A Marxian Response to the Problem of Value Determination in a Joint Production System

In Steedman's book "Marx after Sraffa", he proposed that in a joint production system, the labour values of commodities can be negative, which is in sharp contrast to Marxian theory of labour value. I am not meant to revisit his original argument and mathematical model here. If someone is interested in Steedman's argument, he/she can read the book "Marx after Sraffa". What I want to propose here, is a mixed version that makes me feel satisfied. This answer comes from Anwar Shaikh's "Real Competition Theory" and two Chinese modern classical economists: Feng Jinhua (冯金华) and Hou Hehong (侯和宏).

Feng and Hou

Let me introduce Feng and Hou's response to Steedman's critique at first. In 2011, they wrote a paper "Can Negative Surplus Value and Positive Profit Coexist?" (《负剩余价值和正利润可以同时存在吗？》), which was published in Journal of Renmin University of China (《中国人民大学学报》). In this paper, Feng and Hou point out that the labour term that appeared in Steedman's joint production system is "natural labour time", rather than "socially necessary labour time (SNLT)". 

More specific speaking, they found that the net products of the two production processes are not equal. In the first production process, one unit of labour time corresponds to one unit of commodity 1 and one unit of commodity 2. However, in the second production process, one unit of labour time corresponds to three units of commodity 1 and two units of commodity 2.

That means the labour term that appeared in Steedman's joint production system is not SNLT, because in Marxian theory, one unit of SNLT input can not correspond to different amounts of net outputs. Thus, this labour term is "natural labour time", which you can observe directly from reality. 

Feng and Hou argue: in terms of Commodity 1, the net output of unit labour input in production process 2 is three times greater than the counterpart in production process 1, while in terms of Commodity 2, the net output of unit labour input in production process 2 is two times greater than the counterpart in production process 1. Therefore, the "comprehensive" net output of production 2 should be two to three times greater than the counterpart of production process 1. In other words, according to Marxian labour theory of value, the labour values created by unit labour input of production process 2 should be two to three times greater than the counterpart of production process 1.

Suppose the labour value created by the unit labour input of production 1 is 1, and the labour value created by the unit labour input of production 2 is 2.45 which is in the interval [2, 3]. Then, we can easily have the following correct and Marxian joint production system. At last, we can know the value of Commodity 1 is 0.45 and is 0.55 for Commodity 2. 

Please be noticed that we exogenously set the labour values created by unit labour inputs of these two production processes. Can we do not exogenously set them?  Furthermore, what is the exact value of SNLT in Steedman's model? Can we know it? Unfortunately, Feng and Hou think we cannot get the exact value of SNLT directly. However, we can get an interval of the relative values of SNLT created by unit labour inputs of these two production processes.

In my opinion, that is the shortage of the I/O paradigm. When an economic system has surplus products, the labour term that appeared in the I/O paradigm cannot represent SNLT anymore. Marxian Economics has to exogenously set the value of SNLT in this case. I think this shortage shows that the I/O paradigm cannot good enough to show the (surplus) labour extraction process that is happened in the production sphere when this economic system has surplus products.

Anwar Shaikh and the Notion of Regulating Captial

Regulating capital is the most important notion proposed in recent years for modern classical economists I think. Regulating capital is the kind of capital that has the best reproduction condition for investors. 

In Feng and Hou's paper, they focus on the equilibrium case where supply equals demand. Of course, according to the theory of regulating capital, in this case this means two production processes jointly determined the value of SNLT (despite we cannot get the exact value of SNLT in I/O paradigm), which is in line with regulating capital theory.

What I want to add, are disequilibrium cases. To some extent, I think in Steedman's model these two production processes are doing inter-industry competition (because they produce the same kinds of commodities). Therefore, there is no role of uniform profit rate in his model (?). I am not very sure of it, I am welcome to discuss this problem.

According to regulating capital theory, I think if:

1. there is a continuing disequilibrium that moves around the equilibrium prices, then we can say two production processes jointly determine the value of SNLT.
2. supply is continuingly greater than demand, then the state-of-art production process (i.e., process 2) will determine the value of SNLT. Process 1 does not play any role.
3. demand is continuingly greater than supply, then the old production process (i.e., process 1) will determine the value of SNLT. Process 2 does not play any role.

Overall, this is my answer to Steedman's critique. First, Steedman wrongly thinks of natural labour time as SNLT. Second, actually we cannot know the exact value of SNLT in an I/O paradigm if the economic system has surplus products, because I/O paradigm fails to show the surplus labour extraction process. Third, according to regulating capital theory, in different cases processes 1 and 2 may jointly determine SNLT, or SNLT may be solely determined by one of them.