Wednesday, May 24, 2006

Corn Models

D-Squared recommends my blog. I showed this to one of my colleagues, and he had trouble reading to the end, what with laughing and all. I suppose he liked this:
"Sraffians also have a frightening habit of creating 'simple examples' to illustrate their system; this is Sraffian for 'something which starts off by calmly claiming that there are two goods called corn and iron, and five minutes later has ballooned into a wretchedly complicated optimisation problem with no differentiable production function, no equilibrium and all sorts of strange terminology, illustrated with a graph that is if anything more incomprehensible than the model'."

D-Squared is talking about examples like in this series of posts. The equilibrium here is my add-on to Garegnani, but I suppose some find Figures 5 or 6, for example, drawn to D-Squared's specs.

When Sraffians talk about the "corn model", however, they usually are referring to something different. They are talking about the interpretation of Ricardo Sraffa puts forward in his (and Dobb's) introduction to the first volume of The Works and Correspondence of David Ricarod (otherwise known as Ricardo's On the Principles of Political Economy and Taxation).

The model on page xxxi of the introduction is easily explained. Consider an economy in which a single agricultural commodity, "corn", is produced. Suppose the capital goods used up in producing corn consist solely of corn (i.e., seed corn). And suppose workers are paid solely corn, which is treated as exogeneously specified, at least as far as the theory of value goes. Profits in agriculture, the excess of the corn produced in the year over the corn advanced for seed and wages, also consist of a physically specified quantity of corn. So you can see that the rate of profits is physically determined in agriculture. In industry, outputs and inputs are heterogeneous, since wages are still in terms of corn and outputs are some other commodity. Thus, if a tendency exists for a common rate of profits to be established among all sectors in an economy, the prices of manufactured commodities must adjust to bring the rate of profits in industry to equality with that in agriculture.

This model helps Sraffa explain Ricardo's interest in the Labor Theory of Value. Workers consume a mixture of commodities, and Malthus insisted that in no industry are the advances and output composed of the same commodity. But if one evaluated commodities in terms of the labor embodied in them, one could form a physical ratio of labor values of the ouput of agriculture (on marginal land) and the labor values of the capital advanced, including the labor value of wage goods. Thus, if the Labor Theory of Value were true, Ricardo would be able to retain the insights of the corn model.

Sraffa explicitly states the corn model "is never stated by Ricardo in any of his extant letters and papers." Sraffa hypothesizes Ricardo put forward the corn model in lost letters and papers in March 1814 or in oral conversations with Malthus. All interpretations of "what Ricardo really meant" have been hottly disputed in the last third of a century or so. Probably Samuel Hollander is the most learned opponent of Sraffa's interpretation to read. It doesn't help matters that Ricardo and Malthus, in their letters, would often formulate their claims in terms of (what they took to be) the other's system. This makes it very confusing to figure out who is claiming what, instead of merely echoing back what they think their opponent is saying. They probably sometimes confused themselves.

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