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

From: Ian Hunt (ian.hunt@FLINDERS.EDU.AU)
Date: Wed Sep 12 2007 - 08:11:50 EDT


Dear Fred,
The system that is explicitly based on Brody is 
in the footnotes. With one slip fixed up, it is:

p (C + vl + Kr) = p,
where C is the matrix of constant capital inputs 
(cij) , ie the matrix of inputs j into the 
production of i per year, v is the wage bundle 
per hour, l is the vector of labour inputs li 
into the production of i per year, and K is the 
matrix of capital stocks cij . tij + vli . ti , 
where tij is the turnover period of the capital 
input j into the production of i and ti  is the 
turnover period of the variable capital input in 
the production of i. The turnover periods are the 
capital stock inputs divided by the capital flow 
inputs. I hope this is clear enough,
Cheers,
Ian

>Quoting Ian Hunt <ian.hunt@FLINDERS.EDU.AU>:
>
>>Dear Fred,
>>My paper explicitly refers to the turnover period of capital in
>>industry i, so that implicit in that is the possibility that. It is
>>not the same as Medio's. It is based in fact on Brody and I only
>>follow Medio in taking prices to be prices per unit of value (Medio's
>>theory is does not distinguish between fixed and circulating by
>>making the assumption you mention).
>
>Hi Ian,
>
>Thanks for your clarification.
>
>I will take another look at Brody (although unfortunately neither I nor
>my library has a copy).  Maybe Brody is an improvement over Sraffa on
>the issue of turnover times.  We shall see.
>
>I wondered what the Sraffians think about Brody’s treatment of fixed
>capital and turnover time, and I took a look at Kurz and Salvadori’s
>Theory of Production. There is one reference to Brody in 500 pages, and
>it is about heterogeneous labor, not turnover time.
>
>I will try to return a consideration of Brody's treatment of fixed
>capital and turnover times, when I get a copy of the book, and as time
>permits.  In the meantime, would you please summarize for me your
>system of equations that determines prices of production and the rate
>of profit.  This is not clear to me from your article.  Thanks.
>
>Comradely,
>Fred
>
>>The turnover of capital in industry i = the turnover of fixed capital
>>in i plus the turnover of period of constant capital in i plus the
>>turnover period of variable capital in industry i. These turnover
>>periods are not assumed to be equal across industries in any of these
>>cases. I get turnover periods by distinguishing between stocks and
>>flows. The rate of profit, of course, is the annual rate of profit on
>>my model but it can rise and fall because of changes in turnover
>>periods. Thus one counteracting tendency to the tendency of the rate
>>of profit to fall is that the turnover period of constant and
>>variable capital in some industries declines, due eg to "just in
>>time" inventories of parts. The applicability of "just in time', of
>>course, varies between industries.
>>
>>I don't think that my model makes any assumption about when
>>commodities are exchanged, although it does assume that the rate of
>>profit on capital is a temporal rate. It does make some
>>idealizations, of course: prices per unit of value are really
>>averages of a range of prices per unit of a range of values, etc. The
>>assumption that the price of inputs is the same as the price of
>>outputs is based on the fact that purchases and sales of a product
>>intermingle, so that the price of a commodity as an input and its
>>price as an output will be determined on the same day for at least
>>some firms.
>>
>>Turnover periods are different because different stocks of money
>>capital are required to generate different sorts of flows: relating
>>the distinction between stocks and flows to exchange is just
>>confusing: in fact, for really small turnover periods (less than 1,
>>say, if a year is taken as the reference point) you have to have
>>stocks of capital replenished by sales that occur in shorter periods
>>than a year (one of the bases of the separation between commercial
>>and industrial capital is just that effect)
>>Cheers,
>>Ian
>>
>>>Quoting Ian Hunt <ian.hunt@FLINDERS.EDU.AU>:
>>>
>>>>Dear Fred,
>>>>The paper is titled 'An Obituary or a New Life for the Tendency of
>>>>the Rate of Profit to Fall' and can be found in  Review of Radical
>>>>Political Economics, 15:1, 1983, pp. 131-148. It has got a few typos
>>>>in it (URPE did not in those days always return the text to authors
>>>>for checking) but these are relatively easy to sort out - if you have
>>>>any trouble let me know and I will tell you what they are supposed to
>>>>be. I am trying to produce a decent scanned copy: if I do, then I
>>>>will send that electronically, with typos fixed.
>>>>
>>>>By turnover period, I mean the sum of the turnover period of fixed
>>>>capital plus the turnover period of constant capital plus the
>>>>turnover period of variable capital, which can of course all differ
>>>>and contain different variants. These differences are explicitly
>>>>taken into account in the paper.
>>>
>>>Hi Ian,
>>>
>>>The differences in turnover periods between fixed (constant) and
>>>circulating (constant and variable) capital are not what I am talking
>>>about.  Rather, I am talking about the differences in turnover periods
>>>of circulating capitals in DIFFERENT INDUSTRIES.  These differences are
>>>not taken into account in your paper.  Your paper is based on Medio’s
>>>model which explicitly assumes an equal turnover period in all
>>>industries.  Medio wrote (p. 332):  “Consider an economy of n
>>>industries, each of them producing a given amount of a single commodity
>>>in a GIVEN INTERVAL OF TIME, let us say a YEAR.” (emphasis added)  This
>>>is the assumption I am talking about.
>>>
>>>And my point is that this is a necessary assumption in Sraffian theory
>>>because, if there were unequal turnover periods, then the rate of
>>>profit determined by the simultaneous equations would be equalized
>>>across different turnover periods, which in turn would imply unequal
>>>annual rates of profit, contrary to the prevailing tendency.  Plus,
>>>simultaneous determination requires that all commodities are exchanged
>>>at the same time, which in turn requires that they all must have the
>>>same turnover period.
>>>
>>>Comradely,
>>>Fred
>>>
>>>
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>>
>>
>>--
>>Associate Professor Ian Hunt,
>>Dept  of Philosophy, School of Humanities,
>>Director, Centre for Applied Philosophy,
>>Flinders University of SA,
>>Humanities Building,
>>Bedford Park, SA, 5042,
>>Ph: (08) 8201 2054 Fax: (08) 8201 2784
>>
>
>
>
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--
Associate Professor Ian Hunt,
Dept  of Philosophy, School of Humanities,
Director, Centre for Applied Philosophy,
Flinders University of SA,
Humanities Building,
Bedford Park, SA, 5042,
Ph: (08) 8201 2054 Fax: (08) 8201 2784


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