Now that we are familiar with the basic formula of a capitalist enterprise, c+v+s=w, we can begin to explore how this relates to the economy as a whole.

Marx’s reproduction schemes, models of the economy moving through an economic cycle, derive from Quesnay’s tableau économique, and are subjected to a rigorous mathematical analysis in Michio Morishima’s, Marx’s Economics: A Dual Theory of Value and Growth.

Morishima praises Marx’s work, writing:

It is no exaggeration to say that before Kalecki, Frisch and Tinbergen no economist except Marx, had obtained a macro-dynamic model rigorously constructed in a scientific way. His micro-model, the foundation of his macro-model, might on the other hand, as I have mentioned, be compared with Walras’ general equilibrium model of capital formation and credit. These are the most elaborate models we have ever had, though Walras’ is more detailed than Marx’s in the analysis of consumer demand for commodities. This last point has often been reckoned as one of the defects of Marx’s theory, but it must be remembered that only by drastically simplifying the aspect of consumers’ choice was he able successfully to derive definite dynamic laws concerning the working of his system through time. It was a very practical bargain, which has become popular among us since Keynes’ General Theory….Thus many contemporary economists believe that it is more important to obtain a theory which can describe dynamic movements of the economy, rather than one which can elaborate consumers’ preference. This is exactly the choice which Marx made.

 For now, we will look at the basic two-department scheme of simple reproduction. This model is called “simple” reproduction because it represents an economic cycle in which no growth occurs. We begin with a set of conditions and after the cycle we “reproduce” the same set of conditions. (Another scheme, which is only slightly more involved, is called extended reproduction and it accounts for growth. We discuss that later.)

Marx’s reproduction schemes can be thought of as an aggregation system. They could, in theory, be made as complicated as one wants, but their beauty lies in their simplicity. To create his two-department scheme, Marx aggregated all  economic activity into two sectors.

The beauty of it is that he chose as his two departments the two types of capital investment used in the basic equation c+v+s=w. Department 1 represents the aggregate of all economic activity that produces the items which are purchased as constant capital investments  (c)— machinery, buildings, tooling, etc., these are commonly referred to as capital goods. Department 2 represents the aggregate of all consumer goods. This is the aggregate of v, because the variable capital investment constitutes the wages of the workers. For simplicity’s sake it is assumed that the workers spend all of their income on consumption, with no savings, a situation not too far from reality for millions of workers even today. (We could account for workers savings and investments but to keep the model simple we ignore it for now.)

So, how does department 1 function? Like every capitalist enterprise,  c+v+s=w. Only now, to designate this as department 1, we write it as:  c₁+v₁+s₁ = w₁

Department 2 is:  c₂+v₂+s₂ = w₂

Now let’s set these in motion and see what happens.

Demand for capital goods is represented by the variable c. Both departments need to invest in capital goods to operate so the total demand for capital goods is c₁+c₂

The only supply of capital goods is the output of department 1 (by definition), so in order for supply to match demand:  w₁= c₁+c₂

Since w₁ = c₁+v₁+s_1, we can write: c₁+v₁+s₁ = c₁+c₂

If we eliminate c₁ on both sides of the equation we are left with: v₁+s₁ = c₂

This is telling us that in order for supply to meet demand and for the economy to remain in equilibrium the amount that department 2 invests in capital goods should equal department 1’s demand for consumer goods and luxury items. The luxury items are represented by s, the capitalist’s surplus value. Of course it is not realistic that the capitalist spends all of the surplus value on consumption. Extended reproduction schemes, which we will consider later, account for this, but our goal here is a simple model to understand the basic concepts.

Looking at department 2 we find: c₂+v₂+s₂ = v₂+s₂ + v₁+s₁ 

We simplify this to: c₂ = v₁+s₁  The same equation we were left with before. So again, all that we need for supply to equal demand is for department 2’s demand for capital goods to equal department 1’s demand for consumer and luxury goods. Those are the basics of simple reproduction.

In our next post we will examine what happens to this simple reproduction scheme when human workers are replaced by robots.