[OPE-L:4231] Part Two of Volume III of Capital

From: Rakesh Narpat Bhandari (rakeshb@Stanford.EDU)
Date: Sun Oct 22 2000 - 22:42:42 EDT

Let's begin with your table:

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

I am NOT assuming simple reproduction; for me this tableau has to be 
seen in terms of a realistic sequence, characterized above all by 
rising labor productivity.

So then what do we have here? Let us assume each unit of output value 
represents a natural unit of the good. So we have 375 mp. 300wg, 200 
lg in their natural units.

Now let us assume productivity has increased 5% this period. What 
does this mean?

It means that the inputs represent 357 natural units of mp and 286 
natural units of wage goods.

Please recognize this simple complication of your scheme. Every thing 
else follows easily.

You and Steve have yet to understand what I am doing.

Now take Marx's transformation

	  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

OK what do we have to do now? We have to figure out what individual 
and total cost prices would have been had the inputs totalling 357 
and 286 natural units of the mp and wg, respectively, sold at their 
prices of production. Modifying the cost prices will necessarily 
modify the output Div prices even if r were to remain the same.

Marx never followed through with the consequences of transforming the 
inputs. I do agree.

So we have:

mp: 357 unitsx1.05unit value
wg: 286 unitsx1.05unit value

But we know that mp sold above and wg below value or vice versa at t0 
as a result of the above tableau.

So we need PV ratios, we need to transform the inputs.

Now we have unit prices of prod for the outputs because of the one 
unit of value/one natural unit of the output assumption which I made; 
let us suppose as well that unit prices of production were higher at 
t0 than at t+1. It is a more than a reasonable assumption to make if 
we are allowing for the reality of rising productivity while holding 
the value of money constant.

This gives us some indication of the unit prices of production into 
which the inputs have to be transformed.

Now I just did a quick calculation. Let us say that the unit price of 
production was 1.12 for the input mp as opposed to 1.09 for the 
output mp (1.09 is the rounded  PV ratio above) .

If we hold total cost price constant, this means the unit input price 
for the wg would have been .96 instead of .95 as with the output.

That is, we now have 400 +275 for the transformed inputs which in 
value terms had been 375+300.

This of course means the cost prices for each of the industries will 
now be modified on the basis of the unit input prices of production.

So for Div I, k in price of production terms now becomes  322 (c+v= 
240+ 82) instead of 315 (225+90); unit output price of production now 
declines to 1.1 from the input unit price of production of 1.2 if we 
keep r at 1.29.

k for Div II in price of production terms becomes 217, instead of 220 
as it was in the value scheme.

Of course if we modified cost prices for all three divisions, we'll 
end up with the same total cost price as before and thus the same r 
and thus the same total krs. This is built into my assumptions.

I liked this easy result because it showed what seemed to me a 
reasonable decrease in unit prices of production over the period. It 
is obvious we can constrain the the changes in unit prices of 
production over the period to small, reasonable, realistic, even 
statistically insignificant changes.

Now Steve is absolutely correct that I am just playing with numbers 
here. Why not allow total cost price to change when the inputs are 
transformed? No reason except that it would allow me to keep r the 
same, and we could see how little it could matter for the value 
theoretic determination of r that the inputs are transformed. 
Moreover, I have shown that it could be interesting if we treated the 
transformation tableau not in terms of simple reproduction but rather 
as one period in a realistic sequence.

But you object on other grounds:


"No, when the assumption of increasing labour productivity didn't
"do the trick" you introduced the additional assumption that the
_value_ of the means of production carried forward had
increased.  This was unrelated to your previous ad hoc
assumption, which implies only that the physical quantity of
means of production carried forward would be greater than that
used up at the outset.  The value of means of prod carried
forward can increase only if the rate of surplus value increases
or there is more labour employed.  Either of these assumptions
would, as I said, simply "change the subject" by altering the
value system that we were trying to transform to prices of

But you will see that you are absolutely wrong--I truly hope that you 
admit this; the value of the means of production remains 375 for both 
the inputs at t0 and the outputs at t+1. Where in the above did I 
change this?

What has happened is that we have modified (c+v's) for each of the 
three branches in accordance with the unit prices of production *for 
the inputs*.

  This means the krs or output price of production will change for 
each department as well.

The total prices of production for the input mp and wg will not equal 
the total prices of production for the output mp and wg, respectively.

For example, the sum of the output price of production for the means 
of production is now about 415 while the sum of the input price of 
production is only 400. 415 is the price of prod for the 375  natural 
units of mp at t+1; 400  is the price of production for the 357 
natural units of mp at t0.

But the total value of both remains 375. Now you may reply that it is 
unreasonable for the same value of mp to have two different prices of 
production  as inputs and outputs.

And you would be correct of course if we were still assuming simple 
reproduction but we are not! I am on my way to expanded reproduction. 
This is my point, and I truly don't see what is so difficult about 
it. Please respond to what I am saying.

There are three important things to note here.

1. The system is not incoherent, for the unit prices of prod are not 
changing unrealistically. In fact they are changing just as we should 
expect with rising labor productivity and a constant value of money..

2. Since we have not changed the total cost price or the total value 
in the system, the r in the system will remain the same.

3. there will be more total value/price at t+2 than there is at the 
completion of this period, t+1.

  This is primarily because  the *physical quantity* of the means of 
production and *the number of workers* carried forward increase.  Not 
the value as you say.

This conclusion follows simply from Marx's analysis:

...the development of labour productivity contributes to an increase 
in the existing capital value, since it increases the mass and 
diversity of use values in which the same exchange value is 
represented, and which form the material substratum, the objective 
elements of this capital, the substantial objects of which constant 
capital consists directly and variable capital at least indirectly. 
The same capital and the same labour produce more things that can be 
transformed into capital, quite apart from the exchange value. These 
things can serve to absorb additional labour, and thus additional 
surplus labour also, and can in this way form additional capital. The 
mass of labour  that capital can command does not depend on the its 
value but rather on the mass of raw and ancillary materials, of 
machinery and elements of fixed capital, and of means of subsistence, 
out of which it is composed, whatever their value may be. SINCE THE 
NEWLY ADDED TO IT GROWS AS WELL.  Capital 3, p. 356-7. vintage

That is, total value/price increases at t+2 from t+1 because of the 
greater quantity of use values at t+1 allows more labor to be 
absorbed in the following period. You will see that I have made this 
point twice to you. That is, I twice said that since at t0 we only 
had 286 wage goods, only 29 workers could be hired (assuming ten wage 
goods are needed for a working year); their labor hours are absorbed 
into the output at t+1.

  But since at t+1 we now have 300 wage goods, more labor hours will 
go into the output of t+2 (30 working years) , and for this reason 
total value will be greater than at t+1.

All the best, Rakesh

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