A Rejoinder to Mr. Murphy
Roger Garrison's Obfuscatory "Double Interpretation"
As poorly as this misunderstanding (whether to look to future consumption or past costs of production for the source of value) reflects on Murphy, this is not the principle source of his confusion. Murphy believes, incredibly, that supply and stock are the same thing, which leads him to contend that the only disagreement that I have with Garrison is over the use of an exponential or a linear construction. Actually, as early as 1990, Skousen was using an exponential function for his Aggregate Production Structure, APS, though not very well. "Skousen draws the APS as a slightly concave line which abruptly intersects the time axis (1990, p. 206 et passim), demonstrating that he never really believed it was exponential and/or he does not know what exponential functions look like" (Aguilar, p. 3).
In fact, the principle question that divides Garrison and myself is not the form of the graph (though that is important too), but what it represents: The Aggregate Production Structure, APS, represents income and the Distribution of Wealth over the Capital Structure, DWCS, represents wealth. This distinction has profound implications. In particular, attaching the APS to the Production Possibilities Frontier, PPF, as Garrison advocates (2001), puts a maximum limit on the interest rate.
Are supply and stock (or, more generally, income and wealth) the same thing? Murphy writes, "At the most basic level, there is nothing at all irregular about a graph meaning one thing ’and also something else.' For example, a physicist could graph the vertical displacement of an object against time, and say that the graph meant height and also the potential energy stored in the object" (Murphy, p. 2).
The obvious retort is that height and potential energy are linearly related, that is, one can be obtained from the other by an equation of the form y = mx + b. Potential energy is mass times the acceleration due to gravity times height. For instance, if an elevator cab with a mass of 920 kilos is raised to the top floor of a skyscraper 412 meters above the ground, it will have 3.7 MJ of potential energy, (920 kg)( 9.8 m/s2)(412 m). If the cable breaks, it will crash through the lobby with 3.7 MJ of kinetic energy. The potential energy of the elevator cab, in joules, is 9016 times its height, in meters.
A graph can mean height and also potential energy for the same reason that one can put Fahrenheit and Celsius side-by-side on the same thermometer. They are linearly related to each other: F = 1.8C + 32. Similarly, the displacements of American and also Japanese engines can appear on the same chart in spite of the fact that American manufacturers cite cubic inches while Japanese manufacturers cite liters. A liter is 61 cubic inches. They both measure the same thing, volume.
But are stock and supply linearly related? No. Supply is the derivative (change in) stock. The stock of houses in town is determined by driving up and down the streets and counting them. The supply of houses is determined by calling county records and asking them how many building permits have been filed recently. The units for the former are houses, e.g. "There are 5472 houses in town." The units for the latter are houses per year, e.g. "Twenty-eight new houses were built last year." In physics, this is the difference between position and velocity. If I am driving on the freeway, my position is five miles west of Phoenix and my velocity is 80 mph, eastbound. Not only do these two statistics have different units, but they are completely different things.
Every function has a unique derivative, but not a unique antiderivative. For instance, if f(x) = x2 + 5, then its derivative is f`(x) = 2x. But 2x has many possible antiderivatives, x2 + C, with C an arbitrary number. C could equal five, but it could also equal four or 327.28 or any other number. That is why antiderivatives are called indefinite integrals"because, without further information, we do not have any definite knowledge of what C is. Murphy is wrong when he claims that there is a one-to-one relation between stock and supply in the same way that there is a one-to-one relation between height and potential energy.
Garrison was obfuscating when he wrote, "The time dimension that makes an explicit appearance on the horizontal leg of the Hayekian triangle has a double interpretation. First, it can depict goods in process moving through time from the inception to the completion of the production process. Second, it can represent the separate stages of production, all of which exist in the present, each of which aims at consumption at different points in the future" (2001, p. 47). He knew very well that his triangle represented supply or he would not have attached it to the Production Possibilities Frontier, PPF, which illustrates how a nation's budget is partitioned. The term "production" is defined as how much of something is produced in one year, e.g. "Twenty-eight new houses were built (produced) last year." The term never refers to how much of a thing exists at the moment.
Murphy is no better. He gives an example of what is basically my DWCS (Murphy, p. 3) with wealth measured in wine bottles, both the 1987 vintage that are ready to consume now and the nouveau ones that that will not be ready for consumption until 2027, with the former being of more value than the latter because the latter are discounted for time-preference. As I describe, "Inventory items that do not depreciate are discounted for time-preference on the expected time until they make their contribution to final consumption" (Aguilar, p. 5). But then, after having illustrated my DWCS, Murphy easily slips into defending Skousen's conception of the APS and Garrison's plan to attach it to the PPF, apparently not noticing that he is now discussing something completely different from what he illustrated.
Here is a hint for the confused student: When your Austrian professor draws a triangle on the chalkboard (or an exponential function if you have one of the more enlightened professors who knows what exponents are), ask him, "What does the area under that graph represent?" If he answers, "the wealth of the nation," then his graph is of the DWCS, even if he has got it backwards, with the tail on the left. If he answers "gross national output" or some other phrase2 denoting national income, then his graph is of the APS. Now hold him to it! If he says his graph represents wealth and then, later, draws a PPF graph off to the right and connects the two figures with dashed lines, remind him that production is not wealth, it is income.
"Skousen is at least consistent but, unfortunately, he is consistently wrong. He definitely means the amount of goods flowing by every year. This seems to be the modern interpretation of Hayek's structure of production" (Aguilar, p. 5). It is because of his intellectual honesty that I chose Skousen's 1990 Structure of Production to be canonical. Garrison (2001) was also consistently wrong, particularly when he attached the Hayekian triangle to the PPF and thus inadvertently allowed the 100% limit on the marginal propensity to consume to put an upper limit on interest rates. But, with his talk of "double interpretations," he is too slippery to be considered canonical.
1 Murphy quotations Rothbard, "net saving means a change in the level of gross saving over the previous period of time" (Murphy, p. 4). Does anybody else think that this is what the word "net" means? Obviously, Rothbard did not understand the difference between a function and its derivative any more than Murphy does.
2 The letter O in Skousen's GNO can be either "output" or "outlays," which he considers synonymous.
3 Murphy writes, "I [Murphy] used [Skousen's] Economics on Trial when lambasting GDP figures in intro classes" (Murphy, p. 1). Since Skousen's alternative to the GDP is gross national output (1991, pp. 38-46), not the wealth of the nation, it is clear that Murphy, along with Garrison, are using Skousen's APS and consider the area under it to be GNO"income, not wealth. Murphy's attempt to distance himself from Skousen is, as far as I can tell, just infighting between the Mises Institute and the Foundation for Economic Education. Besides attaching the APS to the PPF and abandoning Skousen's abortive attempt to understand the exponential function, I see no evidence that Garrison has advanced or altered in any way the theory set forth in Skousen's "magnum opus," Structure of Production.