# [OPE-L:4032] Re: Re: Re: transforming the inputs (was no subject)

From: Allin Cottrell (cottrell@wfu.edu)
Date: Mon Oct 09 2000 - 11:30:24 EDT

```On Sun, 8 Oct 2000, Rakesh Narpat Bhandari wrote:

> I argue that Marx sets a constraint to the transforming of
> the inputs--that the sum of their (transformed) prices of
> production should equal their total value just as the total
> value of the outputs equals the sum of their prices of
> production....

OK, let's try it.  I show below my iteration, revised so as
to satisfy the condition you cite.

Value table (same as before):
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 transformation (same as before):

c	  v	  s     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

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.

(1A) [new] The sum of c+v computed in this manner doesn't
equal the original total c+v (= 675.00).  To preserve
equality in this regard we rescale the new c and v figures:
each one is multiplied by the same factor such that the
total comes to 675.00.

(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 (as before).

round: 1
c	  v   profit    price   pvratio
I  238.46   83.27   95.33   417.06   1.1121
II  105.98  111.03   64.30   281.31   0.9377
III   52.99   83.27   40.37   176.64   0.8832
Tot.  397.43  277.57  200.00   875.00   1.0000

round: 2
c	  v   profit    price   pvratio
I  241.86   81.57   95.83   419.26   1.1180
II  107.49  108.76   64.07   280.33   0.9344
III   53.75   81.57   40.09   175.41   0.8770
Tot.  403.10  271.90  200.00   875.00   1.0000

round: 3
c	  v   profit    price   pvratio
I  242.72   81.14   95.96   419.82   1.1195
II  107.87  108.19   64.02   280.08   0.9336
III   53.94   81.14   40.02   175.10   0.8755
Tot.  404.53  270.47  200.00   875.00   1.0000

...

round: n
c	  v   profit    price   pvratio
I  243.00   81.00   96.00   420.00   1.1200
II  108.00  108.00   64.00   280.00   0.9333
III   54.00   81.00   40.00   175.00   0.8750
Tot.  405.00  270.00  200.00   875.00   1.0000

Things now look good: total profit = total surplus value = 200,
and total price = total value = 875.00.  Total cost-price in
prices of production = total cost-price in value terms = 675.00.
The aggregate pvratio = 1.00.

There's a problem though.  The iteration has stabilized (there's
no further tendency for the numbers to change when the algorithm
above is re-applied), but we can't give the table a coherent
economic interpretation.  Try cross-referencing the entries in
the "price" column and the column totals for c and v.

Dept I has an aggregate price of output of 420.00, yet the
purchases of its output come to only 405.00.  Dept II is
producing output to the monetary value of 280.00, yet the
purchases of wage-goods amount to only 270.00.  Profit is
appears to be "equalized", but only on the impossible assumption
that the price realized by the sellers differs from that paid by