Introduction

The debate on the transformation of values into prices of production has generated an extensive literature, which space does not permit us to cover in its entirety. Instead, we present, in a condensed form, some analytical points that will be further developed elsewhere. We present a new approach which both 'solves' the problem and refutes the principal neo-Ricardian claims.

The first part recalls how the two essential propositions of the neo-Ricardian analysis are established: we show that what we call the 'steady state hypothesis' plays a central role and that without it, these two propositions cannot be established. In contrast, the logic of Marx's schemas is fully reconstituted. The second part advances a new reading of Marx, which shows that the error described by Bortkiewicz (1907) can easily be corrected without calling into question the validity of the chapter of Capital which deals with the transformation of values into production prices.

A critique of the neo-Ricardian model

Neo-Ricardians demonstrate 'the nonsensical character of the law of value'

The data of the problem. Neo-Ricardians begin directly with a description of the technical conditions of production, among which one may include the workers' consumption standards, which Sraffa (1960) does not do. As a starting point, we therefore have at our disposal a set of technical relations. These can be schematized with the help of a numerical example which avoids the use of mathematical formulae, without calling into question the generality of the reasoning:

240 [M.sub.1] + 10 [M.sub.2] + 200 labour [right arrow] 500 [M.sub.1]

50 [M.sub.1] + 20 [M.sub.2] + 100 labour [right arrow] 100 [M.sub.2]

90 [M.sub.1] +60 [M.sub.2] [right arrow] 300 labour

These relations read as follows. During the single period of production under consideration

* 500 units of commodity [M.sub.1] are produced by means of 240 units of commodity [M.sub.1], 10 units of commodity [M.sub.2] and 200 units of labour;

* 100 units of commodity [M.sub.2] are produced by means of 50 units of commodity [M.sub.1], 20 units of commodity [M.sub.2] and 100 units of labour;

* Finally, the 300 total units of labour used require the consumption of 90 units of [M.sub.1] and 60 units of[M.sub.2].

With these basic data, it is possible to build two systems: the first one being prices of production (neo-Ricardian theory) and the second being values (Marxist theory).

The system of prices of production. We can transform the relations of production ([right arrow]) into equalities, after assigning prices to commodities:

* [p.sub.1] and [p.sub.2] are the prices of commodities [M.sub.1] and [M.sub.2], respectively;

* w is the wage (the price of a unit of labour).

The supplementary rule which is necessary to write down these equations is the existence of a uniform rate of profit R. Under these conditions, one obtains the following system of equations:

(1) 500 [p.sub.1] = (1 + R) (240 [p.sub.1] + 10 [p.sub.2] + 200 w)

(2) 100 [p.sub.2] = (1 + R) (50 [p.sub.1] + 20 [p.sub.2] + 100 w)

(3) 300 w = 90 [p.sub.1] + 60 [p.sub.2]

This system can easily be solved and gives the following values for our example:

R = 25%, [p.sub.1] = 10m/7, [p.sub.2 = 20m/7 and w = m

where m is a parameter which can take any positive value; in other words, we get a system of relative prices.

A more detailed mathematical treatment of the problem shows that 1/(1+ R) is the dominant eigenvalue of the matrix of unit technical coefficients obtained when the wage is replaced by its equivalent in commodities. The vector ([p.sub.1], [p.sub.2]) of relative prices is the eigenvector associated to this eigenvalue. In the simple case examined here, where each commodity is produced by a single method of production, one can demonstrate that this solution is unique and is such that the rate of profit and all the prices cannot be negative. For this property to be established, a condition must be met, that can be interpreted in an economic way by saying that the economic system under study must at least ensure its self-reproduction.

That being said, the first important result of this calculation is that the knowledge of the conditions of production in the broad sense (that is to say, including the standards of consumption) is sufficient to determine the rate of profit and the relative prices.

The system of values. If we define the value of a commodity as the quantity of labour necessary (directly or indirectly) to produce it, then it is possible to build a system of values using the same data. The unknowns are [v.sub.1] and [v.sub.2], the values of the commodities [M.sub.1] and [M.sub.2]. This system, which formalizes the Marxist theory of value according to the neo-Ricardians, is the following:

(1) 500 [v.sub.1] = 240 [v.sub.1] + 10 [v.sub.2] + 200

(2) 100 [v.sub.2] = 50 [v.sub.1] + 20 [v.sub.2] + 100

(3) 300 [v.sub.f] = 90 [v.sub.1] + 60 [v.sub.2]

The first two equations suffice to calculate values by themselves-, in our example, they are [v.sub.1] = 170/203 and [v.sub.2] = 360/203. The third equation allows us, in a second step, to calculate the value of a unit of labour, which in our example is [v.sub.f] = 123/203. This calculation allows us to distinguish Variable capital' from 'surplus-value' and calculate the rate of surplus value as:

(unit value of output-unit value of labour)/unit value of labour = (1 - [v.sub.f])/[v.sub.f] = 80/203

The new value created during the period (variable capital' + surplus-value) is equal to 300, that is to say, the total expenditure of labour during this period. But it should be clear that this fact is already implicit in the way the system of values is written, and cannot therefore be interpreted as a result of this calculation.

Relationship between production prices and values. We can compare the two systems with the use of Table 1, showing the relevant aggregates and ratios.

This table shows that there is no way to pass from one column to another: this is a fundamental result because it helps us understand why it is fruitless to try and solve the problem by adding an additional rule. To assume, for instance, that the value of a particular commodity is by definition equal to its price, or choose as numeraire a commodity with a price equal to 1 by definition, is to use the degree of freedom that the parameter m allows. But such an attempt cannot in any way reduce the gap between the two rates of profit, since this discrepancy is independent of m. Postulating an equality between variables such as total profits and surplus value leads to the same impasse.

It is equally impossible to satisfy, at one and the same time, the previous equality--which here implies that m = 120/203--and another equally significant equality between the two methods for calculating the value of total production, since this latter relation implies that m= 121/203.

It is, however, possible to extract from the system under consideration a sub-system defined by a uniform proportion between total production and total consumption of each commodity. In our example, this standard system is obtained by combining the entire industry producing [M.sub.2] and 4/5 of that producing [M.sub.1]. In this case, the rate of profit calculated on the basis of the value system is exactly equal what we get from the price system, that is to say 25%. But it remains evident that the existence and properties of this standard system do not call into question the conclusions that the neo-Ricardians draw from a study of the model presented here.

Two fundamental neo-Ricardian claims. These two central claims can be summarized as follows:

(i) For knowledge of the conditions of production in the broad sense (including the norms of consumption) lets us calculate, in two different ways, a system of relative prices and the rate of profit, and a system of values, respectively

However, as Napoleoni (1972), cited by Benetti (1974), insists, 'Instead of the transformation of values into prices, we obtain a scheme which determines prices independently from values'.

The prices of production are not transformed values and, a fortiori, the theory of value cannot claim to account for the determination of the rate of profit.

(ii) There does not exist--except in special cases--any way to get from values to prices of production, that is to say, any relation between the relevant variables or rates. In particular, total profit, expressed in prices of production, cannot be connected to the mass of surplus value produced during the period. The Marxist theory of surplus value as source of profit is not only unnecessary but also wrong.

In view of these results, it is perfectly legitimate to conclude as do the collective authors of 'Value, Price and Realization' (Auteur collectif 1976-1977) that

Consequently, if by 'law of value' we understand a law according to which the prices of production of the commodities and social profit are directly or indirectly determined by the labour content of these commodities, then we are asserting a nonsense. These propositions can be summarized by means of the following diagram, where the double vertical line indicates the impossibility of a passage from one system to the other.

A critique of neo-Ricardian claims

The central neo-Ricardian hypothesis

However, the following hypothesis, which is nowhere stated, is needed in order to write down the equations of the system of prices of production. Recall the first of these:

(1) 500 [p.sub.1] = (1 + R) (240 [p.sub.1] + 10 [p.sub.2] + 200 w)

The way that the data (in terms of the relations of production) are translated into this equation is the central problem of the neo-Ricardian approach. The underlying assumption is apparently harmless and has never been discussed in a systematic manner.

To write this equation down, it is in fact necessary to give the same price [p.sub.1] to the 240 units of [M.sub.1] used up in production, and to the 500 units of this same good produced during the same...