Differenciation among individual industrial capitals

 

As the previous article shows, industrial capital is subject to the contradiction between the uncertainty of circulation and the certainty of production. This contradiction can be temporarily resolved by allocating the circulation capital, especially money capital (i.e., cash on demand). However, it cannot be contained over the long time.  

Let us now consider this problem from a purely theoretical perspective. In this case, the production volume per unit time is constant, while sales per unit time are unpredictable and independent of past values.

Let us denote:

𝑃: the value of products produced per unit of time

𝑀: the value of materials (circulating capital) injected into production per unit of time

𝑆𝑖: the value of sold products per unit of time

These values circulate as shown in the figure below.

If the costs of circulation and the profit from fixed capital are assumed away, the profit rate per unit of time is given by P/M − 1.

We assume that the capitalist uses all profit for personal consumption, implying simple reproduction as our basic assumption.In the circulation process, Ri must always remain above zero so that industrial capital can continue purchasing materials and producing goods. Otherwise, idle fixed capital sit would result in a significant loss. The following inequality must hold:

Since M and profit are constant over time, the inequality can be rewritten in monetary terms as:

In terms of inventory changes, Inequality (3) can be rewritten as follows.

When sales are strong, money capital increases. When asles are weak, it decreases.

When sales are good, money capital increases. Meanwhile when they are not good, money capital decreases.

The case of storong sales

The case of weak sales

The key issue here is whether the cumulative value of Si− P fluctuates around zero without excessive bias or not.  

Let us denote Xi=P−Si ​.
Since Si is subject to the uncertainty of circulation, Xi is also unpredictable and independent of its previous value. The recurrence formula for Xi ​ is:

 ​

For simplicity, we assume εi∼N(0,1) i.i.d. 

Since the cumulative sum of Xi​ follows a random walk, the value rarely returns to its initial level. The figure below shows the nine series of random walk. In a random walk, the mean is zero, but  the standard deviation increases proportionally to the square of time.

Some series fluctuate around the mean (zero), while others go far away from it. The latter  implies that some industrial capitals will continue to suffer from a lack of reserves, while others accumulate excess reserves.

From this uneveness, commercial credit and commercial capital emerge. That is, industrial capital with strong sales and excess money either sells its products on credit to those with weak sales, or purchases the same type of commodity from them. The former leads to the formation of commercial credit, whereas the latter gives rise to commercial capital.

Thus, the emergence of the credit can be explained by the difference among industrial capitals caused by uncertain circulation.