must be 'critical' of the data; which pre- sumably means rejecting the data which does not support previously accepted conclusions. Another widespread tendency is the frequent and unquestioning appeal to the authority of quotations from great Marxist thinkers.

For a number of political and historical reasons Marxism has devel- oped at a slow pace in the last thirty years. The substitution of appeals to authority for analysis, and a negativist attitude to the facts of recent experience, have reinforced this stagnation. Complex postwar develop- ments have largely caught Marxists unawares. The success of every strategy, from the Communist Parties' parliamentary road to socialism, to the Trotskyists' 'Transitional Programme' has been absolutely minimal. Isolation and lack of success has created a type of quasi- religious dogmatism for Marxian theory, and a refusal to attempt to come to grips with the changed situation. I n place of an effective revolt against capitalist social relations and institutions has been a refuge in an idealist rebellion against the oppressive power of 'the facts'.

If Marxists shun empirical data, then they will also define their categories in such a way that they have no possible point of contact with empirically given concrete reality. Hence the 'rate of profit' becomes a mystical category that has no relation with the empirically given rate of profit, price of production has nothing to do with actual prices, the organic composition of capital is regarded as intangible and unobservable, and so on. Theory becomes purely rationalistic: trapped inside the mind. From Marxism we are led back to Hegelian rational- ism. Whereas in the quotation from the Grundrisse cited above, Hegel's

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method is rejected precisely on the grounds that it conceives the real 'as the product of thought concentrating itself, probing its own depths, and unfolding itself out of itself'.

Features of a Marxian epistemology

In a masterly essay on the subject of fetishism in Capital, Geras (1971) argues convincingly that the the immediate, common sense, surface appearances in capitalist society are 'absurd', and fetishised by capi- talism itself, but 'This is the absurdity not of an illusion, but of reality itself, and to this extent it is an absurdity which is true.' Colletti has made a similar point elsewhere: 'In fact, reality itself is upside down. It is therefore not just a question of criticising the way in which economists and philosophers have depicited reality. I t is necessary to overturn reality itself . . .' (Colletti, 1972, p. 233). In other words, paraphrasing Marx: the point is not to deny appearances but to change them.

But, it must be emphasised, Marxism is not an empiricism. It does not accept the empiricist notion that the immediate facts contain all truth. In fact it completely rejects the notion of the 'the facts' that is shared by both empiricism and its negativist reaction. The latter viewpoints do not understand that any perception of the world is forced into the mould provided by the conscious or unconscious conceptual structure of the observer. The empiricist finds truth in the immediate facts, the Hegelian-style negativist finds truth in their complete negation. In contrast, the Marxist asserts that the journey from the abstract to the concrete continually reconstructs the significance and meaning of the 'given' facts and appearances, as the result of a develop- ing theoretical structure.

The construction of theory, however, is not an arbitrary matter. We cannot simply select the facts according to our own preconceptions. The system of theoretical concepts must, somehow, be validated as scientific. Joan Robinson makes a similar point: 'It is easy enough to make models on stated assumptions. The difficulty is to make assump- tions that are relevant to reality' (Robinson, 1971, p. 141). In contrast, one of the main features of empiricist neoclassical economics is the arbitrary nature of the theoretical concepts employed, which are utilised without scientific validation.

But the danger of theoretical arbitraryness exists for Marxism as well. The adherents of Marx's solution to the transformation problem have found themselves supporting a theoretical definition of prices of production and the rate of profit that has no contact with the empirical concrete, and no external means of scientific verification. The sort of external verification that must be employed need not exclusively, or even primarily, consist of checking with empirical data. In fact the

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Bortkiewicz solution is scientifically validated without any appeal to simple facts and figures on prices and profits. But some external valida- tion must exist, otherwise the accusation of arbitraryness must stick.

We have already hinted in a former passage what the basis of Marx's method of conceptual validation comprises. Marx starts not from 'society in general' or 'human nature' or any other arbitrary abstraction. 'Capital is not the study of society as such, . . . but a study of this particular society. Which means that the analysis concerns not an idea (an ideal object) but a materially determined or real object' (Colletti, 1972, P. 3). If, instead, we start from an arbitrary idea this prevents us from undertaking a study of the real objective facts; we cannot engage with a real object but only with an idealised objectivity. The aim of science is to re-establish these 'facts', to understand them as real processes, uncluttered by ideal, mystical and metaphysical garbage.

We shall expand on the latter point by examining the concept of abstract labour in Marxian political economy.

The example of abstract labour

As noted above, Marx starts from the concept of the commodity. He analyses its two-fold character: its use-value and its exchange-value. Later he goes on to discuss labour power as a particular type of commodity. Again he sees the two-fold character of this special commodity. Its use-value concerns the particular qualities of labour power, such as weaving, digging, cobbling, and so on. Its exchange- value concerns the general objective quality of labour power as a commodity: the fact that it is sold on the market with other labour powers for money-the socially accepted standard of price. Clearly we are not dealing here with unverifiable ideal abstractions. Marx is being both analytical and, in a sense, descriptive at the same time. When a worker describes himself as 'a welder earning Eqo a week' he is relating to the categories of use-value and exchange-value, respectively.

Now the fact (perhaps the use of the word 'fact' deserves emphasis) that labour power is sold on the market with other commodities for money means that, in reality, all labour powers are reduced to a common socially objective standard-the money unit. This does not mean that all wages are the same, but that the heterogeneous labour powers are all reduced to equivalent homogeneous units. Exchange in a money economy, by its nature, equates the different labour powers by means of the common measuring rod of the universal unit of money.

A number of important conclusions follow from this interpretation of Marx, which was originated by Colletti. One of these concerns the theory of alienation (Colletti, 1972, pp. 84-5). But the crucial conse- quence which concerns us here relates to method. The concept of abstract labour i.e. the unifying essence of all labour powers, is not

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derived as a mere mental generalisation or abstraction. The 'abstraction' of abstract labour takes place daily in the reality of exchange itself. I t is a real process that operates outside the heads of Marxists (Colletti, 1972, pp. 79-84). The scientific character of Capital consists, in this case, of the fact that Marx 'lays bare' this process and expresses it in a theoretical form.

Althusser has come close to this interpretation, but expressed it less forcefully than Colletti : 'Marx says that the reality of labour in general, of abstract labour, is produced as a phenomenal reality by capitalist production' (Althusser, 1970, p. 124).

The plausibility of Colletti's interpretation of the concept of abstract labour can be judged by the following quotation from Marx's Grundrisse:

. . . this abstraction of labour as such is not merely the mental product of a concrete totality of labours. Indifference towards specific labours corresponds to a form of society in which individuals can with ease transfer from one labour to another, and where the specific kind is a matter of chance for them, hence of indifference. Not only the category, labour, but labour in reality has here become the means of creating wealth in general, and has ceased to become organically linked with particular individuals in any specific form. Such a state of affairs is at its most developed in the most modern form of existence of bourgeois society-in the United States. Here, then, for the first time, the point of departure of modern economics, namely the abstraction of the category 'labour', 'labour as such', labour pure and simple, becomes true in practice. (Marx, 1973, pp. 104-5, our emphasis.)

Marx's method of abstraction, therefore, is in profound contrast to the empiricist concepts of neoclassical economics. Marginal utility, for example, has no immediately demonstrable social existence apart from the sphere of ideas. I t is just an idea from which 'correct pre- dictions' may be derived about consumer behaviour. I t is an ahistorical, asocial, intangible, unmeasurable, unreal, ideal abstraction.

Abstraction and the concept of value

A further defect of the view of abstract labour as a mere mental generalisation is that it opens the door to the transformation of other categories, such as value itself, into abstract generalities or ideas as well. Every Marxist worth his salt will come out with the correct point that value 'is not just a thing, but a social relation', and so on. But these assertions, albeit often correct ones, are not enough. Value must have some phenomenal external form. Critics of the labour theory of value usually fail to see any phenomenal form of value, and they use this as

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a reason to dismiss that theory. Bernstein, for example, writes: 'value is a mere thought-construct'. He finds a modern echo in Joan Robinson: 'value is just a word'.

Faced with this type of criticism Marxists have often taken one of the following two alternatives: either they have held on to a mystified conception of value, asserted that it is, in principle, unmeasurable, 'just a social relation', and so on, or they have asserted that value takes a direct and at least approximately measurable form in price. The latter alternative is coupled with the assertion that prices do in fact gravitate around values. In other words, value is at least numerically equal to average market price.

The latter assertion is inconsistent with even Marx's solution to the transformation problem. This shows that prices of production of individual commodities permanently deviate from their values. If this were not so the transformation 'problem' would not exist at all. Individual prices would approximately equal values and that would be that. The additional problem of price fluctuations on the market, which is not the concern of the transformation problem, would be the subject of supply and demand.

I am not altogether sure, to be honest, that Marx did not hold the view that values are the centre of gravity around which market prices fluctuate, even after the section on the transformation problem in the third volume of Capital. Certain ambiguous passages in his work give rise to this doubt (Marx, 1962, p. 170,175,279, etc.). His extensive and confused terminology (market price, market value, price of production, etc.), supports this doubt. In his presentation of the transformation problem he calls c + v the 'cost price', when, quite clearly, he means a value. But if he did hold the view that values are the centre of gravity around which market prices fluctuate, then this is an inconsistency in Marx's work. I t is not even consistent with the problem that is posed when the question is raised of the transformation of values into prices. Furthermore, if Marx did hold that view, then he would have more in common with Ricardo, who repeatedly confused values with prices, than he would had he consistently demarcated between value and price.

We have strayed from the outstanding question: what is the phe- nomenal form of value? The answer is not short and straightforward, but we shall attempt it all the same. Consider a capitalist economy that can produce a net product consisting of a physical bundle of hetero- geneous goods. We wish to find the socially necessary labour time embodied in one unit of one of these goods, let us call it good G. All we need to do is to compare the amount of socially necessary labour time employed in the economy with another economy, which is exactly the same, except that one extra unit of good G is produced, and conse- quently more labour time is required. The net amounts of every other good that is produced remains the same. The extra amount of socially necessary labour time employed is equal to the value5 of one unit of

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good G. It may be argued that the comparison is purely hypothetical, and hence not phenomenal. But a real capitalist economy has significant periods when the technology of production does not change a great deal, and in those periods the net output will alter, however slightly. In this situation the value of the extra bundle of physical goods in the net product (assuming for simplicity that no good appears in a lesser quantity in the net product) will be equal to the extra socially necessary labour time employed.

Hence, we may argue that the concept of value is not a purely theoretical mental generalisation, but also a category with a measurable phenomenal aspect or form. It is also, of course, a social relation, but that is not entirely separate from what we have discussed above.

Abstraction and the rate of profit

We have already argued that the rate of profit has a phenomenal form, and we have also shown that Marx recognised its phenomenal character, but failed to define it correctly. This point needs slightly more elabora- tion and clarification.

Capitalists shift their funds around from firm to firm in search of a higher rate of profit. In a competitive situation there will be a tendency for the different rates of profit to be equalised. The influence of finance capital, the stock market, and the rates of interest will all lubricate the process of equalisation of the profit rates. As we have argued, this process leads towards an equalisation of the rate of profit in price terms ; there is no process which leads towards an equalisation of the rate of profit in value terms. Price, not value, is the socially recognised universal basis of account.

But there are many barriers and frictions that prevent a complete and exact equalisation of the rate of profit, especially under monopoly capitalism and state monopoly capitalism. Also differences in the rate of profit exist between different countries, and these permeate national boundaries by means of trade. How do we analyse in all this chaos? Do we hold up our hands in horror and take refuge in the mystified 'rate of profit'? Of course not. We lay hold of what Marx calls the 'force of abstraction'.

At first we consider a purely capitalist economy in which the rate of profit in price terms is equalised. This is not an arbitrary assumption, neither is it wholly unreal. I t corresponds to a real operative tendency which is present under all forms of capitalist society. Even under modern state monopoly capitalism this tendency remains strong, although many obstacles lie in the way of a complete equalisation. The abstract model of a pure capitalist economy in which the rate of profit is equalised allows us to analyse the relation between values and prices of production, and the derivation of the latter from the former. Our

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Marxian epistemology and the transformation problem 383

results are both scientific and relevant to all capitalist economies. But later, in our progress from the abstract to the concrete, the analysis is embellished by a consideration of monopoly, merchant capital, foreign trade and so on. This does not invalidate the former analysis, it merely makes it more concrete and specific. It is also necessary to examine dynamic situations, with the interaction of the rate of profit with the rate of interest, for instance. But a correct equilibrium analysis is a prerequisite. - ~ b o v e all a scientific solution to the transformation problem is not based upon the equalisation of the rate of profit as a mere mental generalisation, but as a real process, with a phenomenal form, which is an important distinguishing feature of capitalism.6 In contrast, in post capitalist societies, such as the USSR and China, this tendency is absent by virtue of the almost total elimination of money capital and profit as the driving force of accumulation.

Total value and total price

Having established the phenomenal aspect of price of production, value, and the rate of profit we shall return to the Bortkiewicz solution and examine some reasons why some Marxists are afraid of it as an alternative. Often it is maintained that the latter solution, unlike that of Marx, cannot be correct as total value is not equal to total price. A great deal of importance is attached to this assertion; it is even regarded as a central proposition in the labour theory of value.

However, the total value = total price proposition has an ambiguous epistemological status. Is it just a corollary of the definition of price of production, or does it tell us something about real phenomena in the capitalist world? If prices of production are defined as the logical product of Marx's method of transforming values into prices, then the assertion that total value equals total price is a mere tautology. I t contains no basis upon which it can be checked or feasibly refuted, and it has no phenomenal manifestation. This is a complete mystification of Marx's concept of price of production. Marx did not define prices of production in an empiricist manner, but his intention was to scientifically construct the theoretical concept of price and thereby explain the empirical phenomena. Hence, as we have shown, he regarded prices of production as 'the centre around which daily market prices fluctuate'. He was mistaken, however, to believe that the latter concep- tion was consistent with the definition of prices of production in his solution to the transformation problem.

The simplest way of arguing against the total value = total price proposition is as follows. Consider the gross product in its physical form in an economy for a specific period. This same gross product can be measured firstly in terms of its total price, and secondly in terms of

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its value, i.e. embodied labour. There is no reason to suppose that these measures are equal. Similarly, the physical surplus product can be measured either in price or in value terms. Hence, in addition, total profit is not in general equal to total surplus value.

But the dispute has been made more complicated than that. How- ever, the argument in the previous paragraph is still important and entirely valid.

In 1948, the economist Winternitz adapted the Bortkiewicz trans- formation so that total value was set equal to total price. He tried to avoid a tautological interpretation of the total value = total price proposition. He wrote :

This is not a tautological or meaningless thesis. It says that the sum of all prices changes if and in so far as the number of hours necessary to produce the aggregate output or the value of the money commodity changes. As a matter of fact, the price level goes up and down in the trade cycle at variance with the sum of values and the equation holds true only in the average over a whole cycle. (Winternitz, 1948, p. 279)

Before we discuss this we must note that Winternitz has defined prices (or more correctly, prices of production) in a rather special manner. Prices here are divided by the nominal price of the amount of the money commodity that contains one unit of embodied labour. In other words prices are expressed in terms of the amount of the money commodity, measured in value units, for which they will exchange. This is a way of converting the price units themselves into value units. Hence Winternitz writes that prices (i.e. expressed in these value units) will change 'if the value of the money commodity changes'. He does not express this method of converting the units precisely or clearly, but it seems to be his implicit conception. It also seems to be the conception of Mandel when he writes that prices of production 'have nothing to do with money or monetary units' (Mandel, 1973, p. 63).

Although we are not convinced of the usefulness of this choice of numeraire, we shall go along with it and examine the total value = total price proposition. To make it clear that we have not slipped back into the everyday notion of prices in money terms, we shall call prices that are converted in the above manner 'money value converted prices', MVCP's for short.

Unfortunately for Winternitz, the total value = total MVCP prop- osition turns out to be clearly and unambiguously false. Let us assume that the economy is in equilibrium and, for once, total value = total MVCP. Consider what happens when the rate of surplus value then changes, and according to the Bortkiewicz-type transformation, a new general rate of profit is formed. New price coefficients are derived, and even if these are converted into MVCP coefficients, they will change in a disproportionate manner. and the sum of all values will no

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longer equal the sum of all MVCP's. In general changes in distribution or in the technical conditions of production will alter total value, total price, and total MVCP in a disproportionate manner.

Does this lead to the conception that value can be created other than in production? It does not. Even if we accept Marx's solution to the transformation problem then prices must permanently deviate from values, and, as a result, commodities of equal price on the market will not have equal value. Hence, even in an equilbrium situation, we can gain extra value in individual exchange transactions outside production. But in the economy as a whole, in both Marx's and Bortkiewicz's solution, all value is created in production, nowhere else. The exchange process can only redistribute it between individuals.

But total MVCP can change without any change in total value. If, for instance, the value of the money commodity changes, and another commodity changes value to compensate. This does not mean that value is created out of nothing as MVCP's are not actual values, they are just measured in value units. They are the hypothetical amounts of value in the money commodity that could be exchanged for a given commodity. They are purely exchange equivalents. If it is argued that the total non-money product must exchange for the equivalent value in money, otherwise value would be lost or created in exchange, then we are committing the sin of regarding society as a single firm on the microeconomic level, and forgetting that if exchange takes place then none of the commodities that participate in the exchange are magically destroyed. Hence the value of the money and the value of the other commodities remains intact. I t is only the small capitalist that can forget about his products once he has exchanged them for money.

A more crude version of the total value = total price proposition consists of the assertion that ordinary money prices, on the average, keep in step with values. However, the phenomenon of price inflation completely invalidates this idea. Quite clearly, in recent years, total price has raced ahead of total value. But is the thesis correct if prices are deflated by some index of price inflation? The answer is no, for similar reasons to before. A price index is calculated according to the actual price of a chosen bundle of goods. Changes in distribution and in the technical conditions of production will cause the proportions between prices to alter. Consequently the chosen bundle of commodities cannot always be an 'average' and representative standard.

Total profit and total surplus value

It is also argued that total surplus value must be equal to total profit. Again this proposition must be open to two interpretations. Is profit defined as redistributed surplus value? If so, the proposition is a tautology once more; it follows logically from the definition of profit.

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The proposition becomes meaningful, on the other hand, if profit is defined as the difference between revenue from sales, in price terms, and production costs, again in price terms (ignoring rent, for simplicity, and including interest in the profit itself, not in production costs, as is habitual in bourgeois economics). This is not a theory of the origin of profit, it is just the accepted meaning of the word.

It is in fact possible to adjust the Bortkiewicz price coefficients so that the equality holds. But, in general, we cannot have total value equal to total price, and total profit equal to total surplus value at the same time. Furthermore, any change in distribution or the technical conditions of production is likely to violate the equality.

To state that total surplus value and total profit are, in general, unequal is not to assert that either profit or surplus value can be either created or destroyed in circulation. Indeed competition can only redistribute surplus value that is created in production. But the precise character of this redistribution needs to be spelt out. In Marx's solution is the implicit conception that surplus value magically wanders from firm to firm in the process of formation of prices of production. This sloppy thinking will not do . Let us examine an economy in which the periods of production and exchange are all synchronised. Capitalists start with capital goods and money.' These have a certain value. The capitalists buy labour power, and the workers exchange the wages they are paid for some of the goods. The total amount of value remains the same. Then production commences, and in their breaks the workers gradually consume the wage goods. More goods are produced, over and above those used up in production and consumed by the workers. The capitalists end up with a different pile of goods, the original amount of money, plus some extra money that was produced in that period. Surplus value is produced, but it is not all in a money form. It is embodied in the surplus product, which includes the extra amount of money produced, the latter is held in the hands of the money-producing capitalists. The original amount of money is not in the surplus product as it is not part of the net social product.

We shall assume that the economy is in equilibrium, but not neces- sarily in simple reproduction. Hence the prices of each good are known and given. But the total price of the surplus product is not necessarily the same as the total value. The capitalists then exchange some or all of the goods, including, of course, money. I t is then that a redistribution of surplus value takes place: by the physical transfer of goods. No surplus value is lost in this redistribution. I t is also important to note that the capitalists cannot all simultaneously hold their profit in the form of money, but individually it is possible on certain occasions in the exchange process. The total profit is the price of the total surplus product, and this is not equal to the surplus value in that same surplus, even if the profit is measured in MVCP units. Implicit in the veryposing of the transformation problem are two separate accounting systems, a

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Mamian epistemology and the transformation problem 387

value system in terms of hours of socially necessary labour time, and a price system. If these are confused, value becomes the same thing as price; a trap which Marx criticised Ricardo for falling into.

Marx failed to give a completely rigorous separation of the value, price, and physical aspects of production. These are not mutually equivalent alternative aspects, they are dz$erent aspects of the same whole. Borkiewicz, and later writers such as Wolfstetter (1g73), gave a rigorous separation of these aspect^.^ The trite dismissal of either of these writers as 'neo-Ricardian' ignores the fact that they eradicate a faulty part of the Ricardian heritage to be found in Marx.

O n the labour theory of value

If the labour theory of value is not a mere tautology it must uncover relations that exist in concrete reality. I t must pass beyond the bounds of mere definition. Unfortunately the theory is often misunderstood. Its most ancient and enduring misinterpretation is that commodities exchange at prices which are proportional to their values. Often this is modified and it is asserted that the proportionality holds only in the long run average sense. But both these views are inconsistent with even Marx's solution to the transformation problem, where prices of pro- duction permanently deviate from values. This version of the labour theory of value has no basis other than a sort of radical prejudice.

Other Marxists accord the statements of Marx himself that total value equals total price, and total profit equals total surplus value, a great deal of importance. I t is felt, like Mandel, that the rejection of these propositions is a rejection of 'the very cornerstone of Marx's economic theory' (Mandel, 1973, p. 63).

The first point to be made in reply is that the Bortkiewicz-type solution, at the formal level, does not exclude a theory in which prices are determined by values. This is not the same thing as saying that they are proportional to values. In our presentation it was shown that the given values in the various departments can be used as sufficient information to determine relative prices and the rate of profit. No other quantity, except the actual values, has any effect on the solution. This can be regarded as a demonstration of the labour theory of value.

However, these transformations only demonstrate, they do not prove or construct the labour theory of value. This theory can only be formulated on the basis of an analysis of the production process itself and key concepts that pertain to the capitalist mode of production.

Colletti argues quite convincingly that the labour theory of value is in fact inseparable from the theory of commodity fetishism (Colletti, 1972, pp. 76-92). Those Marxists who overestimate the importance of the total value = total price proposition in the labour theory of value concentrate attention on the quantitative aspect, and tend to ignore the

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deeper and more profound essence of the theory. In this they continue a tradition which has been prominent since the Second International; a tradition which sees the theory primarily as a theory of relative prices, rather than a scientifically grounded expos6 of exploitation and aliena- tion in capitalist society.

The adoption of Bortkiewicz's formal solution to the transformation problem does not provide us with a theory of exploitation and aliena- tion. I t gives only a small part of such a theory. I t only explains the determination of values from prices in equilibrium. I t does not explain the production of value and surplus value. But that does not invalidate it as a formal solution.

In conclusion

Ever since the publication of Sraffa's Production of Commodities by Means of Commodities in 1960 bourgeois economic theory has suffered a number of traumatic shocks as the implications of Sraffa's work have been drawn out. Other social sciences too have experienced convulsions in recent years, and the signs are that there is about to be a scientific revolution in the social sciences, especially economics, in the next few years. If Marxism is to take advantage of this crisis it must emerge from over thirty years of complete stagnation.

In the past, disputes have been settled by mere appeals to the authority of classic Marxist texts. Parallel to this has developed a basically idealist reaction to empiricism which allows no empirical data or phenomena to bear upon the analysis. As a result there is a stulti- fying tendency to quote rather than to prove, to repeat rather than to reason. An analysis is rejected simply because it produces uncomfortable or questioning conclusions. But Marx's Capital is not the end point in the development of Marxian political economy. Marx founded a science, he did not complete its investigations. Some of Marx's formula- tions require revision, clarification, or even rejection. Marxism is not a dogma but a living science.

The confusion of value and price in many works has severely hindered the development of Marxian theory. As a result, many developments in the capitalist system have not been understood. Some Marxists have taken refuge in a rejection of the facts that indicate these developments. Such categories as price of production, and the rate of profit, have been mystified and scparated from any phenomenal form. The rejection of such a negativist epistemology is a necessary condition for the revival of Marxian science. On this basis it is possible to adopt a scientific solution to the transformation problem. Regarding a more concrete analysis of modern capitalism the transformation problem is of little direct assistance. I t is only the first hurdle.

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Marxian epistemology and the transformation problem 389

Appendix I : The reproduction schemes in the text

The first reproduction scheme in the text that was raised in connection with Bortkiewicz's solution was as follows:

Dept. I 3000 999 500 500 I999 Dept. 2 1270 319 319 319 957 Dept. 3 100 102 51 51 204

Totals 4370 1420 870 870

If the growth rate is 10 per cent we get the following scheme for the next period :

Dept. I 3300 1098.9 550 550 Dept. 2 I397 350'9 350'9 350'9 Dept. 3 I 10 112.2 56-1 56-1

Totals 4807 1562.0 957.0 957.0

Note first that all the entries are augmented by 10 per cent. The output of capital goods in the first period (1999) is equal to total constant capital flow in the next period (1562) plus the increase in the constant capital stock (437). The output of wage goods in the first period (957) is equal to the total variable capital in the second period (957). At the end of the first period an amount of surplus value is set aside for accumulation (437 + 142 + 87) correspondicg to the increases in total k, c, and v. This, plus the luxury goods produced in the first period (204) is equal to the total surplus value in the first period (870). Hence the basic conditions of expanded reproduction are not violated.

The second example stated was as follows:

Dept. I 3000 999 500 500 I999 Dept. 2 I 270 319 319 3I9 957 Dept. 3 650 52 51 51 I54

Totals 4920 1370 870 870

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390 Geoff Hodgson

In the next period all the values have grown by 10 per cent:

k C v S

Dept. I 3300 1098.9 550 550 Dept. 2 '397 350'9 350'9 350'9 Dept. 3 7'5 57.2 56.1 56.1

Totals 5412 1507.0 957.0 957'0

Note that only the values in the third department are different from those in the previous example. In particular the organic composition of capital in the third department is considerably larger. The output of capital goods in the first period (1999) is equal to total constant capital flow in the next period (1507) plus the increase in the constant capital stock (492). The output of wage goods in the first period (957) is equal to the total variable capital in the second period (957). The amount of surplus value set aside for accumulation in the first period (492 + 137 + 87) plus the luxury goods produced in the first period (154) is equal to the total surplus value in the first period (870). Once again the basic conditions of expanded reproduction are satisfied.

It is relatively easy to produce an example with the same first two departments, the same general rate of profit, but a dzyerent growth rate.

Appendix 2: A Bortkiewicz-type transformation

We shall now generalise the illustrative example in the text, retaining the same number of goods and departments. The general rate of profit, in Department I , is given by the following equation:

This gives us three price equations for the three departments:

From the first two equations alone it is possible to eliminate X, and X,

and derive the following quadratic equation in p*:

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Marxian epistemology and the transformation problem

where

c = (v, + s,)s, + C,$, which has the solution:

There is another solution for p*, but that does not yield positive price coefficients and it need not concern us. The prices X, and X, can be derived from the first two price equations with the calculated value of p*; then X, may be derived from the third equation. Note that p*, X, and xz depend on the values in the first two departments only.

Notes

I. I am indebted to Norman Geras, Ian Steedman, and Tony Whelan for valuable discussions and comments on the text. But I am, of course, responsible for the final product. I have also found certain objections, raised both verbally and in writing by Ernest Mandel and David Yaffe, useful in forming and sharpening my own views. See Mandel (1973) and Yaffe (1973). An earlier version of this essay, written in January 1973, appeared in the Bulletin of the Conference of Socialist Economists in Autumn 1973. I a m grateful for permission to use it here. There are slight theoretical changes in this edition, written in July 1974, in the concluding sections. 2. The general formula, according to Marx and Engels, is

where t is the time period of production. See Marx (1962) Chapter 4. 3. Several problems arise when joint production industries are considered, i.e. when some processes produce more than one good in their gross output. 4. This point has been brought up in relation to the recent debate on the theory of the permanent arms economy. Kidron (1968) draws the implication that since the conditions of production in the luxury and arms goods sectors do not effect the general rate of profit then accumulation in those industries has prevented a fall in the general rate of profit. This is false because technical changes are not confined to Department 3. There is nothing to prevent 'normal' technical progress occurring in the wage and capital goods sectors, where the rate of profit is formed. On the permanent arms economy see Hodgson (1973a); Purdy (1973); Mandel (1969) and (1973); Yaffe (1973). My reply to Mandel (1973) is in Hodgson (197313). 5. There are problems with this, and every other, definition of value in joint production systems. 6. If this epistemological approach has a general validity in political economy then the importance and analytic usefulness of Sraffa's 'standard

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commodity' concept is diminished. The latter has no phenomenal form. But the exclusion of this concept from the Sraffa system, or its recognition as just a dispensable mental tool, does not invalidate the crucial and devastating results of his work (Sraffa, 1960). 7. The introduction of liquidity preference for money into an equilibrium model has important consequences. I have attempted to deal with this in my forthcoming paper 'Money, Values, and the Sraffa System'. I t does not undermine the validity of the general Bortkiewicz approach, however. In fact it creates more problems for orthodox Marxian political economy. 8. Although these two approaches are formally equivalent, Wolfstetter's presentation is to be preferred because he pays more attention to the social relations of production, and the production process itself. See also Rowthorn (1973).

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Surplus Capital', in International, Vol. 2, No. I, Spring 1973, pp. 63-4. Marcuse, H. (1963), Reason and Revolution, Humanities, New York. Marx, K. (1962), Capital, Vol. 3, Lawrence and Wishart, London. Marx, K. (1973), Grundrisse, Pelican, Harmondsworth. Marx, K., and Engels, F. (S.C.), Selected Correspondence, Lawrence and Wishart, London, no date. Morishima, M. (1973), Marx's Economics, Cambridge University Press, London. Purdey, D. (1973), 'The Theory of the Permanent Arms Economy-A Critique and an Alternative', in Bulletin of the Conference of Socialist Economists, Spri?g 1973, P P . 12-33. Robison, J. (1971), Economic Heresies, Macmillan, London. Rowthorn, B. (1973), 'Vulgar Economy', part 2, in Bulletin of the Conference of Socialist Economists, Spring I 973, pp. 1-11. SralTa, P. (1960), The Production of Commodities by Means of Commodities, Cambridge University Press, London. Steedman, I. (1973), 'The Transforma- tion Problem Again', in Bulletin of the Conference of Socialist Economists, Aut- 19739 PP. 37-42. Y a e , D. (1973), 'Value, Price and the Permanent Arms Economy: A Comment', in International, Vol. 2, No. 2, Summer 1973, pp. 22-4. Winternitz, J. (1948), 'Values and Prices: A Solution to the So-Called Transformation Problem', in The Economic Journal, June 1948, pp. 276-80. Wolfstetter, E. (1973), 'Surplus Labour, Synchronised Labour Costs and Marx's Labour Theory of Value', in The Economic Journal, September 1973, P P 787-809.

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