Tendency of the rate of profit to fall

(see also, rate of profit; composition of capital)
 
The general rate of profit has a tendency to decrease over time. As capital becomes more competitive, it is required that more and more machinery be employed in production to match the productive output of its competitors.
 
For instance, if the prevailing composition of capital in the economy is 4:1, or $400 worth of machines which must be worked by $100 worth of waged workers, then the capitalist must invest $500 to start a new firm that operates at the same productivity as the rest of the market.
 
However, if a new machine or process is invented, soon all the capitalist firms will need to have it (or its equivalent) in order to maintain competitiveness. Let’s say the new machine costs another $100 and cuts out 1/2 of the necessary wage work. Thus our composition of capital is now $500:$50 or 10:1.
 
Now, the capitalist must have $550 to start his firm. His return is much less. Instead of making profit on the $100 of waged work, he is now reduced to making profit on the $50 of waged work. Let us say that the rate of exploitation is 10:1 for demonstration.
 
At a rate of exploitation of 10:1, the waged workers in the first instance are paid $100 but produce $1,000 worth of commodities. Thus, for $500 worth of capital, the capitalist makes $500. However, in the second instance, the workers are only paid $50 and they produce 10 times their own wages in value – $500. For a $500 investment, the capitalist is now returning merely $500. The rate of profit has shifted from 1:2 to 1:1. 
 
It is important to note here that the machinery is not completely used up in a single cycle, and thus the initial investment of $400 (in the first instance) and $500 (in the second instance) can be pro-rated over many cycles. For the ease of math we have not done that here.

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