From: ajit sinha (sinha_a99@YAHOO.COM)
Date: Thu Jun 08 2006 - 14:44:15 EDT
--- Ian Wright <wrighti@ACM.ORG> wrote: > Hi Ajit > > Apologies for the delay in getting back to you. > > > Ian, now I'm almost convinced that you are making > a > > conceptual error. Take for example Sraffa's > two-sector > > subsistence example: > > 280 qr. wheat + 12 t. iron --> 400 qr. wheat > > 120 qr. wheat + 8 t. iron --> 20 t. iron > > This is self-replacing subsistence economy. Here > you > > have no problem with the price solution of 1/10. > > Yes. > > > Now, let's make it a surplus economy by making one > sector > > more productive such as > > 280 qr. wheat + 12 t. iron --> 400 qr. wheat > > 120 qr. wheat + 8 t. iron --> 30 t. iron > > So the system has 10t. of iron as surplus and let > us > > assume that the capitalists consume the 10 t. of > iron, > > so it is a system of simple reproduction. Now, how > do > > you solve for prices in this system? > > The same way as Sraffa, when this economy is > represented by Sraffa's > surplus equations. However, prices are solved in > terms of a > higher-dimensional homogenous system of equations > when this economy is > represented as a circular flow. The price solutions > are the same in > both cases. > > > Sraffa says that > > you write the system as: > > [280P(w) + 12P(i)](1+r) = 400P(w) > > [120P(w) + 8P(i)](1+r) = 30P(i) > > This solves for r and P(w)/P(i) > > Yes. Note that the extra 10t. of iron for capitalist > consumption is > already treated as a nominal cost in these > equations. > > > But you want to put the 10t. of iron back on the > left > > hand side of the equation so that it becomes like > the > > first subsistence equations. However, the question > is > > how do you allocate the 10t. of iron to the two > > sectors? > > The short answer is that the 10t of iron is not > allocated to the two sectors. > > In the circular flow representation of this > 2-commodity economy there > are 4 sectors: 2 for iron and wheat, 1 for worker > households and 1 for > capitalist households. The 10t. of iron is allocated > to a single > sector, the capitalist household sector. It is not > directly allocated > to either of the iron or wheat sectors. However, I > don't think this > affects the underlying point you are trying to make. > > > You agree that it has be to allocated in > > terms of the profits received by the capitalists > in > > the two sectors and the rate of profits on the > value > > of capital investment must be equal. But then > there is > > no way of finding how to allocate the 10t. of iron > to > > the two sector capitalists unless you solve > Sraffa's > > equations. > > Yes that is true. > > Capitalist consumption coefficients (in contrast to > capitalist > consumption) is the vector of real consumption per > unit of > money-capital supplied. > > I think you mean to say that "there is no way of > finding" the > capitalist consumption coefficients unless we know > the prevailing > prices of production. That's because capitalist > consumption is per > unit of money-capital supplied, but money-capital > supplied depends on > prices. Is this a correct interpretation of your > point? If so, I agree > with you, but not with the conclusion you draw from > this. > > Consider the following: if we start from Sraffa's > surplus equations > then we do solve Sraffa's surplus price equations in > order to > construct the circular flow representation. The > money-capital > coefficients and the capitalist consumption > coefficients are > determined upto the choice of numeraire equation. > Hence, from this > starting point, the circular flow matrix has a > degree of freedom and > is parameterised by a numeraire equation. There is > an infinite set of > circular flow representations corresponding to the > infinite set of > Sraffian price solutions. If a numeraire equation is > specified then an > element from each set is chosen. Their price and > quantity solutions > are mutually consistent. > > This manifests in a simple way in the corn-economy > example in the > appendix of my paper, which will be easier to follow > compared to > Sraffa's 2-commodity example. > > Sraffa's lower-dimensional surplus equations are > embedded in the > higher-dimensional circular flow. ______________________ Ian, I took a look at your corn-economy model. I think it confirms the conceptual error I am talking about. In your corn model, when the rate of profit is zero your real cost accounting and Sraffa's labor-value accounting give the same result, that is the labor-value of 1t. of corn is 500 hours. Then you cut the wages of workers in half, and a rate of profit of 66.3% emerges. Now, in this case also, Sraffa's labor accounting gives you the same labor-value equal to 500; however, your real cost accounting says that the labor-value in the second case must increase to 1000 hours. At this stage, I think, you should have paused for a minute and thought in English rather than mathematics. How could one by simply taking food from the laborers and giving it to the capitalists increase the labor-values of goods? You are saying that the labor-time needed to produce a ton of corn doubles simply by taking half of the corn from the mouth of the laborers and giving it to the capitalists. Now, there has to be something wrong with such a statement, isn't it? The whole question of numeraire and also money in one good corn model makes no sense to me. Here again it seems you have allowed mathematics to take precedence over common sense. Any way, let's stick to my above comment for now. We can discuss all the other issues later, but this one needs to be settled first. Cheers, ajit ___________________________________ > > > But once you have done that the 10t. of > > iron must be treated as 'surplus' and cannot any > > longer be treated as cost. > > Here I do not quite understand you. The 10t. of > wheat is already a > nominal cost in Sraffa's surplus equations. That's > because the surplus > is nominally distributed. > > However, perhaps your concern is with real costs. > The 10t of wheat can > be treated as a real-cost, despite the money-capital > and consumption > coefficients being dependent on the numeraire > equation. This is a > subtle point, but prices cancel when constructing > the technique > augmented by capitalist consumption. Again, this can > be clearly seen > in the corn economy numerical example. This matches > our intuition -- > as real-costs cannot depend on the scale of the > price system. > > > That's why Sraffa said that > > once surplus emerges in the subsistence system, > the > > system becomes self-contradictory. This conceptual > > error of your must show up in your mathematics. > And as > > I have suggested in my previous mail, I think your > > system must be short of one equation. Cheers, ajit > > I think there is probably an important underlying > point that is > motivating your remarks, which you have not yet > managed to > communicate. Maybe you are concerned that because > the rate of profit > manifests as a price in the circular flow then this > will upset > Sraffa's critique of naive marginalism. For what > it's worth, I think > his circularity critique is not threatened, although > I have not spent > time on this aspect. > > Best wishes, > -Ian. > __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com
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