# [OPE-L:4257] Re: Re: Part Two of Volume III of Capital

From: Rakesh Narpat Bhandari (rakeshb@Stanford.EDU)
Date: Tue Oct 24 2000 - 06:36:05 EDT

```re 4252

>Let's correct that.  My next-round figure for the aggregate
>price of the means of production as inputs (408.33) has to be
>
>1) By assuming that the quantities are the same on the input and
>output sides, I have overstated the quantity of inputs by 5
>percent, and hence overstated the aggregate price accordingly.
>Thus we need to divide my figure by 1.05.
>
>2) We assume the value of money is constant (as you said).
>Therefore, aside from any adjustment due to equalization of
>profit, the unit price will be 5 percent lower on the output
>side than the input side, due to the 5 percent drop in per-unit
>value.  My initial calculation ignored this, "carrying back" the
>output price unaltered.  To correct for the drop in unit prices
>from inputs to outputs, we have to multiply my figure for the
>aggregate input price by 1.05.
>
>Thus the combined correction factor is 1.05/1.05 = 1.  In other
>words, no correction to my figures is needed after all.  The
>next table looks like this, if we take a total profit equal to
>the total surplus value from the original value table (200) and
>distribute it in proportion to capital advanced:
>
>           c       v   profit    price
>    I  245.00   85.56   95.33   425.88
>   II  108.89  114.07   64.30   287.26
>  III   54.44   85.56   40.37   180.37
>Tot.  408.33  285.19  200.00   893.52
>
>As I said before, total price (893.52) has come unstuck from
>total value (850).[875--rb]  Hold to one of Marx's equalities and you
>break the other one.
>
>What happened?  Well, it shouldn't really be a surprise.  A
>difference in physical quantities between outputs and inputs
>makes no difference to the value or price of production tables,
>in aggregate terms, since it is completely offset by the change
>in unit values (and prices, given a constant value of money).
>
>There _is_ a difference, but it's invisible in the aggregate
>tables: the _unit_ prices of production are no longer the same
>for inputs and outputs.  As you wished, unit output prices are
>lower.
>
>What do I conclude from this?  "Aha, so Marx was completely
>wrong. We can forget about exploitation of labour as the source
>of profit. Capitalism is fine and just after all"?  Of course
>not.  With this loophole opened, it's possible to cook up
>examples a la Steedman where profit and suplus value do not just
>diverge by a few percentage points, but have nothing to do with
>each other. But as Paul C has repeatedly said, we have to
>subject this sort of thing to sensitivity analysis -- to get a
>feel for what are plausible numbers for real capitalist
>economies.  Steedman's examples are theoretical freaks, of no
>practical significance.
>
>Allin Cottrell.

Allin,

These equilibrium habits are hard to break.

No sooner than you are willing to assume that inputs don't have to be
transformed into the same unit prices of production as the outputs,
you now demand that the former be exactly 1.05 x the latter due to
the productivity increase I built into the system.

This is just an equilibrium price stricture via the back door.

You want to take the output unit prices of production after the first
transformation and then simply apply them to the unit inputs at the
ratio of 1.05.

But this won't do for an obvious reason.

For you:

(1) Output unit prices of production=kr/natural units=Y
(2) Input unit prices of production=1.05 Y=Z

But this assumes the profit rate was the same at t-1 as t+1.

Assume it was smaller, then at the least you need a reduction coefficient so
we now have

(3) Z(.x) for the unit input prices of production

Which means

(4) Z(.x)=1.05k(.x)r

If (.x)<1, then you cannot *fix* or *demand* that the unit input
prices of production be 1.05% or so greater than the output unit
prices of production even if productivity has increased by 5% in this
period, for there is this matter of last period's profit rate  at the
very least to consider.

You are trying to constrain the solution by laying out a price change
stricture. If we don't have prices that differ in the prescribed way,
then the solution is said to have failed. These are the old rules.

To be sure, we know unit values have changed by 5% in this period,
but input prices of production cannot be determined unless we know
the r from the previous period.

And r should have been less at t-1 than at t+1, for at t-2 only 27 or
so workers could have been hired compared to the almost 29 whose
labor was embodied in the product at t+1 so there is at least less
total profit at t-1 than t+1 while cost price would not have been
that much less since the unit values of the inputs would have been
higher at t-2 than at t. That is, r at t-1 is bound to be lower than
at t+1. I can demonstrate this later.

So it seems to me that you forgot to factor in (.x) in transforming the inputs.

So in a sequential system, it does not follow that the changes in
unit values in a given period  determine, as you have it, in linear
fashion changes in the unit prices of production in that period.
There is no rule which we can determine from this period about how
the input unit prices of production must differ from the input output
prices of production even if we know the magnitude of productivity
increase

Why did you assume so?  (Hint: you forgot the time subscripts again.)

The input prices of production will depend on myriad factors in the
period t-2 to t-1, including for example how much the luxury sector
sold below value at t-1, how different the OCC was, the change in the
rate of surplus value.

All this cannot be deduced from looking at this period alone. Once
this is taken into account, it is not reasonable to assume that the
unit input prices of production will be greater than the unit output
prices of production in exact proportion to the productivity increase
in *this* period.

The point is not to transform the inputs on the basis of this
period's data alone whether we do it in the form of simultaneous
equations or other clever equilibrium rules. The problem of input
transformation has no determinate solution on the basis of any one
period model, especially the highly contrived ones with which we are
working.

That productivity is increasing should encouarge us to to end the
search for a solution in terms of a vector of equilibrium prices, no
more. It gives us no rules to determine the unit input prices of
production from the outputs.

To take your example, it becomes possible that the modified cost
prices could have been exactly as you have them, though this implies
that unit output prices won't be  5% less than unit input prices of
production per the unjustifiable rule you have laid out above.

Now if we hold total value constant, we simply subtract this modified
total k(693) from the total value of 875, divide by modifed total k
(693) and arrive at r.

It drops now to .26 from .29 in the unmodified scheme. Here's how it
is possible to go wrong.

Though total profit is no longer the same as total sv, this does no
damage to the labor theory of value:  the average rate of profit is
still shown not to contradict or modify the law of value; rather it
is the form in which the law of value asserts itself.

It turns out that profit is a bit greater than what is needed to
purchase the output of Div III/luxury sector; the capitalists will
make do.

Yours, Rakesh
```

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