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Sunday, February 6, 2011

THE THOUGHT OF KARL MARX PART FIFTEEN

The time has come to see how Marx solves Ricardo's problem. This is going to get a trifle gnarly, so you will have to follow along carefully. Our exposition will take us from Volume One into Volume Three [Chapter 10]. Bear with me. To save space and time, I will simply state the results of solving little equations and carrying out little calculations. Those who are serious about mastering this subject are encouraged to work the equations out for themselves on a piece of paper.

Recall the problem we face: Ricardo was aware that in the general case, when different lines of production exhibit differing degrees of capital intensity, prices are not proportional to labor values. He was convinced that the labor required directly or indirectly in production was still the key to understanding the determination of the distribution of the social product, but he simply could not figure out what happens when some lines of production are more labor intensive and others more capital intensive.

To focus our attention, it will be useful to introduce a new model for analysis. [I trust you understand that everything I say about these little three sector models can be proved quite generally for a system with any finite number of lines of production. The formal proofs are all in the Appendix to my book UNDERSTANDING MARX.] So, consider this new model, with three sectors: corn, iron, and tools. Notice that in this model there are no luxury goods [theology books]. Corn, iron, and tools are all required, directly or indirectly, in the production of all three sectors. This, we shall discover, is essential to Marx's analysis. I will discuss it at length a little later on. Notice also that I have specified the real wage, which is once again 0.2 units of corn and 0.1 units of iron per unit of labor.

.........................Labor...........Corn..........Iron........Tools.........Output

Labor.....................................30...............15..........0................150

Corn.................80................128................2...........3................240

Iron ..................20...............16...............1...............5...............60

Tools.................50.................6..............27..............4...............16

Using Lc to stand for the labor value of corn, Li to stand for the labor value of iron, and Lt to stand for the labor value of tools, we can form three labor value equations, as before, from the input and output data of those three sectors. When we solve the equations, we get the following result, using the symbol "~" to mean "approximately equal to."

Lc ~ 0.9344

Li ~ 1.2168

Lt ~ 7.3712

In Marx's terminology, the total amount of embodied labor required by a sector of production is called its Constant Capital, which he labels C. The total amount of direct labor required he calls its Variable Capital, which he labels V. He uses these terms because the capital inputs yield up a constant amount of embodied labor to the output in the production process, but the labor power inputs yield up an amount of labor that varies according to the capitalist's ability to wring more labor out of his workers.

Having solved the equations for the variables Lc, Li, and Lt, we can now plug these values back into the table and calculate the ratio of constant to variable capital in each sector, which Marx calls The Organic Composition of Capital. This is the same ratio that Ricardo would call the ratio of embodied or indirectly required labor to directly required labor. These are all different terms for the same mathematical quantities. When we do this, we find the following:

The organic composition of the corn sector is 0.1713

The organic composition of the iron sector is 0.1164

The organic composition of the tools sector is 0.2271

The organic composition of the entire system is 0.1746

Quite obviously, this is not at all a case of equal organic composition of capital. We can now set up the price equations, using Pc for the price of corn, Pi for the price of iron, Pt for the price of tools, W for the money wage, and R for the profit rate. Because we have specified the real wage, this system of three equations now has four unknowns: Pc, Pi, Pt, and R. When we set the price of corn equal to 1, we have a system that can be solved. The results are as follows:

Pc = 1

Pi ~ 1.364

Pt ~ 7.455

R ~ 1/3

At these prices, the real wage ~ .3364

As should be obvious, in this system prices are not proportional to labor values.

Pc/Lc ~ 1.0702

Pi/Li ~ 1.12097

Pt/Lt ~ 1.0014

Now Marx makes his move. Tomorrow I shall tell you about Marx's big idea. [Hey! This stuff is so deep in the weeds even my eyes glaze over. I have to do something to keep you coming back.]

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