Transformation Problem:Theoretical Issues And An Empirical Calculation

In the first volume of Capital, Marx usually suppose that goods exchange each other according to the labor materialized in commodities.In the volume3of Capital, however, Marx developed a theory of production price and commodities are supposed to exchange according to production price. Production price is manifestation of labor value rather than negation of it, because labor value system constrains production price system through the "two equal aggregates". The internal logic relations between labor value system and production price system form the transformation problem. There exist two major schools in more one hundred years of transformation problem research:system A and system B. During the beginning of the last century to the80’s, the solution offered by system A was considered as "accepted solution" The conclusions of system A are:Marx’s two equal aggregates are incompatible and the rate of profit in the production price system is independent of value system. Therefore, someone against Marx demonise the labor theory of value as "unnecessary detour". By carefully analyzing A system’s model, we found an common assumption hidden in the model, whether the classical3sectors model by Borkiewicz or transformation model using matrix by Morishima. We also found that this assumption is the root of system A’s solution. Proponents of system A believe that Marx himself determines the value of labor power commodity by worker’s subsistence goods. Studying through text of classical economics and Marx’s wage theory, we found that Marx presume the given wage goods because he want to study the common properties of general capital. However, Labor power is product of worker’s family and not of capital production. Labor power is a commodity but a special commodity. When we determine its value, we have to consider its common properties and its special properties. In fact, Marx has reserved some points about it. In Capital, value of labor power equals the value of worker’s subsistence goods and equals a part of worker’s living labor as well. When we deal with transformation problem, the former will contradict with Marx’s "even rate of surplus value" assumption. Therefore, the given wage goods assumption is unnecessary.Some solutions for transformation problem oppose given wage goods vector assumption. We call these solutions "B system". In1980’s, a school of "new interpretation"(called B-2in this paper) tried to build a conversion relation between value quantity and price quantity based on giving up the assumption of given wage goods. They suggested that turn Max’s "total value equals total production price" into "value of net product equals production price of net prodcut". This kind of change made their theory differ from Max’s greatly."Invariant rate of profit" solution (called B-1in this paper) which existed in this century used a method which was more compatiable to Max’s real intention and solved the transformation problem on the basis of "two equal aggregates".By solving transformation problem, we realized that if given technology decided material consumption coefficient matrix and vector of living labor, we can build a value system and also can connected it with the real market price system and theoretical production price system. Then, Max’s "two equal aggregates" not only can be used in value and production system, but also can be used in the market price system which is between in these two systems. Only slightly modifying existing statistic information, we can make those data meet the requirement of Max’s economics, then "labor value national production account" can be calculated according to input-output table. Existing national account statistical information is based on SNA system which doesn’t differentiate productive and unproductive labor. However, in Maxian economics, there is big difference between these two types of labor. All value is created by productive labor. The payment and total income of unproductive labor come from productive sector. When an unproductive sector joins social economy, from the view of Maxian economics, it only involves in the distribution of surplus value but not creates new value. However in the national account information it increases value of total output. Therefore, according to Maxian economics, existing national account statistical data double account some vaule. And this kind of double accounting should be removed. In this paper, we calculate some variables in China’s national account system by using the method of Maxian economics, and compare with similar research in foreign countries. We discovered that the account system which built on transformation theory and labor value theory is closer to the situation which analyzed in the third volume of Max’s Capital.