# [OPE-L:4575] Re: Re: Re: Re: Re: Re: Re: Re: Re: transformation

From: Rakesh Narpat Bhandari (rakeshb@Stanford.EDU)
Date: Sun Nov 26 2000 - 19:45:35 EST

```re 4573

>On Fri, 24 Nov 2000, Rakesh Narpat Bhandari wrote:
>
>>  Given your definition of surplus value as the value of the output
>>  minus the value of the inputs, surplus value and cost price cannot
>>  remain resolved, antagonistic components of total value but rather
>>  become (at least partially) independently determined magnitudes.
>
>It's perfectly symmetrical.  Given your definition of surplus
>value as the price of the output minus the price of the inputs,
>surplus value and value of inputs cannot remain resolved,
>constant-sum, components of total value.  That seems worse to me
>(of course).
>
>Allin C.

For you C, is the constant sum of total value, which is resolved thusly:

(1) C => (c + v) + s

c and v are the value of the input means of production and wage
goods, respectively; s is the surplus value.

But there is an obvious problem with your formula.

While (you seem to agree) an increase in the value of wage goods
implies a decrease in surplus value,

(2) (c + [v + a]) + (s - a) => C

an increase in the *value* of the used up means of production implies
a rise in total value, not a fall in surplus value.

(3) ([c + a] + v) + s => C + a

If the value of the used up, input means of production rises, so
should the value of the commodity output.

So we need the expression for the *determination* of C, which you
have not given. We need to clarify why an increase in the value of
one input raises total value while an increase in the value of the
other input diminishes surplus value.

Marx's formula for value determination is

(4) Lp + Lc => C

The labor value of the used up means of production (Lp) plus current
labor (Lc) or newly added value determines commodity value.

This shows why a rise in the value of the means of production (Lp)
increases commodity value while a rise in the value of the means of
subsistence which has no effect on Lc has no such positive result.
Given formula (4) a rise in the value of the wage goods does not add
up to higher commodity value and thus higher price. This is so basic
to Ricardian-Marxian analysis that I shall not elaborate.

The formula for commodity value  resolution however is

(5) Cm => k + s

C is total commodity value; m the monetary expression of labor value
which for methodological reasons has been fixed by Marx throughout
the course of analysis.
Total price (P) is of course Cm.

So we have

(6) P => k + s

I maintain that in the transformation procedure, neither the
determination of value nor the given and fixed monetary expression of
labor value changes. This allows the simple prices in the unmodified
scheme to be set equal to the sum of the prices of production in the
modified scheme.

(7) P1 = P2

P1 is the total price in the unmodified scheme (875 in the
Bortkiewicz-Sweezy tableau); P2 is the total price of production in
the modified scheme. Sweezy began this way, and Winternitz rightly
claimed that the invariance condition expressed in (7) is obviously
in the spirit of the Marxian system. P1 can also be set equal to P2
if we assume that the unit of account remains an hour of labor.

k is the cost price of the commodity, the money sums which have been
laid out as constant and variable capital. s is surplus value which
is the  residual once cost price has been taken from total commodity
value or price (its monetary expression). That is, surplus value is
dM or M' minus M or P minus k.

Once P is given, any change in k implies an inverse change in s.

This means that a rise in the cost price--whether it results from a
rise in the value of wage goods, greater ground rent or a *price*
change in the means of production--means a corresponding fall in
surplus value.

Of course if cost price had risen due to a rise in the value of the
used up means of production, then total value and price would have
risen accordingly, instead of surplus value having fallen. But in the
transformation procedure, we are not changing, contra Duncan, the
value of the used up means of production; we are also not changing
current labor. We are merely and only allowing for a change in the
price of the input means of production, as well as the price of the
input means of subsistence.

So if cost price is modified by the transformation of the inputs,
surplus value has to be modified in inverse direction.

Only due to a fantastic misunderstanding of Marx's basic concepts
have Marxist economists (Meek is the leading culprit here) been able
to claim that Marx himself would have agreed that once given an
output of fixed value and price, a modification in  cost price
consequent upon the transformation of the inputs should leave surplus
value unmodified.

Of course the mass of predetermined surplus value is held invariant
as we are transforming the outputs from simple prices to prices of
production. It does not follow on Marxian premises that the sum of
surplus value should remain that predetermined magnitude once cost
price is modified by the transformation of the inputs. As I said, the
complete transformation problem is more complex than Bortkiewicz,
Sweezy and Meek realized. Since we are assuming an output of fixed
total value and price, the complete transformation has to allow the
mass of surplus value to vary inversely with cost price as it is
modified by the transformation of the inputs while having the sum of
dept profits determined by the modified sum of surplus value. This
means we are left with four equations and four unknowns and cannot
reduce the problem to three equations and three unknowns, as
Bortkiewicz and Sweezy had hoped for the purposes of mathematical
tractability.

Now Allin you forebode some dark consequence if one proceeds on the
basis of the concepts as I have defined them (and I am prepared to
argue that this is the correct interpretation of Marx). But you are
quite unclear as to what goes wrong in my interpretation. Would you
care to clarify?

The obvious concern is that if the mass of surplus value is itself
changed in the complete transformation procedure, then the idea that
surplus value is prior to, and determinative, of prices of production
is compromised.

This of course is the concern which my iteration dispels. In order to
keep surplus value a fixed, predetermined magnitude, you took the
inputs as they are transformed by the application of output PV ratios
and then distributed the given sum of surplus value (200) in terms of
a uniform rate of profit.

I suggest another procedure.

(a) transform the inputs in terms of the output PV ratios.
(b) subtract the respective modified cost prices from the respective
final prices to arrive at new Dept surplus values.
(c) sum these new Dept surplus values.
(d) divide that sum by the total modified cost price to arrive at r
(e) multiply each modified Dept cost price price by that r to arrive
at the respective Dept profits.
(f) add each modified Dept cost price to its modified profit to
arrive at new prices of production.
(g) determine the new PV ratios.
(h) apply to the inputs
...iterate until equilibrium...

So it is clear that in each iteration, we have followed Marx's
transformation algorithm; we have indeed  had to determine Dept
surplus values and their sum prior to calculating the average rate of
profit, Dept profits and Dept prices of production. And in each
iteration the sum of surplus values of course equals the sum of
profits. Of course in each iteration, surplus value has been
determined by taking from total price cost price, which is money
*paid* for direct and indirect labor. Which means of course that
surplus value at all points has remain derived from *unpaid* labor,
thereby not putting a chink in the theory of exploitation.

All the best, Rakesh
```

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