On the Falling Tendency of the Rate of Profit

A (very) brief explanation for those not familiar with this issue…
Based on an unfinished exercise by the late Ronald Meek

(if you have read about this before and just want to go to a demo, skip to the very end…)

 

Even if this is a very controversial law – it has always been the subject of polemics and different interpretations – the law of the falling tendency of the rate of profit seems to explain the inherent logic of the capitalist system and its bumpy historical development. This law expresses the contradiction between, on the one hand, the processes of accumulation and its technological progress (spured by the profit motive) and, on the other, the consequent increases in productivity and related relative reduction in employment opportunities for those that have to sell (or lease…) their available work-force.

On the other hand, the manifestation of the law of the falling tendency of the rate of profit expresses itself at the deepest level of economic reality: the level of values. To use a metaphor, the analytical level of values is equivalent to a geological layer upon which is based the «geography» of prices. In this sense, any «earthquake» defined in terms of values, always ends up being reflected in crisis and visible phenomena in monetary terms, such as prices, overproduction of goods and services, lack of purchasing power, monetary movements, inflation and unemployment. These phenomena vary from country to country, both according to geography and to institutional arrangements.

In the «geological» level of values, we then consider the set of relations between constant capital (one that corresponds to stored-up labor from previous cycles (such as technologies, machinery, materials, buildings and other structures …) and variable capital (that which corresponds to the payment of goods and services necessary for the reproduction of the labor-force);

The sum of constant capital and variable capital becomes the total capital invested (both at the level of a single company, a sector of activity or the economic system as a whole. All this is measured in terms of «average number hours of socially necessary labor» (to reproduce whatever it is, in a sense, «from scratch»).

From the relationship between constant capital and variable capital results the concept of «organic composition of capital». At the geological level, this variable capital (the total labor that is spent in production) is supposed to add new value during the process of production. This value that has been added is the one and only source of profit (latu sensu). When these profits are «converted» into price terms, they are the sole source from which «entrepreneurial» profit, taxes, rents and interest will be paid.

In the rudimentary model that is presented here, the rate of «gross profit» (at the «geological» level…) is then expressed as a fraction where the numerator is the value added in each annual cycle and the denominator is the sum of Constant capital and Variable capital. Through an elementary mathematical manipulation (dividing both terms of the fraction by the amount of variable capital) we then obtain an equation somewhat more complex in that the «rate of profit» is equal to «the rate of value added» divided by the sum of the «organic composition of capital» plus one.

In this rudimentary model what is proposed is simply this:

- The system is continuously subjected to a process of accumulation which is achieved at a certain rate. This is called «Flow Back Rate» (the proportion of the product that flows back into the system as new capital…).

- As a result of that flow back rate, there is an impact on both types of Capital with related improvements in productivity of both Constant and Variable capital. This leads to changes in the proportions of Constant and Variable capital in the investment decisions for each cycle (or iteration) of the model.

This seems to correspond to the overall logical principles underlying the historical reality of the capitalist system, at the «geological» level of economic activity.

At this stage of model development, the number of average hours worked by the working population as well as the rate of value added (also known as «exploitation rate»…) is assumed as constant.

What the experimenter can do then is to «assess» the impact of a higher or lower rate of reflux and its impacts in the proportion of constant capital and variable capital.

As can be seen the rate of profit always starts by increasing (as per the «Okishio Theorem»…) rise but eventually comes to stagnate and to decline.