From: Ian Wright (wrighti@ACM.ORG)
Date: Mon May 07 2007 - 13:44:46 EDT
> "the big problem is that Sraffas matrices, unlike Heisenbergs, are not unitary, and as > such do not express conservation relations." I think this is a very important point, but the root cause of non-conservation in PCMC lies elsewhere. The lack of conservation in Sraffa's matrices arises from his transition from Ch.1 to Ch.2, i.e. production for subsistence to production with a surplus. This is because Sraffa tries to combine two approaches: (i) The concept of a circular flow, in which a network of economic relations are formalized in terms of simultaneous equations; and (ii) the concept of an undistributed surplus; a surplus that, by definition, does not have a corresponding cost. An undistributed surplus breaks the symmetries between costs and revenues (whether nominal or real) that obtain in a circular flow. Hence Sraffa's matrices are non-unitary, and conservation is broken. There are revenues that have no corresponding costs (i.e. "matter appears from nowhere"). But Sraffa immediately restores the symmetry in the price system by specifying a nominal distribution of income. Hence Sraffa's price equation is conservative: all costs and revenues simultaneously balance. Yet Sraffa does not restore the symmetry of the real cost system (e.g. labour-values) by specifying a real distribution of income. If we do this the resulting matrix is unitary. We get a closed system of simultaneous equations. But contra Sraffa, this does not imply that there is no surplus or that the economy is subsistence. It merely implies that the surplus is distributed, and is now part of the normal cost structure of the economy. I think that trying to theorise the consequences of a symmetry-breaking event that results in an undistributed surplus using the tools of simultaneous equations is a non-starter. So I agree with Joan Robinson when she says that Sraffa had "half an equilibrium system". Best, -Ian.
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