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A Rejoinder to Mr. Murphy
Victor Aguilar
Robert Murphy's Tactic of Blaming the Messenger
Note that, when I use the acronym APS, I am referring to the Aggregate Production Structure, a term coined by Skousen. Section I of my paper (Aguilar) is titled "The Aggregate Production Structure" and figures 1, 2 and 3 reprint Rothbard's (1970, p. 314), Skousen's (1990, p. 195) and Garrison's (1978, p. 174) conceptions of it. The originator of the term, Skousen, toys with the idea of it being exponential (1990, p. 195), though he does not seem to really know what exponential functions are. Rothbard depicts it as a histogram (1970, p. 314) while Hayek (1967, p. 39) and Garrison (2001, p. 47) depict it as a triangle. Basically, the term "Aggregate Production Structure" is a generalization of the Hayekian triangle to include exponential and histogram depictions as well as triangular ones. But the one thing that all of these men agree on, in spite of some obfuscation about double interpretations by Hayek (1967, p. 40) and Garrison (2001, p. 47), is that the term APS denotes income, not wealth.
When I use the acronym DWCS, I am referring to my own suggested construction, which is about wealth (that is what the W stands for), not income. Murphy writes, "I [Murphy] point out the grave defect that Aguilar's suggested construction breaks down if the (real?) interest rate exceeds 100%" (Murphy, p. 16), and then he quotations a passage from my Critique while omitting the introductory phrase, "If we define the APS to be Arert, then’" (Aguilar, p. 38). If he had quoted the entire passage it would have been clear that I was contrasting the maximum interest rate obtained by using a linear or an exponential function for the APS. I was examining Skousen's conception of the APS as being exponential.
Why does Murphy think that there is no negative sign in the exponent of Arert (Aguilar, p. 38)? That is because the APS has the tail on the left, going back into the past"all the way "back to axes carved by prehistoric men" (Murphy, p. 6). When I defined the Distribution of Wealth over the Capital Structure I wrote, "The DWCS is the exponential distribution scaled up by A, the wealth of the nation. That is, the DWCS is the function f(t) = Are-rt for 0  t < " (Aguilar, p. 14). Notice the negative sign? The DWCS has its tail extending to the right because it sees value in future consumption.6 Murphy is wrong when he refers to the APS as "Aguilar's suggested construction." The term Aggregate Production Structure, APS, and, specifically, the use of an exponential function for it, Arert without a negative sign, is Skousen's suggested construction.
My suggested construction, the DWCS, does not limit interest. The interest rate can be any finite, positive number. It is the inverse of the mean and, since I have defined the domain of the DWCS to be from zero to positive infinity and proven that it converges (Aguilar, p. 14), how could the inverse of its mean not also be defined for any finite, positive number?7 In the context of the APS, attaching it to the PPF requires that there be a maximum interest rate associated with 100% consumption. This is because, once one has decided to forgo saving any of one's income, nothing changes if one becomes even more devoted to immediate consumption.8 The DWCS cannot be attached to the PPF because the former is about wealth and the latter is about income, which, contra Murphy, are not the same thing.
6 "The definition of the produced means of production’ is a remnant of the cost of production theories of value’. But, except as a source of knowledge, the actual history of a particular thing’ is entirely irrelevant. It has nothing whatever to do with the decisions as to how the thing shall be used henceforth. Bygones are bygones in the theory of capital no less than elsewhere in economics. And the use of concepts which see the significance of a good in past expenditures on it can only be misleading" (Hayek, 1975, p. 89). If only Hayek's 1941 Pure Theory of Capital had been more widely read than his 1935 Prices and Production, with its backwards triangles, Murphy would not now, sixty years later, be seeing significance in past expenditures all the way "back to axes carved by prehistoric men" (Murphy, p. 6).
7 Only God, who is immortal, can have a real interest rate of 0%. Setting r = 0 would imply that every event, no matter how far in the future, is of equal importance. For us mortals, the interest rate and its inverse, the mean, can be any finite, positive number. In other words, the DWCS is defined to be exponential and, since the function f(t) = Are-rt is not exponential if one sets r = 0 or r = , r cannot take these values.
8 The marginal propensity to consume is currently (Feb 2007) at 101% for the United States, a record high. So 100% is not an absolute limit, but it can be just slightly exceeded, and then only by a country whose currency is accepted around the world by people who do not (immediately) need to convert their savings into their own currency. The Japanese, for example, sell us millions of cars a year and are willing to accept, in exchange, dollar-denominated savings accounts even though dollars cannot be used for making purchases in their homeland.
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