A Reply to Aguilar
Robert P. Murphy
Part I: The Legacy of Friedrich Hayek
Section IV: The Average Period of Production
In this section, Aguilar once again intersperses substantive criticisms with ones that unfairly paint his foes as innumerate boobs. For example, he quotations Garrison's description of the Hayekian triangle where "the slope of the line is the (simple) rate of interest (profit) when the economy is in equilibrium." Aguilar then retorts, "No, it is not. Compound interest is exponential and interest is always compounded’there is no such thing as ’simple' interest" (p. 11). To make sure the reader understands just how ludicrous Garrison's statement is, Aguilar in a footnote continues: "Nobody accepts that the rate of interest can be represented by the slope of a straight line. That might have worked for a 1930 lecture, but today anyone with $20 can buy a calculator programmed to do time-value-of-money calculations. They may not understand the math, but they know very well it is not linear."
Now this is really too much. The absolute most Aguilar could fairly have said, is that using simple interest is so unrealistic as to render Garrison's diagram unsuitable for its intended purpose. Other than that, Garrison's claim is perfectly true. Simple interest does mean just what Garrison says; if Aguilar doubts this he should Google the term. Moreover, Garrison and other Austrians are perfectly aware that simple interest isn't used in actual business transactions (especially over several years), but then again Garrison explicitly acknowledges this unrealism when discussing the triangle (and Aguilar quotations him doing just this in the conclusion to the Critique). Garrison knows that the spot price of a bond grows exponentially over time, not linearly, but feels (perhaps incorrectly) that this extra realism wouldn't shed much light on the burning issues of capital-based macroeconomics. Not only do I excuse Garrison on this point, but I would go further and say that even the audience members at the LSE in the 1930s knew that exponential growth isn't linear.
But on to the more substantive disagreements. Aguilar recommends that Hayekians stop using the word average because it doesn't mean what they think it means. This too I find largely a semantic quibble; I have heard plenty of people use average as a general term, which could include the mean, median, and mode under its umbrella. In any event, Aguilar thinks that what the Hayekians really mean to say is "the midpoint, half the range." (I note that under the conditions Hayek specifies’namely "in which the original means of production are applied at a constant rate throughout the whole process of production"’his terminology and calculation are perfectly correct.) This is problematic, according to Aguilar, because "neither average nor range [has] any meaning in the context of a continuous distribution defined out to infinity" (p. 12).
It seems that here Aguilar is arguing that his own preferred construct, the DWCS, is constructed from time = 0 to infinity, and since average and range are undefined on such a beast, therefore the Hayekians are in trouble. Again, a quick way out of the difficulty is to realize that average and mean can be interchanged without too much violence to mathematical purity; for the simple (and unrealistic) case Hayek is considering, the mean will work, and this can be defined on a distribution with an infinite domain.
Yet this response overlooks the real problem with Aguilar's formulation. Although he may be right that the Hayekian approach is bankrupt, even so Aguilar's suggested fix doesn't fit the bill. Again, Hayek is trying to describe the entire capital structure that must be maintained if one is to yield a constant stream of consumption goods. This capital structure cannot be defined from the initial time to "infinity," for the simple reason that people can't wait forever to eat (or drive cars or watch TV).
It's true that in the simplest baseline case, what Mises and Rothbard would call the ERE, the periodic output of TVs, cars, apples, etc. would be extended out to infinity. Even so, the structure of production supporting that constant, periodic flow would be finite. In the B’hm-Bawerkian framework, labor and natural factors flow into the production process at the higher stages, flow down to the lower stages, and are finally "released" in the act of consumption. His notorious concept of the average period of production was designed to quantitatively assess how long a unit of factor inputs was "tied up" in the pipeline. Whatever Aguilar's other objections, he can't condemn Hayek for relying on something that is finite in scope. The original factors are necessarily tied up for only a finite time.
Aguilar next goes on to demonstrate the superior precision of his own approach, and in particular his ability to determine precisely where the "fulcrum" point is when interest rates change. In contrast, the Austrians know that there must be some intermediate stage that is unaffected by the change, yet they can't really say which one.
On this point I am in total agreement with Aguilar. If Austrians are going to go to the trouble of using geometry to aid in their exposition, it's not such a qualitatively worse heresy to use algebra and calculus, either. Having conceded the methodological point, though, I would suggest that Aguilar read further in the literature, for there are much more mathematically elegant treatments of B’hm-Bawerkian capital theory than those of Hayek. In particular Samuelson's famous paper, "A Summing Up,"4 as well as Dorfman's graphical exposition,5 would be good places to start if he hasn't read them already.6
4 Quarterly Journal of Economics, 1966.
5 Review of Economic Studies Feb. 1959.
6 He might also keep an eye out for my own "Interest and the Marginal Product of Capital: A Critique of Samuelson," forthcoming in The Journal of the History of Economic Thought probably sometime in late 2007.
