by Michael Roberts
In mainstream economics, the concept of the ‘fallacy of
composition’ is often used. In a general sense, the fallacy of
composition arises when it assumed that the sum of all individual parts
will equal the whole. Sometimes, it does not. There are many examples:
if you stand up at a concert, you can usually see better. But if
everyone stands up, everyone cannot see better as it will lead to
obscured views for the majority of attendees. Therefore, what might be
true for one individual in the crowd is not true for the whole crowd.
This phenomenon happens because the interaction of individual moves can
affect the overall result.
The fallacy of composition is often cited in economics. Paul
Samuelson in his ubiquitous Economics textbook for university students
reckoned “the fallacy of composition is one of the most basic and distinctive principles to be aware of in the study of economics”.
And it is invariably used by Keynesian economists in their advocacy of
government spending to boost the economy. This is the paradox of
thrift. This is the belief that if one individual can save more money
by spending less, then society or an economy can also save more money by
spending less. But if every household reduces spending, then the
overall demand for products and services would decline. This decline
would lead to lower sales revenue and profits for businesses. As a
result, businesses would have to lower wages or lay off individuals.
People would have less income and would save even less. What is true for
an individual in the economy is not necessarily true for the whole
The fallacy of composition in this context has been used by
Keynesians to attack the view of the neoclassical and Austrian schools
that economies are like individual households. Good housekeeping is good
economic policy. But it may be good for a household to tighten its belt
but not for whole economies. So the Keynesians say that there is no
crime in running budget deficits and avoiding ‘austerity’, even if it
means rising public debt levels.
Now I have discussed the issue of whether rising debt (public and private) matters for a capitalist economy in many places. So I’m not going over that ground again in this post.
What interests me is that the fallacy of composition applies in
another area too – in the refutation of one major critique of Marx’s law
of the tendency of the rate of profit to fall. The most famous modern
argument against the law is that by Nobuo Okishio, a Japanese Marxist
economist. Okishio argued way back in 1961
that under competitive capitalism, a profit-maximising individual
capitalist will only adopt a new technique of production if it reduces
the production cost per unit or increases profits per unit at going
prices. So capitalist accumulation must lead to a rise in the rate of
profit not a tendency to fall – otherwise why would any capitalist
invest in new technology? And Marx is used to back up this argument: no
capitalist ‘ever voluntarily introduces a new method of production … so long as it reduces the rate of profit’. Marx 1978a, p. 264
Yes, no individual capitalist would introduce a new technology unless
it contributed to raising profits and market share, the individual rate
of profit. But this is where the fallacy of composition comes in. The
innovating capitalist steals a march on others through lowering the
costs of production against the prevailing market price. Its profits go
up. But that is being achieved by the profits of the other capitalists
beginning to fall as they lose competitive advantage. They must react
by introducing the new technology (or even better technology) that
lowers their costs too. But then the productivity of the existing or
probably reduced labour force for all the capitalists rises and thus
lowers the value per unit of product. Once all the capitalists have
adopted the new technology, the organic composition of capital (the
ratio of money spent on equipment versus wages) will have risen and, ceteris paribus, the general rate of profit will have fallen.
Professor Simon Mohun provided an excellent example from game theory to show why innovation under capitalism and competition can lead to fall in average rate of profit, contrary to Okishio.
There are two capitalists: A and B. Each starts with 3 in profit.
If neither A and B innovate to reduce costs and boost profits, A stays
at 3 and B stays at 3.
But if A innovates and B does not; then A gets a higher profit (4)
while B loses market share and gets less profit (1). Alternatively, if A
does not innovate and B does, then A gets 1 and B gets 4. If both
innovate, then A gets 2 and B gets 2.
There is a drive to innovate because A or B could raise profit from 3
to 4. So there cannot be an agreement not to innovate, leaving A on 3
and B on 3. But if one innovates first to get 4, then the other must do
so or its profit will fall to 1. But with both innovating, they both
end up on 2 instead of 3 (if they had done nothing). So innovation
boosts the individual profit of the leader but eventually when both
innovate, the profit is lower.
Again, this is over time. If A and B could simultaneously introduce
the innovation (as Okishio assumes), then they may not do so, and stay
at 3, rather than fall to 2. But that would not be reality. Reality is
The Okishio theorem is an example of the fallacy of composition. It
simply sums the gain of one individual capitalist to the whole
capitalist economy. But what is good for each individual capitalist is
not good for the profitability of the whole capitalist economy. When
everybody does it, overall profitability falls.
Moreover, each individual capitalist is not doing this ‘voluntarily’
after all, but of necessity to compete and not lose market share. As
Marx says, the law of value and profitability operates ‘behind the
backs’ of the capitalists – it is not in their conscious control. For Adam Smith, it is the ‘invisible hand’ of the market, for Marx, it is an ‘invisible Leviathan’, to use Murray Smith’s metaphor (Murray Smith, Invisible Leviathan, Historical Materialism, forthcoming 2018).