Sraffa 101 - repost of original Sraffa summary

P8475423 at vmsuser.acsu.unsw.EDU.AU P8475423 at vmsuser.acsu.unsw.EDU.AU
Tue Jun 27 12:25:26 MDT 1995


This is an excerpted summary of a debate on Sraffa's
critique of economic theory for the benefit of non-economists
on the Marxism list. Sraffa's model was initially intended
to critique neoclassical economics over its theories of
production, price and distribution. The model was later used
by Steedman to critique Marxian quantitative value theory.
What follows is the initial post that sparked the debate,
my attempt to summarise Sraffa, then some subsequent posts
generated. The debate occurred earl
y in 1995.

One thing which is missing from this is the set of
assumptions which Steedman explicitly made in his critique,
which was excellently summarised by Justin (from memory) in
late June 1995.

-------

Value: There are references to Sraffa, and suggestions from
Jerry Levy that the debate is not being taken much further.

Some people I suspect are not coming in, because they feel
this was all explored in the first four months of this list's
life, July, August, Sept, Oct 1994.

Yes an
d no. I have skimmed the archives for "Sraffa" and it is
much thinner than people might suppose. Perhaps some of the
debate has been had on other lists, but I think it is in the
nature of these e-mail forums that they are living cultures,
they have to create and re-create a shared understanding each
week. It appears to be said this week that Sraffa's critique
was accepted as a substantial critique some time ago, and
therefore should be accepted as a substantial critique now.

But this may be inad
equate and does not fit in with our project
at its best, of listing the strengths and weaknesses of each
model of capitalism.

>From the archives of this list it appears to me
the fullest statement was from Chris Sciabarra on 4th August.
Paul Cockshott asserts that empirically Sraffa has been answered,
I deduced on his own territory as it were.

Other remarks I pick up are that Sraffa was pedantic,
once taking a fortnight to debate where a comma should go, with
another Marxist theoretician. He i
s also said to write in a
highly mathematical style which appears to be impenetrable
to non-mathematicians or non-mathematically-trained economists.

Which all leads me, who does not fit into that category, to start
to dare to wonder whether the emperor is clothed or not. Put more
politely, I have come to believe that the more technical and
apparently scientific an argument is, the deeper you must search
for its value judgements.

I also checked Bottomore's Dictionary of Marxist Thought. The
on
e column entry by Laurence Harris, who I might suspect of not
being sympathetic, is far from disrespectful. I can see that
Sraffa's close links with Gramsci, and his ability to make links
with the Keynesians, and to be settled in one of the most
prestigious colleges in Cambridge University, make
him a figure of considerable credibility. No doubt he was personally
charming in a funny Italian way that endeared him to the English
academics at his college. Besides the rival college next door had
Keyne
s. Everything would conspire to establish his prestige.
The fact that he is difficult to understand would
be an academic asset in the competition between Cambridge colleges,
and between Cambridge and rival universities of international
standing.

But what is surprising to me is that Harris suggests that
Sraffa's "Production of Commodities by Means of Commodities" 1960,
..."provided the starting point of a vigorous school which set out
to criticize the logical foundations of neo-classical economic
s,
and to reconstruct those of Marxist economics, by posing an
alternative theory of distribution based on class struggle over
the level of wages and profits."

The word that amazes me is "alternative" because Marx appears to
me to be littered with statements that the relative distribution
of surplus value between labour and capital is determined by
the relative strength of the two sides. The labour theory of value
would not work in the Marxist model without understanding that
the subsistence le
vel for the reproduction of labour power is a
movable level both in terms of use value and of exchange value !

So I increasingly feel that everyone is groping different parts of
the same elephant; it is just that certain people have got pre-
occupied with certain organs to the neglect of the whole
elephantine organism. In psychological terms, such fetishism with
part objects is difficult but not impossible to treat, if the
patient plays an active part in the treatment.

I get the impression tha
t those who deny the LTV, state as their
weightiest authority, Sraffa, so I feel it is not an unfair
question to ask for a summary of the robustness of Sraffa's position
in a way that would be intelligible to a non-economic Marxist.
Choose your parameters: in say, 100 lines? (or however anybody
feels comfortable doing it).

One way or another I would appreciate a summary of the strengths of
Sraffa's contribution to Marxist economics, and an explanation of
why he thinks it is an advantage to ignor
e the labour theory of
value.

----------

Well, Chris, I'll take up your request to try to outline
Sraffa's critique in 100 lines or less (but probably more!).
Here goes:

(1) Sraffa's critique was of economic theory in general, though
his first target was neoclassical economics. His foundation was
essentially that of the first true economist, Quesnay, who gave
us the "Tableau Economique" in the 18th century: that production
of commodities requires other commodities, and that prices have
to
 be such that it is profitable to produce the vast majority of
commodities. If it is not profitable, then production will
cease: hence, the conditions of reproduction of commodities must
be the basis for the prices of commodities.

(2) He took as his reference point an economy which was in
complete long-run equilibrium: supply balanced demand in all
markets, the rate of profit was the same in all markets, and no
capitalist had any motivation to shift capital from where he/she
was to anywhere else
. (Technological change was left out of the
question). The reason for this reference point was not any
belief that it was a "real" place, but that his main target,
neoclassical economics, presumed that economic processes led to
a general equilibrium. He was asking the question "OK, say we
are in general equilbrium. What then determines prices?".

(3) He constructed a model of an economy with n commodities and
labor. The n commodities were each involved in the production of
each other, as was labo
r: i.e., it takes cotton, steel and labor
to make cotton; steel, cotton and labor to make steel; and
workers consume cotton and steel.

(4) Since workers are not produced (unlike commodities), let
alone produced for a profit, he excepted them from the system
(i.e,, there wasn't a line showing the conditions of
reproduction of labor-power), and he assumed that the wage was a
variable quantity, with a minimum of zero and a maximum of the
entire surplus. Surplus here means the net output of the syst
em,
whereas the gross output includes commodities that are used up
in the production of other commodities.

(4a) He said that he would have preferred to have part of the
wage as "fixed" and reflecting subsistence (i.e., value of
labor-power in Marxian terms) and part variable, but this would
have made the mathematics too complicated for him (contrary to
Chris's belief--and that of many who haven't read Sraffa-he
wasn't mathematically trained; but he did express his logic in a
form of mathematica
l shorthand that he devised for the sake of
logical argument).

(5) His formal system was an algebraic version of the following
(which I have lifted from Steedman's _Marx after Sraffa_ (which
is generally very mathematical, but which he does illustrate
with arithmetic examples):

		Inputs			Outputs
		Iron	Labor		Iron	Gold	Corn
Iron Industry	28	56	-->	56
Gold Industry	16	16	-->		48
Corn Industry	12	8	-->			8
Total		56	80	-->	56	48	8

[A late clarification, given a recent comment by CB. This
doesn't
mean that Steedman (or Sraffa) believed in alchemy. It is just
a numerical example, in which Steedman later uses gold as the
"money commodity", hence he has it being "produced"--which, if
you want a physical analogy, could mean it is "produced" by
workers mining it using iron shovels! As for this meaning that
gold "in the ground" has no value, then in terms of a strict
labor theory of value, this is correct--see Marx's criticism of
Ricardo for thinking otherwise, footnote {1} at the end of
 this
summary.]

This is obviously mythical (it shows gold being produced by iron
and labor), but it illustrates a few points. Firstly, production
is a process that "transforms" inputs into quantifiable but
qualitatively different outputs. Secondly, it takes both
commodity inputs and labor to produce anything. Thirdly, since
56 units of steel are used up producing the total output of 56
units of steel, 48 of gold and 8 of corn, this system is in
"simple reproduction", since it only produces enou
gh steel to
reproduce the same outputs the next time round. Thus the net
output is the 48 units of gold and 8 units of corn (these could
be 48 ounces and 8 tonnes, by the way; they don't have to be in
the same units).

(6) Sraffa's basic point was that the prices that exist in this
state of long-run equilibrium must be such that it is possible
for each above industry to sell its output, and at least buy its
inputs in the next period with the proceeds. On the
presumption--since the economy is in
long-run equilibrium--that
the rate of profit is the same in each sector, the following
price regime must apply:

(28*pi + 56*w) * (1+r) = 56*pi
(16*pg + 16*w) * (1+r) = 48*pg
(12*pc +  8*w) * (1+r) =  8*pc

(where, as with Marx, we show capitalists making their uniform
rate of profit on the basis of a markup on both commodity and
labor inputs; Sraffa actually had profits being made just on the
commodity inputs, Steedman uses the Marxian norm--but it makes
no fundamental difference to the logi
c) (also, this fits in with
Jerry's comments about only using circulating capital; however,
later in the argument, Sraffa introduces fixed capital, using
the concept of "joint production")

(7) The critique of neoclassical economics to which this simple
system gave rise is that (simplifying drastically):

(a) The price ratio can't be determined until you have
previously determined the share of the wage in the net output.
Neoclassical theory presumed that wages were just another price,
and hence
 that the distribution of income was determined by the
price system, and was therefore somehow "fair". Sraffa showed
that in long run equilibrium, the distribution of income had to
be determined separate from and prior to the price system, and
therefore that the wage level and the distribution of income
between workers and capitalists is a power political issue
(class struggle), not a technical (price system) one.

(b) When fixed capital is introduced (by presuming that each
industry produces two
 outputs, the intended commodity and
capital equipment which is one year older, each year until
scrapping), it turns out that the price for this fixed capital
depends upon the wage/profit relationship in a nonlinear
fashion. This means that the most profitable technique at one
wage/profit ratio may cease being the most profitable at a
different ratio, only to once again become the most profitable
at another. This means that there is no simple relationship
between the rate of profit and the price o
f capital, and this is
the real "stake in the heart" of neoclassical price theory. The
rate of profit can no longer be portrayed, as neoclassical
theory would have it, as the "price" of capital.

(8) The critique of marxian economics was a side-effect of the
critique of neoclassicism. This is that: (8a) In equilibrium,
prices cannot be proportional to both the rate of profit and
"labor-values" unless the wage rate is either zero or the entire
surplus. (8b) You don't need labor-values as an interm
ediate
step to calculate prices in equilibrium. In fact, you can derive
prices directly from the input quantities; and if you use an
intermediate labor-value step, you will get the wrong
answer--meaning that you will get price ratios which don't allow
the system to reproduce itself (which, in equilibrium, it must).

To see these points, consider the previous example:

Quantity data

		Inputs			Outputs
	Iron	Labor			Iron	Gold	Corn
Iron Industry	28	56	-->	56
Gold Industry	16	16	-->		48
Corn I
ndustry	12	8	-->			8
Total		56	80	-->	56	48	8

Profit/price requirement

(28*pi + 56*w) * (1+r) = 56*pi
(16*pg + 16*w) * (1+r) = 48*pg
(12*pc +  8*w) * (1+r) =  8*pc

with the additional assumption that the value of the total
labor-power input is 5 units of corn (e.g., 5 tonnes of
corn)--so that the income distribution we are given is that
workers get 5 units of corn, and capitalists get 3 units of corn
and 48 units of gold. This means that the wage paid to the 80
units of labor input must j
ust enable them to buy 5 units of
corn, so that

80*w=5*pc

and we assume that gold is "money", hence we can set its price
to unity:

pg=1

This gives us 4 equations in 4 unknowns (pi,pc,w and r), which
can be solved to yield the following (all this is taken from
Steedman's _Marx After Sraffa_):

r  = 52.08%
pc = 4.2960 units of gold
pi = 1.7052 units of gold
w  = 0.2685 units of gold

If you feed the above values into the above 4 equations, you
will find they are all satisfied exactly
. Now what if you first
try to work out labor values, and then calculate prices on that
basis?

Starting with the iron industry:
Iron Industry	28	56	-->	56

The labor embodied in iron production is the 56 direct units,
plus the labor embodied in the 28 units of iron, which we can
signify as li, meaning "the labor embodied in the iron". Thus in
value terms, this production relation becomes

28*li + 56 = 56*li

And we can simply solve this equation to find that there are 2
units of labor embo
died in iron. This can then be substituted
for the iron input in the other two industries, yielding

lg = 1 (labor embodied in one unit of gold) lc = 4 (labor
embodied in one unit of corn)

(obviously Steedman chose these values to make the maths as
simple as possible)

>From this, we can calculate the total value of labor-power in
this economy as 5 times the value in one unit of corn (since the
total wage bill is 5 units of corn). Thus V is

V = 5*lc = 5 * 4 = 20

Whereas the total labor in
put is 80 units. Thus surplus value,
S, is this total labor input minus V:

S = 80 - V = 60

(Up to this point, I might add, the two systems are not in
conflict. Working as above simply makes labor the numeraire,
rather than gold. The break comes now, since the next step
presumes that the only source of surplus value and hence profit
is labor).

Presuming a constant rate of surplus value between industries,
this means that 1/4 of the labor input in each industry
represents V, and the remainin
g 3/4 represents S. Thus the value
table for this system of production is

	C	V	S	Total Values
Iron	56	14	42	112
Gold	32	4	12	48
Corn	24	2	6	32

where the first column of numbers is got by multiplying the
physical inputs of iron by the value of iron, and the last
column represents the physical outputs of each industry times
the labor-value of each unit of output.

We now introduce Marx's definition of the rate of profit, that
it is

   S
-------
C  +  V

The values for S and V are work
ed out above (60 & 20
respectively); the value for total C can be calculated as shown
for iron only (giving 56+32+24=112). Thus marx's definition of
the rate of profit gives:

       S        60      5
r = ------- = ------ = ---
    C  +  V   112+20    11

For it to be uniform between industries (which is necessary in
equilibrium otherwise capitalists would be shifting from one
industry to another in search of  a higher rate of return), we
must have the labor-value equivalent of the price rela
tion above:

(56 + 14) * (1+5/11) = 112
(32 +  4) * (1+5/11) =  48
(24 +  2) * (1+5/11) =  32

But these sums aren't correct. In fact, the proper answers for
them are:

(56 + 14) * (1+5/11) = 101 9/11
(32 +  4) * (1+5/11) =  52 4/11
(24 +  2) * (1+5/11) =  37 9/11

Now if you try these price ratios, it becomes impossible for the
system to reproduce itself. A labor-value derived price for the
56 units of iron output of 101 9/11 is too little for the sector
to be able to buy its inputs next
time around; and so on for the
other sectors.

The crux of the above is that it is possible to go from physical
data to prices, or from physical data to labor values, but that
you can't go from labor values to prices without making a
mistake: they are two essentially different transformations.

I could go on; but I'm sure I've lost 80% of my readers by now
(4 out of 5?? -:)). There's a lot more to Sraffa, and to the
critique of Marxian economics that Steedman built on his
foundations, than I ha
ve covered above. Anyone who is truly
interested should at least read Steedman's book, and I would
also suggest reading Sraffa's _Production of Commodities..._ as
well (it's under 100 pages, and most of it is NOT maths--though
it is logic!).

The guts of the above is that Marx's analysis must contain a
logical error. The Sraffian response has been to say that Marx
got it wrong on day one by assuming that labor is the only
source of (value and hence) profit, and to ignore the remainder
of his edi
fice. The Marxian approach--in general--has been to
try to find ways around this critique, rather than meeting it
head-on. As it happens, I think both made a mistake: the
Sraffian critique of the LTV is, in my opinion, accurate; but
there is much more to Marx than the LTV, and as it happens, part
of that is a higher system of logic that contradicts the LTV.
This is what I have called Marx's Commodity Axioms, in the paper
to which Chris has alluded.

Cheers,
Steve Keen

------

John Ernst com
ments on Sraffa that

|No doubt Sraffa put forth a unique and interesting treatment of
|fixed capital in his critique.   But now lets get real...It has been
|over 30 years since he published and we see no more of reality than we did
|then.... If Steedman is still hung up with
|prices in an attempt to get real,  then Sraffa remains useful for hitting
|neo-classicals over the head and little else.

As it happens, I agree totally. Sraffa's work was the basis of a critique,
and I believe his followe
rs have been mistaken in trying to turn it into
an alternative theory. It can't be made dynamic, and that's where the
action is in economics. But it IS a litmus test which theories of
economics must be able to pass to be structurally sound if they presume
the existence of an equilibrium state and presume to understand the laws
of economics that apply there. Applying his analysis to both neoclassical
and marxian LTV economics finds them both wanting--and that is still
a significant finding.

Cheer
s,
Steve Keen

Footnotes

1 "Ricardo never uses the word value for utility or usefulness or "value
in use". Does he therefore mean to say that the "compensation" is paid to
the owner of the quarries and coalmines for the "value" the coal and
stone have before they are removed from the quarry and the mine--in
their original state? Then he invalidates his entire doctrine of value.
Or does value mean here, as it must do, the possible use-value and hence
the prospective exchange-value of coal or st
one?" (Marx 1861 Part II, p.
249) [I go on to argue in "A Marx for Post Keynesians" that there is
a second set of axioms in Marx, separate from the labor theory of
value, by which minerals in situ do have value, and that this is what
Marx is alluding to in the final sentence here. This paper is
available by anonymous ftp from csf.colorado.edu in subdirectory
econ/authors/Keen.Steve]



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