# Re: [OPE-L] equilibrium and simultaneous vs. sequential determination

From: Fred Moseley (fmoseley@MTHOLYOKE.EDU)
Date: Mon Sep 17 2007 - 21:41:35 EDT

```Quoting Ian Hunt <ian.hunt@FLINDERS.EDU.AU>:

> Dear Fred,
> I am a bit puzzled by this: the Sraffians have a model of the profit
> rate per 'year', with joint products dealing with inputs that are not
> entirely 'consumed' in a 'year'. The 'year' can be set as the least
> turnover period of capital to deal with variations of turnover
> periods, where the turnover periods are less than an astronomical
> year. You then have to calculate the annual rate of profit from the
> rate of profit per 'year', which involves compounding the 'yearly'
> rate of profit over the no of 'years' annually,

I think that you are confirming what I have been saying about Sraffian

As I understand you, all industries are assumed to have the same basic
turnover period, which is equal to the least turnover period.  Inputs
that are not entirely consumed within this period are treated as joint
products.  Treating these longer lasting inputs as joint products in
effect assumes that all industries have the same turnover period (the
“least turnover period”), and all inputs are turned over in this
period.  The “joint product” method in effect turns all fixed capital
into circulating capital, and assumes an equal turnover period of
circulating capital in all industries.

So it is not only fixed capital proper (lasts longer than the actual
turnover period in each industry) that is treated as a joint product,
but also circulating capital proper (consumed entirely within the
actual turnover period of each industry) in all industries whose
turnover period is longer than the “least turnover period”.  That’s a
lot of “joint products”.

And what happens if the turnover period in an industry is 1.5 times as
great as the “least turnover period”, or any number that is not a
multiple of the “least turnover period”?  The “joint product” method,
which was used by Sraffa WITHIN a single industry (to convert fixed
capital to circulating capital within a single industry), seems to
break down when used ACROSS industries (to convert unequal turnover
periods of circulating capital in all industries into the “least
turnover period”).

But this is not all.  In all industries with turnover periods greater
than the “least turnover period” (i.e. most industries), not only are
the inputs not entirely consumed, but also the products are not fully
produced.  How does the theory deal with these incomplete products?

Ian, do you think that real-world equilibrium prices are determined
simultaneously at the end of each and every of these “least turnover
periods” (including the equilibrium prices of the inputs as “joint
products”), as this theory suggests?  Wouldn’t prices be different
depending on the length of the “least turnover period”?  And wouldn’t
prices change if the “least turnover period” changed?  Is this
plausible?

I would argue instead, based on Marx’s theory, that real-world
equilibrium prices are determined by costs plus the average rate of
profit.  Costs are taken as given, and the average rate of profit is
determined by the labor theory of value.  Costs are calculated over the
actual turnover periods in each industry, not over the “least turnover
period” in the economy.

Thanks again.