Transformation problem

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The transformation problem within the labor theory of value (abbreviated here: AWT) from Karl Marx referred to the question of whether a consistent formal process may be included, which allows to convert the measured in socially necessary labor values ​​into prices of production of goods.

The Problem

According to the law of value goods according to their value, that is, the socially necessary for its production work replaced ( Capital, Volume I ):

• W = Value of goods produced
• C = constant capital ( wear of the means of production used )
• V = variable capital (replacement of the value of this expended labor force)
• M = value added

In Capital, Volume III, however, shall be additional to believe that the agreement reached by the capitalist rate of profit s / (c v) tends to equalize the competition of capitals across all sectors at an average level down.

• K = cost-price
• P = Profit

The calculated under the terms of the redistribution of surplus value production, prices deviate from the so previously calculated amounts from systematically.

Marx assumed here:

• The sum of the values ​​is equal to the sum of the prices.
• The sum of the added values ​​is equal to the sum of the profits.
• The value rate of profit is equal to the price rate of profit.

Now, assuming several branches of production with different profit rates, so you have to also provide the interdependence of the production sectors with each invoice. The difficulty is then to effect a simultaneous transformation that the total added value while the total prices of production equal makes the total profit equal to the total values ​​, with the average rate of profit as invariant link between the two rating systems.

If values ​​are transformed into prices, the ratio of price to value must be the same as in the case in which a given commodity is considered as input, as in the case in which it is considered as output ( an exception to this assumption later the Temporal Single system interpretation of the AWT is discussed, the inputs and outputs explicitly differently rated). After the transformation, the rate of profit in each of the relevant capital as set out must equal ( an exception to this assumption, again represents the later discussed, stochastic -based approach of Farjoun / Machover ).

The proportions of the price value and the rate of profit are regarded as the main unknowns. The transformation problem can thus be traced mathematically it:

" Can the relationships between the various branches of production and the conditions that must be met as a result of the transformation, a determined system of equations are given? "

(The number of independent equations must equal the number of unknowns correspond! )

The Emergence

Karl Marx has the three volumes of Capital and Theories of Surplus Value in almost reverse order written as they were then released. After his death the remaining manuscripts of the capital of Friedrich Engels were issued, the Theories of Surplus Value ( often referred to as the "fourth volume of Capital "), then by Karl Kautsky. Already Publisher Engels had the problem of conversion of values ​​into prices of the public to submit comments ( Prefaces Vol II, Vol III and Epilogue ). It thus came over the decades into one, by Engels as " price puzzle literature " designated wave of proposed solutions.

The first highlight was the controversy between Eugen von Böhm- Bawerk and Rudolf Hilferding, the not yet dealt with the transformation problem in the strict and mathematically formalized sense. Ladislaus von Bortkiewicz began using mathematical methods to the problem of linear algebra. Finally, Paul A. Samuelson has taken the formal solution of the problem raised, claiming that there is no algorithm that would lead to prices of production of labor values ​​for:

"Consider two alternative, contradictory systems. Write this one down. For transformation, take an eraser and erase it from. Then write instead towards the other. Voilà! Thus, the transformation algorithm is finished. "

Samuelson's methodological approach has Paul Mattick (1974 ) rejected from a Marxist perspective in his essay Samuelson transformation of Marxism in bourgeois economic theory in sharp form. The discussion in the wake Samuelson shows that Samuelson's contribution the hoped- for Author " last word " on the subject was not, but the preliminary intermediate stage of a particular interpretative scheme in of an ongoing debate.

Although Marx and Engels acknowledged the solution of this problem especially in its formal representation form a high priority, the question arises why the AWT may be forced to the distribution of income (including the production of surplus value) and the relative price structure in the same model to explain. How Pierangelo Garegnani proven and it has not recently been found in the capital controversy by Paul Samuelson as an alternative favored equilibrium theory is not yet in a position to question the value of determination ( here: the capital) together with the marginal productivity theory to answer.

According to critics of Marx either a fundamental inconsistency has demonstrated in the economic model thinking or shown, however, that the invoice value against the accounting is totally unnecessary in production prices. The background is that you hereby mentioned also the exploitation and surplus value theory for discards. But this view remains to be controversial, because there are a number of consistent solutions of the transformation problem and, therefore, the allegation of a can only be maintained " redundancy theory of value ", if the problem is interpreted in a very specific and narrow way.

The Ladislaus Bortkiewicz solution

The classic and favored by Paul M. Sweezy solution to the problem while maintaining the AWT comes from Ladislaus of Bortkewitsch and was developed at the beginning of the 20th century. In a simultaneous equation system, all merchandise values ​​(even the non-transformed Marx shares of constant and variable capital, ie ) should be transferred to prices of production. Through this system of simultaneous mutual interdependence but had one of Marx's " Invarianzpostulate ":

A ) Sum of prices is the sum of the values ​​or

B) sum of surplus-value is the sum of the profits

Be abandoned. Bortkiewicz chose A), so as not to endanger the (supposedly more important ) theory of exploitation and to make the gold goods to the numeraire. In his system of equations three manufacturing sectors are provided the means of production (Department I), consumer goods ( Division II ) and produce luxury goods ( Division III ). The whole thing has then the following form:

Here, x, y and z is the rate coefficient, which may also be used as the transform coefficients for the conversion of values ​​seen in rates. The same for all three sectors profit rate is 1 r. In each case the left column, the value components of the constant and variable capital are each sector by multiplying by the conversion factor competent ( x or y) and then multiplied with the general rate of profit, so that added to the transformed variable and constant capital the average profit. On the right side of the equation is, for example, in Section 1, the constant capital of all three sectors ( c1 c2 c3), which indeed represents the output of Division I, added together and multiplied by x is the transform coefficients. By the equal sign is guaranteed that all prices expressed in constant capital components at all three sectors with the transformed total cost of the first sector ( of these components produces yes ) are identical. It is here that Say's theorem, consistency of technique and an equal transition time for all capitals. The system is purely static and connects inputs with outputs simultaneously. Time and causality are there in this model world is not therefore, preliminary and final products are in a ratio of quantitative identity, which is not affected by the production process.

As with sector 1 is also dealt with sector 2 and 3. The three equations are, as we can easily see four unknowns opposite: The conversion coefficients x, y and z and the rate of profit r. Bortkiewicz now closes the system by setting z = 1 Thus, the luxury goods department for 3 numéraire and the identity of unit value and price unit in the luxury goods sector taken as given. Thus, by this method, the value-added to the total profit in line, because the added value-added of all three sectors is multiplied by one and therefore not changed. However, this invariance is paid in sector 3 with the effect that value and price sum diverge in most cases. Why is this so?

This is because, as just the organic composition of capital in each sector are also in sector 3 above or below the social average, and consequently the price of luxury goods may also vary. This change is due to yes in that is transformed with the value - price transformation of surplus value into profit, that the basis of assessment of the profitability no longer so is the variable capital, but the constant plus the variable capital. Sweezy so, expressed under the condition that in Sector 3 Gold is produced as a luxury good:

" Since ex hypothesi the price and value of a unit of gold numerically both are equal to one, the fact that its price is higher than ' its value can be expressed only by the fact that the average price of all other goods is lower than its average value. In yet other words: When the organic composition of capital in the gold industry is relatively high, the transformation of value will increase the purchasing power of gold in price ".

The deviation of the value sum of the prize money is thus itself is directly the result of the normalization of the third sector, because sector 3 transforms ultimately, namely relative to the other sectors through its own purchasing power in the price system. Accumulates the total added value is not in this system, but being consumed, so it is a system with " simple reproduction ". Obvious disadvantage of Bortkiewiczschen solution is the quantitative difference between value and price sum that occurs except in the case of very special under the same organic composition of all three sectors or in a multi- value of zero in any other case.

The proposed solution Bortkiewicz ' was, in principle, already 12 years ago Bortkiewicz and thus even before the publication of the third volume of Marx's "Capital ", anticipates and published by the Social Democrat Wolfgang Mühlpfordt. Mühlpfordts study came almost a century into oblivion. Bortkiewicz algorithm was improved several times during the debate and extended by Francis Seton of a solution with three sectors to a solution with any number of sectors. With Seton's contribution from the year 1956, this phase of the discussion came to an end. From the Sraffa then a similar alternative method has been developed that the AWT completely gave up, instead the material entanglement structure made ​​of a " commodity production means goods " to the base and developed a pricing system, which independent of subjective benefit estimates determined the prices of commodities. Sraffa waived the AWT, even if it provides the mathematical basis for the final solution of the transformation problem from the perspective of equilibrium economics.

Whether the solution by Bortkiewicz solves the transformation problem is controversial. Friedrun Quaas for example, holds that "it is possible to derive prices of production from labor values ​​consistent" with the process of Bortkiewicz.

The contribution of Carl Christian von Weizsäcker

Carl Christian von Weizsäcker studied the problem (1962, 1971) under the assumption that the economy is growing at a rate according to the so-called golden rule of accumulation. He comes to the conclusion that can be represented as the prices of production work values ​​. However, the prices of production of a final product are not simply proportional to the sum of the values ​​of all work products that are needed for the manufacture of the final product. Rather earlier work values ​​are " interest " to the time of completion of the final product, the rate of profit, which in application of the " golden rule" is equal to the rate of economic growth, serves as the interest rate.

Marxist answers to the " Sraffa " shock

However, it is clear since Sraffa foundation of modern Neoricardianismus in 1960 that Bortkiewicz ' algorithm can be transformed into a system of equations in the last instance in which work values ​​occur only as a redundant by-products. You come for the computation of equilibrium prices in the formal sense no priority status.

This " Sraffa - shock" has provoked different responses from the Marxist side:

Swell