Abstract

This research delimits the critical studies about the redundancy of the Labor Theory of Value around the 1970’s，with Ian Steedman representing the Neo-Ricardian economics，Paul Samuelson representing mainstream Neoclassical economics and John Roemer representing Analytical Marxist economics.They all used mathematical formulas to show doubts and refute Marx’s transformation of value into price of production problem，arguing that the Labor Theory of Value is redundant and unnecessary.We call it redundancy of the Labor Theory of Value.

Based on the critic of the Classical economists’ Labor Theory of Value，Marx established and improved the Labor Theory of Value.The English economist William Petty and the French economist Pierre Le Pesant de Boisguilbert both raised a simple Labor Theory of Value；Adam Smith was the first Classical economist to systematically expound the Labor Theory of Value.However，concerning the law of value after the capitalist mode of production became dominant，a rupture in his logical thought occurred.Therefore，the determination of the quantity of the value of the commodity by the consummation of the labor was directly re-oriented to the determination of the quantity of the value of the commodity by the value distribution in the market；David Ricardo criticized Smith’s Dual Theory of Value，but was unable to resolve the two difficult theoretical problems and Ricardians finally failed to do so.Considering the Capital as a whole，after Marx brought to light the fundamental content of the Labor Theory of Value by looking at the form of commodity as an element of capitalist wealth in the Volume I of Capital，using a method of explanation from abstract to concrete，in Volume III he put forward the transformation theory from value into production price to resolve the contradiction between the law of value and the law of the average rate of profit.Nevertheless，even before the publication of Volume III of Capital，the critics of Marx continuously raised doubts and tried to ridicule him.After the publication by Friedrich Engels of Volume III of Capital，although Eugen von Bôhm-Bawerk did not really analyze the transformation problem，he rejected the conclusion of the basic theory exposed in Volume III of Capital.Until now，Bôhm-Bawerk still has an enormous influence.From Smith to Bôhm-Bawerk，even though they abandoned or denied the Labor Theory of Value，they do not belong to the category of the redundancy of the Labor Theory of Value.Nonetheless，on the common theory of price，they represent the common character of the vulgar economics.The real problem started in the beginning of the 20th Century with Ladislaus Bortkiewicz，using a“rigorous”method of research.His method was accepted and introduced into the English-speaking world by Paul Sweezy.It has since then attracted widespread attention. Bortkiewicz，Joseph Winternitz，Ronald Lindley Meek，among other economists，developed further propositions as solutions and models.When Francis Seton pushed the research of Bortkiewicz to its summit，at the same time it became a so-called“consensus”in the Western academia.In other words，when Marx put forward his solution to the transformation problem，he did not calculate the inputs in the price of production.This is why it was not appropriate to consider his transformation theory from value into price of production as a successful solution and that it had to be corrected.Each representative of New Ricardianism，Neoclassical economics and Analytical Marxism，based on the“consensus”，especially based on the means of interpretation of the“consensus”，put forward the redundancy of the Labor Theory of Value.

The critical studies of Marx’s transformation of value problem conducted by Neo-Ricardian economist Ian Steedman，flag bearer of Neoclassical economics Paul Samuelson and the Analytical Marxist economics representative John Roemer all appeared after Ladislaus Bortkiewicz established the traditional study of the simultaneous dual system，setting independently the dual system of value and price.Bortkiewicz isolated the dual system of value and price，considering the calculation of the simultaneous progress of the value and price of the inputs and outputs. Concerning Bortkiewicz’s critics and“corrections”to Marx’s transformation of value problem，it was actually based on a misinterpretation of the basic solution of Marx’s transformation theory from value to production price.Firstly，Marx’s transformation from value to production price is not a construction of two mutually independent system of value and price of production.Instead，it is the distribution of the surplus value in capitalist mode of production，in accordance with the principle law of the general rate of profit.In other words，after the capitalist mode of production becomes dominant，the value will have a new form of transformation.The core issue is the formation of the general rate of profit，and the calculation of the production price of the inputs does not influence the explanation of the transformation problem.Secondly，the other important misinterpretation made by Bortkiewicz about Marx’s transformation theory is that he used the conditions of equilibrium reproduction to criticize Marx’s explanation of transformation theory，saying that it has internal contradictions because the conditions of equilibrium reproduction should be satisfied in the construction of value or price system.Yet，using the conditions of equilibrium reproduction to construct the system of value and price，he stayed trapped in the simultaneous calculation of inputs and outputs，which led the research lost in the relation of quantity of material.It is a simultaneous and materialistic trap.Neo-Ricadian economics，Neoclassical economics and Analytical Marxist economics all accepted the simultaneous dual system interpretation as a kind of“consensus”combined with materialism，using mathematical formulas to demonstrate that the Labor Theory of Value is redundant and a useless theory.In reality，the calculation of value by simultaneous interpretation directly make the value redundant.In reality，the redundancy of the Labor Theory of Value shows that the research of the vulgar economics，by revolving around the nature of the problem，only stays on its surface.

From the beginning of the 1980’s，in response to the Neo-Ricardian economics and Neoclassical economics，some Western academic circles have put forward several new explanations concerning the critics of Marx’s Labor Theory of Value，such as the“New interpretation”（NI），Simultaneous single-system interpretation（SSSI）and the Temporal single-system interpretation（TSSI）.The“New interpretation”and the Simultaneous single-system interpretation，in various degrees，raised questions and challenged Bortkiewicz’s traditional research.Compared to the“New interpretation”and the Simultaneous single-system interpretation，the Temporal single-system interpretation fundamentally refutes the misinterpretation made by the simultaneous dual system established by Bortkiewicz.The mathematical formulation of Marx’s value transformation theory by the Temporal single-system interpretation shows that Marx’s solution is not inconsistent.Many scholars，including those opposed to TSSI，consider that TSSI at least refutes the inconsistency in a way to“make Marx make sense”.Since the 1990’s，many Chinese scholars kept putting forward new interpretations and models to Marx’s transformation theory.Among them，we can mention Ding Baojun who used the transformation of constant and variable capital as a starting point to explain by using a model，the transformation problem.His method shows similarities with the Temporal single-system interpretation.Many Chinese scholars consider his interpretation shows that Marx already resolved the transformation problem successfully.The Temporal single-system interpretation method is very important in the interpretation of Marx’s transformation theory from value to production price.

However，in Western academia，even if the Temporal single-system interpretation is able to illustrate by mathematical formulas the success of Marx’s value transformation，yet it also faces the critic that“what the Temporal Single System argument lacks is a clear and persuasive statement of why Marx，after Sraffa，requires a labor-value analysis at all”as well as“the possibility of circular argument，Hegelian type”.The main representative of the Temporal single-system interpretation（TSSI），Andrew Kliman，admitted himself that，regarding the price of production and its dependence on the value，it can only be guaranteed by the total amount relationship.In other words，even in the Temporal single-system interpretation，the necessity of the Labor Theory of Value has not been adequately illustrated by mathematical demonstration.The English economist Steve Fleetwood pointed out，from a Critical Realist perspective，the quantitative model promoted by deductivism，pre-inserted in constant conjunction of events based on a condition of closed system.But reality does not satisfy this kind of situation.Therefore，it is opposed to any form of quantitative explanation.In fact，the mathematical formulation has a positive significance in the development of economics.Fleetwood did not understand that，for the elaboration of the Labor Theory of Value in the Capital，Marx used a dialectical logic deduction based on the principle of the dialectical unity of history and logic.Thus，he could only stay on the concrete aspect of capitalism，leading to contradictions which are incapable to conciliate between Critical Realism and a closed system.Without Marx’s principle of the dialectical unity of history and logic or dialectical logic deduction，constructing the mathematical formulation of the Labor Theory of Value is a significant defect from Western scholars，including pioneers of the Temporal single-system interpretation who studied the transformation theory from value to production price.Marx’s historical and logical methodology can not be lacking in the mathematical model construction which explains the value transformation theory successfully.After a scientific explanation about the value transformation theory in mathematics，based on historical and logical methodology，we can locate value on social necessary labor time and then interpret the Labor Theory of Value in mathematics.This does not only break through the defects which the Critical Realist economics pointed out and provide quantitative and qualitative analysis，but also provides theoretical support for the necessity of the Labor Theory of Value in the mathematical formulation.

Using mathematics in economic research is positive，but it should be based on the fundamental method of the particular discipline itself.Steedman，Samuelson among other economists，in their misinterpretation of Marx’s transformation problem，incorrectly used mathematics which led to the false conclusion that the Labor Theory of Value is redundant.Their conclusion shows the nature of the vulgar economics，which revolves around the nature of the problem，but only stays on its surface.

Keywords：Redundancy of the Labor Theory of Value；Simultaneous Dual System；Temporal Single-system；Dialectical Logic Deduction