# [OPE-L:1138] LVB4:Numerical Interpretation

Alan Freeman (100042.617@compuserve.com)
Tue, 20 Feb 1996 05:52:19 -0800

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An interpretation of the Thought-Experiment
===========================================

This is a nondualist, sequentialist interpretation of Marx's
analysis of the 'Thought Experiment' data given in LVB 1,
together with outline proofs of its main conclusions. It shows
how, in this example, Marx's concept of money and price leads
to completely general definitions of value and price for which
the 'two equalities' must hold for arbitrary market prices,
so that the magnitude of surplus value is independent of prices;
hence the 'pure form' of value is the adequate form to study
surplus value and its formation.

I don't expect readers to agree with this reading but an effort
to understand would be useful. The next post shows why and
how the numbers are different from the 'standard' ones.

I try to do this without the usual equations and matrices. This
will, I hope, show it is simple, as well as corresponding to
Marx. But all the points made with numbers can be translated
into algebra and have been in other places. There may be
numerical errors, for which apologies; I hope not.

I have recast the argument using Alejandro Ramos's term
'monetary expression of labour'. Marx uses this concept less
ambiguously than its inverse, the 'nominal value of money'; bearing
this in mind the argument can always be put back into its more
familiar form.

The argument, not always with proof, runs as follows:

1.On midnight at the end of January 1st 1990, we have
reached the end of C-M-C (simple circulation) and are on the
verge of P...C'. A definite set of historically-given values,
purchased for a definite amount of money, thus make up the
means of production of which C is composed.

2.The monetary expression of labour is given by the amount
of labour this money paid for. 30 mn years were sold for
\$1500bn. The monetary expression of labour is 1500bn/30mn=
\$50,000 per year(\$25 per hour) or, to put it another way, these
two facts make up a single definition.

3.If a commodity sells for a money sum different from its
value (for example if wine worth \$40 sells for \$45), it
represents in exchange a correspondingly greater or lesser
amount of labour. This is a definite portion of the value of
the whole produce of 1989, of which money is one measure and
labour the other; in this case 45/1500bn. The monetary
expression of labour tells us how much labour this represents
(45/25=9/5 hour).

4.The monetary expression cannot be changed retrospectively,
but we can ask if any other set of prices might change the
eventual outcome. We will prove, with the same wage, all sets
of purchase prices yield the same surplus value.

5.This is the basis of Marx's decision in Chapter 5 of
Volume I to use one particular set of prices, namely values, as
the 'pure' form to be studied. It concentrates on purchase
prices (1 and 2 January 1990). A parallel argument in Volume
III proves profit invariant with respect to *sale* prices (1st
January 1991). This is discussed first (cf para 17ff) because

A. listmembers are more familiar with this case

B. separating the two distinct acts of sale and purchase
removes a common source of confusion.

The determination of value and surplus value
============================================

6. C=\$1000bn: The MP employed by the capitalists have cost
them \$1000bn in the money of 1st January 1990 and will transfer
this to the product,

7. C=20 mn years: The same fact may be expressed in labour
time. \$1000bn is two thirds \$1500bn, which represents the total
labour embodied in all goods produced during 1989. This total
labour being 30 mn years, C will transfer 20 mn years to the
product of 1990.

8. L=10 mn years: The workers will add 10 mn years to the
product of 1990 regardless of the wage, regardless of what they
consume, what it's worth, the state of the stock market, the
eigenvalues of the Leontiev, or *anything* except how long, and
possibly how hard, they work.

9. L=\$500bn: 10 mn years has a monetary expression,
10*\$50,000 = \$500bn. This is equally independent anything
except how long, or how hard, the workers worked, *and* the
historically-given monetary expression of labour.

10.X=30 mn years: The product of 1990 will be 30 mn years in
value, = C years + L years.

11.X=\$1500 bn: The product of 1990 will be \$1500bn in value=\$C+\$L.

The same figure results if we express 30 mn years in the
money of 1st January 1990. It doesn't matter how you get there,
the result is the same.

12.We can now generate two expressions for surplus value, and
two methods of calculating it for each expression.

A. S=8 mn years, starting from L in years: total value added
L is 10 mn years and V is \$100bn==2 mn years. Therefore total
S=L-V=8 mn years.

B. S=8 mn years, starting from X in years: total product X is
30 mn years and V plus C is 22 mn years. Therefore total S is X-
(C+V)=8 mn years by this alternative means of calculating it.

C. S = \$400bn, starting from \$L: Total value added by the workers
is \$500bn, and V is \$100bn; total S=\$500bn-\$100bn=\$400bn.

D. S = \$400bn, starting from X in years: total product is
\$1500bn, costs are \$1000bn C + \$100bn V, leaving S = \$400bn

13.These expressions are all the same. A and C are independent
of the purchase price of constant capital because it does not
figure in their definition. But this purchase price can be
eliminated from B and D because of the definition X=C+L
which, we assert, is Marx's. S is thus, on every definition,
independent of the purchase price of constant capital. We have
not yet proven S equals profit; see 17 below.

14.S thus defined depends only on the monetary expression of
labour, hours worked, and the money wage. Price variations on
January 2 1990 could only alter S by changing one of these.

15.Value and Surplus value thus defined are independent of
*sale* prices in 1991, being measured without reference to sale
in either hours or the money of 1st January 1990. Hence both
value and surplus value, in money and in labour terms, are
determined independently of sale, that is the C'-M'-C phase of
1st January 1991.

16.Digression and Note: this provides the inductive proof of
the assumption that labour values on 1st January 1990 were
given independent of sale prices on 1st January 1990.

17.Because S was defined independent of sale it remains to be
proved that no additional value can arise through sale on 1st
Janary 1991. This proof is supplied in Volume III. If it can be
shown that extra value arises on 1st January 1991, it will have
arisen in circulation.

We deal with this next.

18.When the product whose value is 30 mn years (\$1500bn inthe money
of 1st Janary 1990) is realised on 1st January 1991, prices will
be set upon the goods which make it up. These could be any prices
at all. But if we add up all the prices paid for all the goods,
we find, just as on 1 January 1990, that a definite sum of money
(\$1500bn) represents a definite sum of hours (30 mn), the price
and value of the same set of goods - everything sold and everything
bought or the produce of 1990 with, as Marx puts it, a price-ticket
on it.

This creates a new monetary expression of labour, justifying
the inductive premise that the monetary expression of labour
was historically given, and laying the basis for the next
(1992) calculation.

If, for example, the product actually sells for \$1650bn then
the monetary expression of labour has risen to 1650bn/60bn =
\$27.5 per hour.

19.The total of all prices in labour hours is thus equal to
the total of all values. Less obviously, even in money it is
independent of the money in which these prices are expressed
provided proper allowance is made for inflation.

This result can be independently derived. We can always
translate any 1991 price into a 1990 price, dividing by the
sum of 1991 prices and multiplying by the sum of 1990
prices. This very reasonable calculation means that, for
example, if all prices rise by 10% we can eliminate the pure
effects of inflation.

20.Gil has raised two objections:

A.He suggests this calculation cannot be done 'in general';
for arbitrary prices, there is no reason the sum of values
should equal the sum of prices.

B. In [OPE:1013, 8/2/96] he accepts this equality holds for a
suitable definition of the value of money. I will concentrate
on his second argument, that this is achieved by definition. He
does not say what makes a *bad* definition and defines value as
v=vA+L; either all definitions are not evil, or some are more
evil than others.

I will return to these in more detail but here I'm just
trying to state what I see as the points at issue. Another
post provides a more detailed response.

21.Neither total sales in labour hours, nor total sales in
constant (1990) money, is affected by 1991 prices. If on
January 1st 1991 the goods actually fetch \$1650bn, then the
capitalists will record higher money profits, but the change in
money sales decomposes into two independent factors [OPE:973 of
7/2/96]; the change in relative prices and an inflationary
increment. This inflationary increment, regardless of values,
is total original sales times the proportional increase in all
prices. It is thus equal to total value multiplied by the
proportional increase in the monetary expression of value.

22.We can thus completely separate out genuine profits and
purely inflationary effects. In the case above, sales of

A. sales of \$1500bn at 1990 prices, plus
B. a monetary appreciation of \$150bn.

23.The product of 1990 may well sell for different *relative*
prices. This cannot change 22A (total sales at 1990 prices).
But it does distinguish price from value. If wine, whose value
is \$40, in fact sells for \$50, both evaluated in the same
money, then the first is its value and the second is its price,
and these are perfectly distinct. In no sense does the category
of value dissolve into the category of price, as with the Value
Form School.

24.Now consider profit. This is not defined in the same way
as surplus value and their identity is not trivial:

A. Profit is the difference between the value of *sales*
(price) and money costs, and will vary depending on how much
money is paid for the product.

B. Surplus value is the difference between the value of the
*product* (value) and money costs, regardless of what the
product sells for.

Individual producers who sell above or below value will
get higher or lower profits. But if we add up the total profit
of the whole capitalist class, it must equal the total value of
sales less the total value of costs.

25.Total surplus value S is defined as total value of the
product X less the total value of costs C+V. Para 19
established that the total value of sales equals X. Therefore,
total profit equals total surplus value.

This can be considered in another way: like total sales,
total profit, allowance made for inflation, is independent
of sale prices. That is, both total sales and total profit
are the same for all prices, allowance made for inflation.

But, in the special case when goods sell at their values,
profit equals surplus value and the value of sales equals
the value of the product.

Since the total value of sales equals the total value of the
product in this special case, and since it is invariant with
respect to price changes, the two must be equal for all
possible 1991 prices. Likewise total surplus value and total
profit. This fully general result applies to arbitrary set
of market prices, not just equal-profit-rate prices.

26.This vindicates Marx's decision to study surplus value in
the 'pure case' of sale at values. Total profit and total price
are invariants with respect to price changes and their
determinants can therefore be studied independent of price
changes.

27.Note: this invariance relation 'decodes' price variations
into the social relations they express. Suppose one sector
achieves abnormally high prices. Then it secures in exchange a
higher aliquot portion of a definite total independent of
prices; other sectors receive lower portions of this same
total. Each set of price differences defines a corresponding
set of *value transfers* between capitals. A higher price turns
out to be merely the disguised form of a value transfer.

28.The set of all price differences is also isomorphic to the
set of all differential profit rates. Thus in a precise,
quantifiable manner, every price corresponds to a profit and
every profit to a price. Two apparently different surface
appearances correspond to the same underlying thing. These
surface appearances are:

A. price-value differences
B. superprofits

Value transfers between capitals underlie both these
appearances. Price movements are hence the phenomenal
form of competition, a struggle between 'brother enemies'
for a share of a pot created by the workers they employ.

29.We looked at sales because we expect Volume III invariance
principles to be more familiar even though the numbers are
question 1: can a new set of prices, established on 2 January,
change profits?

30.We can separate out the total change in profit during 1990
into two parts; extra profit on 2 January 1990, and the in the
rest of 1990.

31.If C and V change on 2 January, new values and profits arise on
the basis of the new C and the new V. The profit of the rest of
1990, an invariant with respect to sale prices, is the difference
between sales X and costs C+V. X is (the new) C + L.

32.The new profits are hence L-V regardless of what happens
on 2nd January; if C rises, then X=C+L is pro tanto higher and
profit is still (C+L)-(C+V)=L-V. Thus C may go down to, say,
\$900bn but in this case X goes down to \$1400bn, costs to
\$1000bn and profits remain \$400bn. L, however, is constant,
Hence only a change in V can alter the profits realised *after*
2 January 1990.

33.Extra profits could only arise on 2 January if the
value in the hands of the capitalists rose on that day.

34.The sum (\$1600bn) of C, V, and MC is, either in hours or
in the prices of 1 January, independent of the prices of 2
January. Just to emphasis the point: any other conclusion means
that without making or consuming anything at all, just by
trading at different prices on 2 January, new value can be
created out of nothing. If this is challenged, I think it is
not Marx but the proponents of this astonishing economic
innovation who have some explaining to do.

35.Thus the only way the value in the hands of the capitalist
class can increase is if V decreases.

36.Therefore, only one variable affects the magnitude of
profit; V. But this is precisely what Marx proceeds to study in
the 'pure form' where goods are assumed to sell for C + L.

37.Finally, even this assumption does not require the
elements of either C or V to be purchased for their value since
both are given by the value of the money spent by the
capitalist, not the value of the goods purchased with this
money. Profit L - V is unaffected by any variations at all in
C, or by any variations in the value of goods purchased with V.

Alan