"The Impossibility ... [Of] ... A Single Magnitude Representing ... The Quantity Of Capital"

Figure 1: From Sraffa's Production of Commodities by Means of Commodities

Suppose people save more. A neoclassical and Austrian school¹ idea is that then the supply of capital will have increased, in some sense. One would expect its price, the rate of interest, to be less, absent intervention by the monetary authorities. Entrepreneurs, if they were alert, would adopt more capital-intensive - that is - longer techniques of production. After these techniques came online, output per worker would be higher.

Suppose that the length of the period of production of a technique were defined in terms of purely physical data. Given a complete list of inputs and outputs, including the times at which they flow into and out of the production processes, one would be able to measure the (average) period of production of the technique composed of those processes. Then reswitching shows the above story cannot be universally valid.

Austrian-school economists and economists sympathetic to the Austrian school have had at least two reactions to this demonstration of the logical invalidity of the above story. One reaction is to assert that an aggregate measure of capital-intensity, such as a physical measure of the average period of production, is not needed for the story to go through. Supposedly, entrepreneurs shift resources, in response to low interest rates, to time periods further before the production of consumer goods. In the technical jargon, entrepreneurs tend to move resources towards producing goods of higher orders and away from producing goods of lower orders. I have shown² that this response fails to evade a critique based on reswitching.

The second reaction is to define the average period of production as dependent on the interest rate, as well as physical properties of techniques of production. Thus, the average period of production for a given technique will be different at the interest rates associated with different switch points. Apparently, Edmond Malinvaud, drawing on some work of J. R. Hicks, made this argument in a 2003 paper about Knut Wicksell's contributions. Saverio Fratini, in his paper presented at the recent 50th anniversary conference on Sraffa's book, took the opportunity of Malinvaud's paper to argue that this reaction also cannot be sustained as a response to a critique based on reswitching and capital-reversing.

I associate this second reaction with Leland Yeager, who, in a couple of papers in the late 1970s, argued that waiting has the dimensions of the product of value and time (for example, dollar-years). I find it hard to find a valid non-tautological argument here. I think Fratini's paper could be revised to point out that he refutes Yeager, as well as J. R. Hicks and Edmond Malinvaud. I would like to be referenced too, although I don't know about the conventions of referencing working papers.

Footnotes
¹ Both William Stanley Jevons and Eugen von Böhm-Bawerk expounded this idea.
² Due to a recent hard-disk crash, I have lost originals from which I generated some PDFs, as well as reviewer comments on recent revisions.
References

• Saverio M. Fratini (2010). "The Hicks-Malinvaud Average Period of Production and 'Marginal Productivity': A Critical Assessment", Sraffa’s Production of Commodities by Means of Commodities 1960-2010, Roma, Italy (2-4 Dec.)
• Robert L. Vienneau (2010) "Some Capital-Theoretic Fallacies in Garrison’s Exposition of Austrian Business Cycle Theory"
• Leland B. Yeager (1976). "Towards Understanding Some Paradoxes in Capital Theory", Economic Inquiry, V. 14: pp. 313-346
• Leland B. Yeager (1979). "Capital Paradoxes and the Concept of Waiting", Time, Uncertainty, and Disequilibrium: Exploration of Austrian Themes (ed. By Mario J. Rizzo), D. C. Heath and Company