Marx defined the rate of profit as the ratio of profit to investment. A long-term feature of capitalism has been the tendency for this rate of profit to fall - for booms to get shorter, and slumps deeper and longer.
This was not a phenomenon noted only by Marx. Early pro-capitalist economists such as David Ricardo had attempted to explain a declining profit rate by comparing the economy to agricultural fields reaching the limits of their fertility. But there is no obvious reason why this should apply to the manufacturing of commodities. Marx saw the answer in the nature of capitalist accumulation.
Marx described capitalists as a "band of warring brothers". He said they are locked in a continual battle to undercut each other to make commodities more cheaply than their rivals. They plough capital back into production but this leads to investment largely in machines - what Marx called "dead labour".
He divided investment in production into two categories. Raw materials, machines and other goods used to produce commodities have inflexible value. These were the "constant capital" invested by capitalists.
The second investment is in labour. It is here that a capitalist can be flexible as workers' wages can be driven down - the labour which a capitalist buys is therefore his "variable capital".
Capitalists can increase output by investing in more of the same variable and constant capital - by employing more workers with more of the same machines. But a better alternative would be to make the factory more efficient by using new technology that reduces the time needed to produce the commodities.
For example, a capitalist manufacturing TVs could put £2,000 into employing workers (variable capital), £2,000 in machines (constant capital) and out of this receive £2,000 profit. If the workforce produces 40 TVs a day each TV will embody £50 variable and £50 constant capital, and £50 surplus value.
A capitalist might choose to invest in more expensive machinery which can produce more TVs in one day. For example, if the new machinery costs £4,000 in constant capital but can now produce 100 TVs a day, each TV now embodies only £20 variable capital as the workforce is the same, and £40 constant capital.
So it seems that in the second case both the constant and variable capital have decreased. But at the same time the ratio of variable to constant capital has changed. There is more constant capital relative to variable capital. In effect this means workers are harnessed to more machinery.
Marx called the ratio of the value of investment in machinery compared to labour the "organic composition of capital". Under capitalism it has a tendency to rise. The first capitalist who invests in new machinery can make large amounts of profit because initially they undercut other capitalists.
But as every capitalist starts to buy the new machines the first capitalist loses this advantage.
On the face of it this can seem very beneficial - it was after all the advance to mass production that brought TV prices down to the point where they are now available to most people.
But commodities don't only embody constant and variable capital. They also embody the surplus value that the capitalist can only extract from workers.
As we saw with the TV example, investment in the workforce stays the same. Because profit can only come from human labour, as more and more capitalists invest in the new machinery the average labour time required to produce each commodity falls. This is what makes the rate of profit fall, as the ratio of surplus value to investment falls across the whole system.
But this is only a tendency rather than an iron law. There are things that capitalists can do to counteract falling rates of profit, including attacks on workers' conditions.
Increasing the hours of the labour force, without increasing pay directly gives the capitalist more surplus, while taking away tea breaks and putting in supervisors also allows capitalists not only to gain surplus through efficiency but allows them to make the most of machines before they go out of date.
Finally capitalists can resort to wage cutting or holding wages below increases in profit. Marx maintained that none of these were absolute laws, but ways used by capitalists to counteract falling profit rates. All these things could be resisted by workers.
The great contradiction in capitalist production is that the more a capitalist accumulates, the greater the problem for the capitalist system as a whole - and yet the logic of accumulation is central to the system. Capitalism not only destroys the environment and lives of those forced to work under it, but dooms itself to greater and greater crisis.
The rate of profit is the ratio of profit to investment
Over time investment in machinery rises relative to labour, squeezing the rate of profit
Capitalists try to offset this fall by attacking workers' conditions
Next month: do Keynes's ideas offer a solution to the crisis?