Critique of Austrian Economics
Part I: The Legacy of Friedrich Hayek
Section III: Sideways and Backwards?
The first thing any mathematician will say about the graph of the APS (Figures 1 and 2) is that it is sideways and backwards. From Skousen’s equations 1 and 2 it is clear that time, t, is the independent variable and independent variables always go on the horizontal axis, not the vertical one.
Hayek (1967, p. 41) writes:
It is convenient to treat the quantity of intermediate products at any point of this stream as a function of time f(t) and accordingly the total quantity of intermediate products in the stream as an integral of this function over a period p equal to the total length of the process of production. |
Having written that he would “treat the quantity of intermediate products as a function of time f(t),” Hayek too should have known better than to put the independent variable, time, on the vertical axis.3
Thus, for the DWCS, time goes on the horizontal axis. But should we put consumption goods to the left and investment goods to the right, or the other way around? In other words, does time run forwards or backwards?
Skousen writes, “Capital goods manufactured prior to the current year are not incorporated in the APS even though they may be used in the production of current goods and services” (1990, p. 185). But then he contradicts this view by writing that “the APS can be viewed as a representation of the economy in the past, present, and future” (p. 197). He got it wrong both times. The DWCS includes all wealth currently in existence, which was (of course) all manufactured in the past. But its date of manufacture is irrelevant since its value is determined entirely by considerations of the future. By the subjective theory of value, all goods are valued for their contribution towards future consumption, not for their past cost of production.
Thus, consumption goods should be on the left side of the graph at time zero. That is why producers’ goods are called “higher-order goods;” because they get a higher position on the time axis. Rothbard has the numbers one through six on his graph printed backwards.4
Rothbard’s mistake originated with Hayek, who consistently used the terms “earlier stages” and “later stages” backwards. This is ironic since the great contribution of Menger and Böhm-Bawerk, under whom Hayek studied, is the subjective theory of value. Using Menger’s “law of imputation,” Böhm-Bawerk (1984) led the attack on Marx’s labor theory of value and, more generally, on the cost-of-production theory of value. As Skousen says, “Menger had reversed the direction of causation between value and cost. A consumer good is not valued because of the labor and other means of production used. Rather, the means of production are valued because of the prospective value of the consumption goods” (2001, p. 182).
Menger (1981) and Böhm-Bawerk (1959) did not use the terms “earlier stages” and “later stages” but spoke only of higher and lower-order goods. When Hayek uses these time-specific terms he is speaking from the perspective of the owner of the final product looking back on his costs of production. He is speaking from Marx’s perspective. And that is the perspective that Böhm-Bawerk (1984) went to such pains to refute. In 1941 Hayek (1975, p. 89) dropped these terms and wrote:
The definition of capital as 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. |
But Prices and Production was more widely read than The Pure Theory of Capital, so this initial mistake of Hayek’s was perpetuated by Rothbard and then by Skousen, even after their master had himself rejected it. The perspective that we want is from right now, at time zero, looking forward into the future. Thus, the DWCS is defined from zero to positive infinity.
3 Hayek (1967) provides no explanation for why he put time on the vertical axis. His contemporary Strigl, who is a Neo-Ricardian and does not employ Hayekian Triangles, titled a chapter of his book (2000) “The Vertical and Horizontal Connectivity of Prices” and seems to assume (p. 38) that readers already associate “vertical” with the law of costs and “horizontal” with the principle of substitution. Skousen writes, “The direction of economic activity can be illustrated by an assembly line. Another way to look at the transformation of goods through time is as the branches of a tree, which Morishima calls the ‘genealogy of production’” (1990, p. 140). Genealogical charts, which have time flowing from top to bottom, date back well before Henry Ford invented the assembly line, which moves horizontally. Skousen’s APS should be depicted as a conveyor belt with a queue of products on it that physically get bigger as they approach final assembly, but that is because the APS graph depicts a flow. The DWCS graph depicts a distribution and mathematicians have always drawn distributions the same way, with the independent variable on the horizontal axis and advancing rightward, so there is really no debate about how it should be oriented.
4 Garrison has time on the horizontal axis though he still has it backwards: “The axes have been reversed for convenience of exposition.... The production process begins at point T in Figure 1 and proceeds leftward” (1978, p. 171). Figure 1 (p. 172) has the horizontal axis labeled “<-- time” with the arrow showing time running backwards. It should be consumption expenditures on the left, arrow pointing to the right.
