It is always instructive to speak to Joe Stiglitz. In a conversation
in Paris which we had after his talk at the INET conference, he pointed out
that the elasticity of substitution between capital and labor greater than 1
(which is often assumed by Piketty in his “Capital in the 21st
century”), combined with technological progress which does not fall like manna
from heaven but develops in response to the existing factor prices, would lead
to an explosive process that would end only with capital owning the entire net
income of a country. How?
Suppose that we have a given r (you can imagine that it is 5%
as is often mentioned by Piketty) and a
given wage (w). Suppose also that at this ratio of factor prices, it is profitable
to invest in more capital-intensive processes (that is, they reduce unit cost
of output). So capitalists will replace labor by capital and K/L and K/output
ratios will both increase. Since elasticity of substitution between K and L is
greater than 1, r will only slightly decrease while wage will only slightly increase.
Although factor prices, being sticky, will not have budged much they would have
moved ever slightly further in making capital intensive processes even more attractive.
So there would be another round of increased capital investment, and again K/L
and K/output will go up with only minimal effects on prices.
This will continue round after round until the entire output
is produced practically only by using capital and perhaps just an infinitesimal
quantity of labor. Both r and w will remain almost as they were at the
beginning, but instead of (say) 100 machines and 100 workers, we will, at the
end, have 100 robots and 1 worker. Almost all output will belong to the owners
of capital. Piketty’s alpha will be close to 1.
This is why, in my interpretation, Stiglitz argues that the elasticity
of substitution greater than 1 combined with endogenous technical progress
leads ultimately to an explosive equilibrium. Now, this interpretation is, to repeat,
mine and it is quite possible that Stiglitz might not agree or that I got something
wrong.
But, after talking with Joe, on the way back to the hotel, I
thought of something else. Isn’t this in some ways almost the reverse, and in
some ways, very similar, to Marx’s process of increased “organic composition of
capital” eventually leading to the euthanasia
of a capitalist (to use Keynes’ term in a Marxist framework)? In Marx, the assumption
is that more capital intensive processes are always more productive. So capitalists
just tend to pile more and more capital and replace labor (very similarly to what
we have seen they do in the Stiglitz example). This in Marxist framework means
that there are fewer and fewer workers who obviously produce less (absolute)
surplus value and this smaller surplus value over an increased mass of capital
means that the rate of profit goes down.
The result is identical if we set this Marxist process in
a neoclassical framework and assume that
the elasticity of substitution is less than 1. Then, simply, r shoots down in
every successive round of capital-intensive investments until it practically
reaches zero. As Marx writes, every individual capitalist has an interest to
invest in more capital-intensive processes in order to undersell other capitalists,
but when they all do that, the rate of profits decreases for all. They thus
work ultimately to drive themselves “out of business” (more exactly they drive
themselves to a zero rate of profit).
What are the similarities and differences between the two outcomes?
In both cases, labor will be replaced by capital to an extreme degree, so in both cases, production will be conducted
mostly by robots. Employment will be negligible. In Marx, the ultimate equilibrium
would be with r at almost zero, and wage (by assumption in Marx) at the subsistence—with
of course a huge “reserve army of the unemployed”. In the Stiglitz case, capitalists
will end up with an unchanged r and with pocketing the entire net product. In the
Stiglitz equilibrium, that sole remaining worker will have a higher wage, but
again, no one else would be employed.
Net income, in Marxist equilibrium, will be low because only
labor produces “new value” and since very few workers will be employed “new
value” will be low (regardless of how high capitalists try to drive the rate of
surplus value). To visualize Marxist equilibrium, imagine thousands of robots
working in a big factory with only one worker checking them out, and with the useful
life of robots being one year so that you keep on replacing robots continuously
and thus run enormous depreciation and reinvestment costs every year. The composition of GDP would be very interesting. If total GDP is 100, we could have consumption=5, net investment=5 and depreciation=90. You would live in a country with GDP per capita of $500,000 but $450,000 of that would be depreciation.
(To see how this works, imagine having income of $1100 per
year and in order to earn it needing to have a laptop which costs $1000 and whose
useful life –everybody would agree on that—is one year. So every year you just use most of your income to replace the
laptop and your net disposable income remains small. To make the situation
worse, assume that every additional year, as you are competing with other guys
with laptops, you need to increase the number of laptops you own by 5%; your net income will
keep on decreasing although you would live in a cornucopia of laptops.)
The Stiglitz equilibrium, in some ways, looks very similar:
there would the same immense factory halls with thousands of robots but their net
marginal product will be high and the entire net product will be appropriated
by the capitalists.
For labor, in either case, there is almost nothing—simply because
practically no one will be employed. Quite a negative utopia either way, one
could say. But not quite: in the Stiglitz case, you could tax the capitalists
and use that income to keep potential workers happy enjoying lots of leisure,
watching TV and playing funny games on their laptops. In the Marxist
equilibrium, net income will be low although we would live in a world full of
complicated machines. So, there would not be much income to redistribute. Your pick?