In “Why I am not an Austrian Economist,” the neoclassicist Bryan Caplan criticizes the Austrians’ rejection of utility functions; he thinks that the Austrian view of individuals’ value scales and the neoclassical view of individuals’ utility functions are functionally identical. The Austrians, however, insist that the two approaches differ radically in that the Austrian approach entirely rejects the false idea of cardinal (measurable) utility, while the neoclassical approach implicitly employs the notion despite explicitly perceiving its falsity.

            According to economist Murray Rothbard of the Austrian school, all utility is ordinal; individual valuations can be ranked on a hierarchical scale—but there is no way for an economist to measure the “distances” between such rankings. Thus, assigning quantity X to the utility an individual derives from one good and assigning quantity Y to the utility he derives from another is a concession to the fallacy of cardinal utility. This means that, in practice, Rothbard rejects the mainstream theorem that in equilibrium the ratio of the marginal utilities of various distinct goods equals the ratio of their prices.

            Caplan thinks that Rothbard and the Austrians misinterpret the position they are attacking. He considers the mainstream approach to have been developed specifically with the aim of avoiding invocation of cardinal utility. According to Caplan, when a mainstream economist says, “a bundle of goods has utility Y>X, while another has a utility X,” this just means that the first bundle is preferred to the second. Caplan supports his assertion by pointing out that any given utility function is defined up to a monotonic transformation, which means that it can be rescaled in any way one likes so long as the original order of rankings is preserved. If U(y)=Y > U(x)=X, then one can harmlessly redefine the utility functions to be U(y)=Y+1 > U(x)=X+1 or even U(y)=Y² > U(x)=X².

            In “Economic Science and Neoclassicism,” Austrian economist Jörg Guido Hülsmann responds to Caplan that, while it is indeed possible to model an individual’s preferences by utility functions that do not alter the order of those preferences, this does not preserve the neoclassical model from fatal flaws. What is most significant, notes Hülsmann, is that preference ranks cannot be divided by one another and compared to a ratio of prices. Preference ranks and prices are altogether different kinds of indices. A price has units in goods (often monetary goods) and a definite magnitude. A preference rank, however, is just an ordering; it has no cardinal dimension. One cannot say, “Rank A has magnitude X and is twice as large as rank B, which has magnitude X/2.” If we cannot say how objectively large a preference rank is, the very operation of division makes no sense with preference ranks. Hülsmann thinks that dividing preference ranks by one another is as absurd as dividing rabbits by piano concertos.

            Hülsmann also sees problems with division of prices by one another. A price is not just a dollar amount. It is a comparison of valuations of two different goods. If the price of a hamburger is $3 and the price of a steak is $6, dividing the two prices by one another would be dividing “3 dollars/ hamburger” by “6 dollars/ steak,” which would produce the absurd result of “1 steak/ 2 hamburgers.” This ratio would be incommensurable to any other ratio, such as “3 cokes/ 2 hamburgers.” There is no way to compare those two ratios with one another—nor to derive any sort of equivalence or correspondence between the unit of one ratio and the unit of another. Thus, Hülsmann shows the nonsensical nature of both sides of the mainstream theorem that, in equilibrium, the ratio of the marginal utilities of various distinct goods equals the ratio of their prices.

G. Stolyarov II is a science fiction novelist, independent filosofical essayist, poet, amateur mathematician, composer, contributor to Enter Stage Right, The Autonomist, Le Quebecois Libre, and the Ludwig von Mises Institute, Senior Writer for The Liberal Institute, and Editor-in-Chief of The Rational Argumentator, a magazine championing the principles of reason, rights, and progress. His newest science fiction novel is Eden against the Colossus. His latest non-fiction treatise is A Rational Cosmology. Mr. Stolyarov can be contacted at gennadystolyarovii@yahoo.com.