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Chris Harman, economic dynamics, simultaneous equations

March 16, 2013

It’s ten years ago this month that the Marxist economist Michael Kidron died. Kidron’s work today is woefully and unfairly neglected, but his concerns – around the fusion of state and capital, and environmental destruction especially – now look far ahead of their time.

It was in the course of writing an appreciation of Kidron that I was ended up rereading Chris Harman’s Explaining the Crisis, and noticed a glaring theoretical flaw I’d failed to spot in the past (pp.24 et seq.). Harman, in seeking to defend an orthodox interpretation of Marx’s Capital with the falling rate of profit as the principle theory of crisis, attacks those making use of simultaneous equations solutions to the transformation problem.  (It’s around about here that things are going to get obscure – apologies.) In particular, he – correctly – indicates that input prices for commodities used in production will vary from output prices, but then claims that the use of simultaneous equations solutions to the price system enforce an equation between the two. His preferred “solution” to the transformation problem involves taking a set of input prices for the production process, and then allowing them to be transformed (through the production process) into a different set of prices. The prices change because of the application of labour to the input commodities; the new output necessarily reflects a different labour content. Simultaneous equations solutions, Harman claims, collapse this dynamic process of production.

But this won’t do. As Ajit Sinha notes of Andrew Kilman’s Reclaiming Capital, in his devastating review, it involves a fundamental misunderstanding of the procedure of simultaneous equations. The problem is that once the outputs have been produced by the economy, they then re-enter a further round of production, forming another new set of input prices. This process is continuous under capitalism: the system does not just produce (say) one year’s worth of output, and then stop. In other words, we can’t just calculate one round of production – we have to keep running the system forward until we arrive at a stable set of prices for the economy, so that every year’s worth of output forms the following year’s input, and so on.

This is precisely what the simultaneous equations method attempts to do: they attempt to show how the system, on the basis of Marx’s assumptions about the labour theory of value, produces a stable set of prices for all commodities produced. All Harman has done here is to (in effect) follow the first step in finding  a solution to simultaneous equation solution, and then declare that the entire system is thereby solved. It isn’t.

So Harman got the working substantially wrong – echoing, it would seem, the same error made by Marx. His defence, in Explaining the Crisis, of the falling rate of profit, collapses as a result of it. But he got the *intuition*  correct. It is absolutely true that capitalism is a dynamic system because it depends on the production of commodities, not just “by commodities” (in Sraffa’s phrase) but over time by labour. Simultaneous equations solutions to the price system assume away too much, collapsing that dynamic production process into a problem of the exchange of produced commodities only. To grasp that dynamic, however, requires to specify it properly – the “commonsense” solution provided by Harman, and its scholastic elaboration by Kliman, is not adequate to the task. The approach of Duncan Foley (1982), specifying formally the dynamic systems of prices and values, looks much more promising – and has been used fruitfully in recent work by Paulo dos Santos and Giorgos Galanis, for instance. As far as I can tell, Harman never referred to it, which is a great shame: his basically correct insight might not have lead, then, to a basically incorrect theory.

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One comment

  1. […] But this takes us right back to where we started. The method we have applied, following Harman’s own economic logic, gets us to a stable economy-wide rate of profit. But this method is identical to solving a simultaneous equations problem, and gets us to an identical outcome! All we have done is apply a recursive technique to finding the solution. Harman’s “critique” of simultaneous equations methods is nothing of the sort – it is simply the first step in finding the solution to a simultaneous equation. (I have blogged on this earlier.) […]



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