[OPE-L:4018] Re: transforming the inputs (was no subject)

From: Allin Cottrell (cottrell@wfu.edu)
Date: Sun Oct 08 2000 - 15:27:28 EDT

```On Fri, 6 Oct 2000, Rakesh Narpat Bhandari wrote:

> I am quite happy that you have responded to me. Let's leave
> TSS and everyone else out of this but Marx, you and me. And
> I shall be quite simple and as brief as I can.
>
> Please go to the tableaux Capital 3, p.256.

Can we take a tableau which represents a complete system, so we
can figure the interdependencies?  I use a simple 3-department
one below.  I'll set out the example then try to say something

The starting numbers here are the ones Sweezy uses to
illustrate Bortkiewicz's transformation (Theory of Capitalist
Development, p. 121).  The rate of surplus value is presumed
to be 2/3 for all Departments.

The initial value table:

c	  v	  s     value
I  225.00   90.00   60.00   375.00
II  100.00  120.00   80.00   300.00
III   50.00   90.00   60.00   200.00
Tot.  375.00  300.00  200.00   875.00

Marx's first-step transformation takes the given total s
and distributes it in proportion to (c+v).  Thus:

c	  v    profit   price   pvratio
I  225.00   90.00   93.33   408.33   1.0889
II  100.00  120.00   65.19   285.19   0.9506
III   50.00   90.00   41.48   181.48   0.9074
Tot.  375.00  300.00  200.00   875.00   1.0000

where "pvratio" is the ratio of price of production to value.
At this point total profit = total surplus value and total price
= total value.

We now continue the iteration...

(1) Take the price-to-value ratio for each Department, and
use it to revalue the inputs.  E.g. the pvratio for
Dept I above is 1.0889, and doing 1.0889 * 225.00 gives
245.00 for the price of production of constant capital
used in Dept I.  Similarly for all the c and v numbers.

(2) Calculate output price for each Dept as revalued c
plus revalued v plus an aliquot share of total profit,
which is presumed to be the same as total surplus value,
that is, 200.

round: 1
c	  v   profit    price   pvratio
I  245.00   85.56   95.33   425.88   1.1357
II  108.89  114.07   64.30   287.26   0.9575
III   54.44   85.56   40.37   180.37   0.9019
Tot.  408.33  285.19  200.00   893.52   1.0212

(Note that the aggregate pvratio is no longer 1.0.)

round: 2
c	  v   profit    price   pvratio
I  255.53   86.18   95.83   437.54   1.1668
II  113.57  114.90   64.07   292.55   0.9752
III   56.78   86.18   40.09   183.06   0.9153
Tot.  425.88  287.26  200.00   913.14   1.0436

round: 3
c	  v   profit    price   pvratio
I  262.52   87.76   95.96   446.25   1.1900
II  116.68  117.02   64.02   297.72   0.9924
III   58.34   87.76   40.02   186.13   0.9306
Tot.  437.54  292.55  200.00   930.09   1.0630

...

round: 46
c	  v   profit    price   pvratio
I  288.00   96.00   96.00   480.00   1.2800
II  128.00  128.00   64.00   320.00   1.0667
III   64.00   96.00   40.00   200.00   1.0000
Tot.  480.00  320.00  200.00  1000.00   1.1429

At this point the numbers are the same as those obtained
via the Bortkiewicz simultaneous equations approach.  Total
surplus value equals total profit, but total price does
not equal total value.

> If value had been redistributed in the previous period to
> equalize profit rates, the total value of those means of
> prod and wage goods simply could not have changed as a
> result thereof...

Agreed, and this is consistent with the example above.  Total
value of means of prod and wage goods = 675 throughout.

However, this does not constrain the total cost-price of those
items, evaluated at prices of production, to equal 675.

> ... if total value and total prices of production and total
> surplus value and total profit are equal in the second
> tableau, there is no way that they could become unequal from
> the transforming of the inputs.

In the example above, total price diverges from total value at
round 1, due to the revaluation of the given quantities of the
inputs at the prices of production derived in Marx's first-step
(round 0) transformation.

> We still have the same total value and total cost price and
> total profit and total surplus value from the second
> tableau; they are necessarily unaffected by transforming the
> inputs.

You'll have to show me an example of what you mean.  How would
it differ from what I've shown above?

Allin.
```

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