# Re: [OPE-L] models with unequal turnover periods

From: Ian Hunt (ian.hunt@FLINDERS.EDU.AU)
Date: Mon Sep 24 2007 - 00:44:43 EDT

```Dear Fred,
I am a bit puzzled. Turnover periods are relevant to the rate of
profit. So, in the equations I gave you earlier, they entered into
the capital stock matrix K. When the rate of profit is zero, as it
would be if you wanted to use the equations to calculate labour
values (this is so both in Brody's system and Sraffa's, although
Brody calculates rate of profit on variable capital also, while
Sraffa treats profits as a fraction of value added ), the turnovers
of capital disappear. However, for fixed constant capital flows, they
still indirectly enter the value flows per period. Whatever period
you take, anything whose value is not entirely consumed in that
period will give up its value, as Marx says, in more than one period,
so  you cannot simply take the value of an output as its value as an
input.

So, I do not assume uniform turnover periods in calculating values
where they are not relevant, nor do I assume equal turnover periods
when they are relevant, in calculating the rate of profit.

While the flow of value from a piece of fixed capital will vary with
its age and efficiency, the flow from a balanced stock (with items
from every age) can be represented as its value divided by its age.
Strictly speaking, the economic age of fixed capital depends on
prices but we can take it as empirically determined, since
capitalists are not fully profit maximising in conditions of limited
information and imperfect competition. With joint products you get
another complication which  can be solved if you take value to be
divided among components of output in proportion to their prices.
(Details on this can be found in the mathematical appendix of my
paper "The Labors of Steedman on Marx" in RRPE, 14: 4 (1982): 65-68.)

As to partly finished goods, I will look for the references for you.
This may take some time.

On "real world equilibrium prices of production", I agree with Jerry
that there is nothing real world about them, especially if you are
looking for prices which hold when activity levels are constant. I am
aware that you after these but I think the quest is under motivated.
There is only a tendency for profits to be proportional to capital
advanced,  for uniformity of prices, for elimination of inferior
techniques. I think we would all do better thinking of the labour
theory value as having purposes other than determining long run
equilibrium prices of production,
Cheers,
Ian

Associate Professor Ian Hunt
Dept of Philosophy
School of Humanities
Flinders University
Box 2100, GPO,

On 23/09/2007, at 2:34 AM, Fred Moseley wrote:

> Quoting Ian Hunt <ian.hunt@FLINDERS.EDU.AU>:
>
>> Dear Fred,
>> It is what Medio does. Brody shows that inputs can be measured in the
>> quantities of any basic good and doesn't think there is any decisive
>> reason for favouring value as the units. My view is that value is
>> favoured because control and discipline of social labour is in all
>> industries a crucial component of social relations of production.
>>
>> In the simple case, assuming one technique of production of
>> production and no fixed capital or joint products you can get the
>> value units from the equation l = A l + L. You can get the value
>> units in more complicated cases, but they will depend on expectations
>> of profitable lifetimes of machines (to get the flow of value from
>> fixed capital) and prices of products for dividing the value of
>> output between joint products.
>
> Hi Ian,
>
> How are unequal turnover periods taken into account in this equation?
> Does it assume that all industries have the same turnover period?
>
> Would you please also give the equation(s) for fixed capital, since
> Medio does not do that?  And what are the elements in the A matrix
> that
> correspond to fixed capital?  How are they determined?
>
>
>> Sraffa was engaged in a different exercise from regarding the
>> division of social labour as the the basis of laws of development of
>> commodity production (He was interested in the inverse dependence of
>> the rate of profit on wages rather than laws of development)
>
> I am not talking about a theory of “laws of development”, but rather a
> theory of long-run equilibrium prices, that takes into account unequal
> turnover periods across industries.
>