Before continuing this exposition and
explication of the evolution of the Smith/Ricardo/Marx Labor Theory of Value,
let me just note that none of these luminaries made the slightest use of even
the relatively elementary algebra readily available in their day. It is simply extraordinary that without the
aid of correctly worked-through quantitative examples, they were able to intuit
very deep formal truths. [Marx tried to
carry out a numerical example in Capital,
but got it wrong, even though the deeper proposition he was attempting to prove
is, as it happens, true.]
With the aid of the linear algebra that I
taught myself that cold Northampton January, I was able to read and grasp the
mathematical reconstruction and reinterpretation of classical Political Economy
carried out around the world in the 60's to 80's of the last century by a score
of gifted economists. Indeed, I was even
able to offer formal proofs of a few interesting propositions myself, although,
alas, the most important of them was anticipated by a year by a Spanish economist
[a fact pointed out in print by the most mathematically gifted of the American
Marxist economists, John Roemer. So much
for immortality.]
Ricardo claimed that equilibrium prices [or
"natural prices," as the classicals called them] are determined by
the quantities of labor directly and indirectly required for their
production. He quite well understood
that this explanation excluded such scarce goods as Old Masters and "wine
grown on a particular side of the hill."
[Ricardo had a rather comfortable lifestyle.] In mathematical terms, this means that the
prices of commodities would be proportional to their labor values. Since a good deal hinges on this simple
claim, let me, at the risk of totally alienating the innumerate among my
readers, take a moment to explain exactly what Ricardo was asserting.
Each of the commodities bought and sold in the
marketplace has a natural value, or, as modern economists would say, an
equilibrium price. [The economy is
equilibrated by movements of capital and of prices until there is a single set
of prices and a single profit rate throughout.]
Suppose we use the lowercase letter p to represent price, with
subscripts to indicate which commodity we are referring to. Thus pc will stand for the natural
price of corn, pl will stand for the natural price of linen, and so
forth. Let us also adopt the modern
convention of using the lowercase Greek letter lambda, or λ, to represent the quantity
of labor directly or indirectly required to produce a unit of a commodity,
which is to say the labor value of
that commodity, with subscripts employed in the same fashion. If corn is measured in bushels, linen in
yards, money in shillings, and labor in hours, then Ricardo's Labor Theory of
Value asserts that:
The price in shillings of a bushel of corn is
to the price in shillings of a yard of linen as the labor value in hours of a
bushel of corn is to the labor value in hours of a yard of linen, which, using
our newly defined symbols, can be stated succinctly as: pc/pl = λc/λl.
Even though Ricardo never translated his claims
into convenient symbols of this sort, he grasped intuitively, and with great
insight, that this proposition, which he himself had asserted, is not in
general true! What is more, he
understood exactly what had to be the case in order for it to be true.
Briefly, the natural prices of commodities are proportional to their
labor values only when the ratio of the quantity of labor directly required to
the quantity of labor indirectly required is the same in all lines of
production. This is the situation that
Marx was later to call "equal organic composition of capital." The point is that some production techniques
are what we have come to call "labor intensive" while others are
"capital intensive." In an
economy with production techniques of both sorts being employed, prices will in
some industries lie above their labor values and in other industries below
their labor values. [As is perhaps
obvious by now, I find this whole subject absolutely fascinating, but I am
quite well aware that not everyone, to quote the old joke about philosophers,
wants to know "that much about rainbows." Readers who share my geekish enthusiasms are
invited to consult the relevant chapters of Understanding
Marx.]
After publishing the Principles of Political Economy and Taxation in 1817, Ricardo spent
the remaining six years of his life struggling unsuccessfully with this deep
problem with his Labor Theory of Value. Marx
was well aware of this, and in Capital
Volume Three offers a brilliant solution that is almost [but not quite]
correct. And yet, despite the fact that
the materials of his entire hauptwerk
were worked out before 1867, Marx chose to write all of Volume One on the
assumption of equal organic composition of capital! Why on earth would he make so odd a choice,
considering that he had in his back pocket, as it were, a solution to Ricardo's
problem? Tomorrow I shall answer that
question and carry our story forward into Capital
Volume One itself.
3 comments:
Great post, or series of posts I should say. Just one thing, in fact, part of what the capital debates of the 1960s did show is that one cannot say whether a productive process is capital intensive or labor intensive, since there is a possibility of reswitching and reverse capital deepening. I would suggest that it would be more appropriatte to say that there are processes with different proportions of labor to means of production. Sraffa in fact avoided the use of the term capital prefering always to use means of production.
Okay. I am trying desperately to keep this as simple as I can, but you are right.
No complaints. I understand perfectly. Really great posts.
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