Fundamental Marxian Theorem Research Articles

A Proof of Labor Theory of Value Based on Marginalist Principle

Because anti-Marxist's criticism against Fundamental Marxian Theorem (FMT) is based on an assertion that this proof can be understood as a “natural-resources exploitation,” if we assume, for example, “natural-resources theory of value,” we should prove not only exploitation but also labor theory of value itself. Therefore, this article aims to prove labor theory of value mathematically by focusing on the historically conditional proportionality between labor input and amounts of products which is assumed in labor theory of value. By this proof of the conditional proportionality, we show that marginalist principle does not disturb labor theory of value in capitalism at all. Furthermore, marginalist principle is important to show the labor process as a subjective optimization process which is not by the sun but only by human beings. In this way, we use anti-Marxist's marginal principle to object anti-Marxist criticism against labor theory of value.

A PROGRESS REPORT ON MARXIAN ECONOMIC THEORY: ON THE CONTROVERSIES IN EXPLOITATION THEORY SINCE OKISHIO (1963)

AbstractThis report explores the development of exploitation theory in mathematical Marxian economics by reviewing the main controversies surrounding the proper definition of exploitation since the contribution of Okishio. The report first examines the debates on the Fundamental Marxian Theorem and Class‐Exploitation Correspondence Principle, developed mainly in the 1970s and 1980s, followed by the property relation theory of exploitation by Roemer. Then, the more recent exploitation theory proposed by Vrousalis and Wright is introduced. Finally, the report introduces and comments on recent axiomatic studies of exploitation by focusing on the work of Veneziani and Yoshihara.

La producción como origen del plusvalor en la teoría marxista

El objetivo de la presente investigación es doble. Por una parte, consiste en dilucidar que la fuente misma de la ganancia, esto es, el plusvalor, dimana de la esfera de producción. Por otra, demostrar que la condición necesaria y suficiente para el sostenimiento del orden de sociedad capitalista reside en que entre el capital y el trabajo ha de mediar una relación de dominación expresada en la explotación de la fuerza de trabajo. Para este propósito, se confronta la teoría de Marx con el enfoque marginalista. Seguidamente, se descifra el secreto del plusvalor en la compraventa de fuerza trabajo, manifestando de esta suerte el carácter dual del sistema de cálculo marxiano. Finalmente, por medio del teorema marxiano fundamental se verifica la hipótesis de que la explotación de la fuerza de trabajo es condición necesaria y suficiente para que los capitalistas obtengan ganancias positivas.

A PROGRESS REPORT ON MARXIAN ECONOMIC THEORY: ON THE CONTROVERSIES IN EXPLOITATION THEORY SINCE OKISHIO ()

AbstractThis report explores the development of exploitation theory in mathematical Marxian economics by reviewing the main controversies surrounding the proper definition of exploitation since the contribution of Okishio. The report first examines the debates on the Fundamental Marxian Theorem and Class‐Exploitation Correspondence Principle, developed mainly in the 1970s and 1980s, followed by the property relation theory of exploitation by Roemer. Then, the more recent exploitation theory proposed by Vrousalis and Wright is introduced. Finally, the report introduces and comments on recent axiomatic studies of exploitation by focusing on the work of Veneziani and Yoshihara.

Reflections on the Concept of Exploitation

This paper describes the author’s three reflections on the concept of exploitation. The first one is concerned with the Fundamental Marxian Theorem. It is shown that exploitation as defined in a usual way exists irrespective of whether profits are positive or negative, so long as workers do not save and an extended productiveness condition is met. The second reflection deals with the concept of exploitation in models with heterogeneous labour. We may consider the rates of exploitation separately for individual type of labour, or the common rate of exploitation based upon abstract labour, fusing heterogeneity into one abstract category. Some features of these two concepts are explained. In the third one, I argue that the unemployed should be counted as exploited, and thus present some reasons why the unemployed are exploited, and a simple way to define the rate of exploitation for a capitalist system as a whole.

STRONG SUBJECTIVISM IN THE MARXIAN THEORY OF EXPLOITATION: A CRITIQUE

This paper critically analyses the strongly subjectivist approach to exploitation theory proposed by Matsuo on this journal, in general convex economies with heterogeneous agents. It is proved that the Fundamental Marxian Theorem is not preserved and that no meaningful subjectivist exploitation index can be constructed. A minimal objectivism is necessary in exploitation theory, whereby subjective preferences do not play a direct, definitional role. An objectivist approach related to the ‘New Interpretation’ is proposed which captures the core intuitions of exploitation theory, provides appropriate indices of individual and aggregate exploitation, and preserves the Fundamental Marxian Theorem in general economies.

Interpretations of Marxian Value Theory in Terms of the Fundamental Marxian Theorem

This paper focuses on the theoretical status of the fundamental Marxian theorem in various interpretations of Marxian value theory, particularly with regard to the logical consistency rather than the analytical implication. It will be shown that each interpretation proves the fundamental Marxian theorem in its own way, and therefore the proof of the theorem is not a decidability criterion for the correct interpretation of Marxian value theory.

MAURICE POTRON'S LINEAR ECONOMIC MODEL: A DE FACTO PROOF OF ‘FUNDAMENTAL MARXIAN THEOREM’

ABSTRACTMaurice Potron was a French mathematician whose largely unknown contributions to economic analysis should be acknowledged as pioneering achievements. The purpose of this paper is to (1) reconstruct Potron's core model in terms of modern input–output analysis, (2) show that Potron proved de facto Fundamental Marxian Theorem (FMT) 48 years earlier than Morishima, Seton and Okishio by adapting the Perron–Frobenius theorems to economic problems, and (3) claim that Potron proved de facto FMT by considering heterogeneous labours 65 years earlier and even more generally than Bowles and Gintis.

PROFIT, SURPLUS PRODUCT, EXPLOITATION AND LESS THAN MAXIMIZED UTILITY: A NEW EQUIVALENCE PROPOSITION ON THE FUNDAMENTAL MARXIAN THEOREM

Morishima's Generalized Fundamental Marxian Theorem (GFMT) is an extended form of Okishio's Fundamental Marxian Theorem, which showed the equivalence between positive profit and the exploitation of labor. GFMT is not developed as a system of equivalence proposition between five conditions, which I call ‘The Strong System of Exploitation Theory’. But by the definition of this system, there remains the possibility of positive profit without exploitation. In this paper, I demonstrated an alternative system of equivalence proposition, naming it ‘The Weak System of Exploitation Theory’, in which positive profits always mean exploitation. Here I introduced workers' utility function to define the exploitation concept. Then I could also show that the exploitation is equivalent with the situation where workers' utilities are under-maximized.

Reclaiming Marx's Capital: A Refutation of the Myth of Inconsistency

Chapter 1 Introduction: The Question of Internal Inconsistency Chapter 2 Marx's Value Theory and Contending Interpretations Chapter 3 A Brief History of the Controversy Chapter 4 Making Marx Make Sense: On Interpretive Method Chapter 5 Simultaneism, Physicalism, and the Law of Value Chapter 6 Was Marx a Simultaneist? Chapter 7 A Falling Rate of Profit Controversy Chapter 8 The Transformation Problem (1): Marx's Solution and Its Critics Chapter 9 The Transformation Problem (2): If It Ain't Broke, Don't Correct It Chapter 10 The Fundamental Marxian Theorem Chapter 11 An Empirical Defense of the Law of Value? Chapter 12 Summary and Conclusions

On the TSSI and the exploitation theory of profit

In a recent article in this journal, Kliman (2001) has argued that only a temporal single system interpretation (TSSI) of Marxian value theory preserves the fundamental Marxian theorem (FMT) and hence finds the origin of profit solely in exploitation. This paper first outlines the TSSI in order to emphasise the particular and controversial definition of value on which it depends. Kliman's logical demonstration of the FMT is then shown to fail on exactly the same grounds for which he indicts rival interpretations.

Simultaneous Valuation vs. the Exploitation Theory of Profit

This paper shows that interpretations of Marx's value theory which value inputs and outputs simultaneously imply that surplus-labor is not the sole source of profit—even in the absence of joint production. Contrary results, such as the Fundamental Marxian Theorem, rely crucially on restrictive and implausible conditions that are shown to be unnecessary for reproduction. In contrast, the temporal single-system interpretation conforms to the exploitation theory of profit under completely general conditions.

An elementary proof of the Bowles-Gintis-Morishima fundamental Marxian theorem with heterogeneous labour

This note gives an elementary proof of a Marxian fundamental theorem with heterogeneous labor originally proved by Samuel Bowles and Herbert Gintis. The fact that a quasi-irreducible matrix is a Sraffa-matrix combined with the vertical integration approach in the theory of value is the key to this new proof. (c) Academic Press Limited Copyright 1996 by Oxford University Press.

On the Theory of 'Value"

This paper presents a new concept of 'value" which is developed in the author's general equilibrium framework (1988a). A traditional concept of labor value and a relatively new concept of commodity value are uniformly shown from this "value" as its normalized forms. A so-called fundamental Marxian theorem is then generalized in the sense that it holds for any level of real wage rates determined in a joint-product market economy. These arguments, it is emphasized, are only meaningful at temporary and long run market equilibria. Finally, the paper briefly summarizes some criticisms of the labor theory of value presented by Morishima (1973, 1974), Steedman (1975, 1981) and Roemer (1981, 1982), and systematically criticizes them in light of the author's general equilibrium approach.

Exploitation and the Labour Theory of Value: a neo-Marxian reply

It is argued that the purpose of the Labour Theory of Value is to provide a theory of capitalist exploitation, not a theory of relative prices. As such, the Morishima-type approach to the Steedman critique offers a convincing restatement of the Fundamental Marxian Theorem associating profit with the performance of surplus labour time. By comparison, the Roberts approach involves some strange arithmetic and the importation of a hybrid price/value term which makes it difficult to infer the Fundamental Marxian Theorem.

Marxian inequalities in a von Neumann setting

We have shown, that even in a multi-sectoral model, admitting for joint production and heterogeneous labour, there exist some simple relations between the rates of profit, growth and surplus. These relations may be called Marxian Inequalities, because of its resemblance to certain assertions made by Marx. Especially, using these Marxian Inequalities, the Generalised Fundamental Marxian Theorem of Morishima was extended from homogeneous to heterogeneous labour.

Heterogeneous Labour and the Fundamental Marxian Theorem

As was pointed out by Morishima at the end of his famous book on Marx's Economics, the heterogeneity of labour is a serious dilemma for Marx's theory of exploitation, especially for the so called Fundamental Marxian Theorem. The problem, which should be separated from the peculiarities of joint production, consists in finding an appropriate reduction of the various types of labour to one common unit. Recently Bowles and Gintis have undertaken an interesting reformulation of the Marxian theory of value with respect to heterogeneous labour by avoiding any reduction at all (Bowles and Gintis 1977, 1978. Cf. also Steedman 1977, Holliinder 1978). But for the purpose of the Fundamental Marxian Theorem this only shifts the problem from the heterogeneity of labour to the heterogeneity of the respective rates of exploitation. The aim of the present paper is to extend the Fundamental Marxian Theorem (without joint production) from homogeneous to heterogeneous labour (Section 3). This extension is based on a new concept called the standard reduction of labour, because of its dual relationship to Sraffa's standard commodity (Section 2). For some arguments a certain type of matrices, called Sraffa matrices, is needed, which generalize the quasiirreducible matrices as introduced by Bowles and Gintis (Appendix). Standard reduction implies always a uniform rate of exploitation, whereas the same is true for the reduction by wage rates only in special cases (for example: uniform consumption; labour inputs only; prices proportional to labour values. For the first two cases cf. Morishima 1978). Hence, in general standard reduction and reduction by wage rates are different.

Positive Profit without Exploitation: A Comment on F. Petri's Note

However, his example is based on an extreme assumption that the capitalists' propensity to consume, c, is unity. If, like Marx, we instead assume that c 0. To show this we use the generalized von Neumann model [2, 3], of which Petri's example is no more than a special case with c = 1. Assume c 0. By the two Lemmas to the Generalized Fundamental Marxian theorem [1], we know that e > 0 implies IrW > 0 and gC implies e > 0. Hence e > 0 rr > 0 ro > 0 gO > 0. Conversely 7r°> 0 g° > Ogc > 0 e>0O. Thus e>0 0 O. Thus, provided the capitalists save at least a part of their incomes for accumulation, the Generalized Fundamental Marxian Theorem holds not only for the warranted rate of profit and the capacity rate of growth but also for the equilibrium rate of profit and rate of balanced growth.

Positive Profits without Exploitation: A Note on the Generalized Fundamental Marxian Theorem

PROFESSOR MORISHIMA [1, pp. 621-622] has interpreted his own Generalized Fundamental Marxian Theorem (GFMT) as an extension to the joint production case of the theorem stating that, for systems without joint production, a positive rate of exploitation is a necessary and sufficient condition for a positive rate of profit [2, pp. 63-68]. In fact the GFMT only establishes that a positive warranted rate of profit requires a positive rate of exploitation as defined by Morishima; it does not establish that the same holds for a positive equilibrium rate of profit. An example will now be presented which shows that in fact, under the same assumptions as for the GFMT, a zero rate of exploitation is not incompatible with a positive equilibrium rate of profit. Consider an economy where there is only one (constant returns to scale) technique, consisting of a single process, which jointly produces two goods, z and y, utilizing good z and labor L as inputs, in the following proportions: 2z®1L->4z81y

FUNDAMENTAL MARXIAN THEOREM IN CASE OF MULTIPLE ACTIVITIES

ABSTRACTIt is proved in this paper that in a non‐joint production system of Leontief type which allows the simultaneous operation of multiple activities for each commodity production there exist unique labour values of commodities defined as the best minimal labour contents and the so‐called fundamental Marxian theorem can be verified and extended. An appendix studies a generalization of Hawkins‐Simon conditions in our framework.