# [OPE-L:4017] Re: The Transformation Non-Problem and the Non-Transformation Problem

From: Andrew_Kliman (Andrew_Kliman@email.msn.com)
Date: Sun Oct 08 2000 - 15:21:01 EDT

```In reply to OPE-L 4013:

BACKGROUND
==========
Rakesh had argued that Marx didn't say that the prices of production of
inputs had to equal the prices of production of outputs.  Lefteris said
that Rakesh's proposition "implies two systems of prices of production
[--] one for inputs and another one for outputs [--] and as a result two
average rates of profit."

I replied:  "The proposition implies a single system with a single
average profit rate, namely

P[t+1]*B = (1+r)*P[t]*A

(or something similar), where the P's are the price vectors of two
different moments t and t+1, r is the uniform profit rate, and A and B
are matrices of inputs and outputs."

Lefteris now writes:
"O.k. Is this is a joint production system? what exactly is this B?"

B is a matrix of gross outputs, which is a diagonal matrix if production
is single only.  So joint production is not excluded but also not
required.

Lefteris:  "what is this r?"

r is the uniform rate of profit.  Note that this definition does not
imply that the actual rate of profit will be uniform.  The output prices
P[t+1] are the prices that would obtain IF the rate of profit were
uniform (given A, B, and P[t]).

Lefteris:  "does r change with time?"

Yes, at least potentially.  So do A and B!!!

Lefteris:  "how do you determine it?"

That is the key question of all quantitative value theory of whatever
stripe (neoclassical, post-Keynesian, Sraffian, etc.), IMHO.  The answer
depends on the theory in question.  P[t] is given BEFORE production, and
let's assume A and B are given.  Then either the P[t+1] are determined
exogenously (e.g., by "demand," as in PK theory) which then determines r;
or r is determined exogenously, which then determines the P[t+1].

Marx argues in the latter way.  Total surplus-value or profit is
determined by (and is the monetary expression of) the amount of
surplus-labor extracted in capitalist production -- BEFORE the outputs B
are sold.  And the capital advanced (= P[t]*A IF there's no fixed capital
and IF A includes wage goods) is already determined at the start of the
period.  Hence the profit rate is fully determined as a result of the
production process, BEFORE commodities go to market.  The profit rate and
output prices are NOT determined simultaneously in Marx's theory.  And
they don't need to be determined simultaneously, despite what the
"Sraffians" tell us.  They can be determined, for instance, just as Marx
determines them.

Lefteris:  "the TP has not been discussed in terms of joint production
but in terms of single production."

There is no TP.  The thing became a "problem" essentially when
Bortkiewicz claimed to have proven an internal inconsistency in Marx's
account of the transformation.  But Bortkiewicz's "proof" was disproved
14 years ago.

If you examine MARX's discussion of the transformation, you will see that
neither single production nor joint production is specified.  Marx's
account of the transformation is inclusive of BOTH possibilities.  The
above equation system reflects that generality as well.

Lefteris:  "So in case of single production the above system must be
written as:

P[t+1]= (1+r(t))*P[t]*A

Certainly, such a system is in disequilibrium, ... "

It is in "disequilibrium" in the sense that the input and output prices
differ.  So what?  The problem at hand is the determination of production
prices.  These are, BY DEFINITION, prices at which the rate of profit is
uniform.  In order to have production prices, then, it is not the case
that everything in the world must be in equilibrium.  What must be in
equilibrium are profit rates.  And the profit rates here ARE in
equilibrium.

(BTW, to anticipate what I expect I would otherwise hear as a retort, the
equilibrium profit rates here are the rates of return on capital
advanced.  The "profit rates" measured on the basis of replacement costs
are not equal, but firms don't invest on the basis of them.  And the
rates of profit to which Marx referred were rates of return on capital
advanced, not on the replacement cost of capital.)

Why did people wrongly think the input and output prices must be equal in
order to have production prices?  Marx never said a word about that, nor
did Smith, nor did Ricardo.  It was because of Bortkiewicz's false proof
that reproduction breaks down if the input and output prices are unequal.
It just isn't so.  So there's nothing wrong with a uniform profit rate
without uniformity of input and output prices.

Lefteris: "and if we allow for time t->infinite and the eigenvalue of A
is less than 1 then we get

lim P(t+1)/Pt=1 for t->infinite

it follows that P(t+1)=Pt=P*

where P*  is the pop of the system and the eigenvalue of A=1/(1+r) etc.
that is a single price of production and a single rate of profit as
expected."

So what?  What is the justification for holding the matrix of
technological and real wage coefficients, A, constant over time?  They
aren't constant over time.  And you're allowing everything else to change
over time -- the input prices, the output prices, the profit rate.  So
why not allow A to change over time?

Once you allow A to change over time like everything else, your
convergence theorem just does NOT hold.  As a result, the physicalist
dogma that "the" rate of profit is solely a function of physical
quantities (technology and real wage coefficients) does NOT hold either.

Lefteris had written::  "Furthermore, what is an input and what is an
output is also problematic because inputs are outputs and outputs are
inputs at the same time[,] i.e. there is a single market for both inputs
and outputs when the economy is viewed as a totality."

I replied:  "Inputs and outputs are not distinguished by the nature of
the good.  They are distinguished functionally."

Lefteris responded:  "This is O.K. but still are bought and sold in the
same same market, which is the point that I made."

My rejoinder now:  I know what your point was.  I don't see that it has
any force.  So what if the corn in the market is the output of this
year's harvest and an input into next year's?

It is clear that THIS corn must have only one price -- the price for
which a bushel is sold must be the same as the price for which it is
bought.  What the inequality of input and output prices means is that the
price of corn now, as an input into next year's production, need not be
the same as its price as an output of next year's production.

It is simultaneous valuation that is logically flawed on this point.
Imagine the production of corn by means of corn.  In year 1, 9 bushels of
seed-corn and 9 units of labor yield 10 bushels of corn.  The unit value
of corn as an input is 9; the unit value of corn as an output is 9.  In
year 2, technology changes.  1 bushel of seed-corn and 9 units of labor
yield 10 bushels of corn.  The unit value of corn as an input is 1; the
unit value of corn as an output is 1.

Notice that the same stuff has TWO DIFFERENT VALUES at one and the same
time.  As an output of year 1, a bushel of corn is worth 9; at the same
time, as an input in year 2, is is worth only 1!

Andrew Kliman
```

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