2. Foundations of Microeconomics

Modern neoclassical economics derives from a few crucial microeconomic building blocks. Prominent among these are utility functions, indifference analysis, and the Kaldor-Hicks (or "cost-benefit" or "potential Pareto improvement") approach to welfare economics. Mises and Rothbard reject all three of these elements, building economic theory upon a different foundation. This is definitely a sufficient basis for an alternative Austrian school of thought. However, Mises and Rothbard reject the foundations of modern neoclassical economics too quickly, and their substitutes are inadequate.

2.1. Utility Functions vs. Value Scales

Modern neoclassical economists habitually use "utility functions" to describe individuals' preferences. For example, they may posit that an individual's utility U=a*ln(quantity of apples)+(1-a)*ln(quantity of oranges). Rothbard instead preferred to discuss the "value scales" of individuals. For example, an individual's preferences might be given by {1st apple, 2nd apple, 1st orange, 3rd apple,...}. Both approaches provide an obvious interpretation of "utility maximization": for neoclassicals, an individual selects the highest feasible value of U, while for Rothbard, a maximizing individual satisfies the highest-ranked feasible preferences on his value scale.

Both approaches seem quite similar; so similar, in fact, that neoclassical economists might call them identical. But Rothbard noted some underlying differences, and concluded that the "value scale" approach was the right one. Why? According to Rothbard, the mainstream approach credulously accepted the use of cardinal utility, when only the use of ordinal utility is defensible. As Rothbard insists, "Value scales of each individual are purely ordinal, and there is no way whatever of measuring the distance between the rankings; indeed, any concept of such distance is a fallacious one."[3]

At first, Rothbard appears to limit his criticism solely to "Those writers who have vainly attempted to measure psychic gains from exchange" by their consumer's surplus.[4] But it soon becomes clear that Rothbard rejects the entire utility-function approach as incoherent: "The chief errors here consist in conceiving utility as a certain quantity, a definite function of an increment of the commodity... Utilities are not quantities, but ranks..."[5] As if to emphasize the strength of his disagreement with the mainstream approach to utility, Rothbard goes on to dismiss the standard intermediate micro theorem "that in equilibrium the ratio of the marginal utilities of the various goods equals the ratio of their prices. Without entering in detail into the manner by which these writers arrive at this conclusion, we can see its absurdity clearly, since utilities are not quantities and therefore cannot be divided."[6] What initially appeared to be a slight difference in nomenclature yields serious disagreement about some fairly basic issues.

As plausible as Rothbard sounds on this issue, he simply does not understand the position he is attacking. The utility function approach is based as squarely on ordinal utility as Rothbard's is. The modern neoclassical theorists - such as Arrow and Debreau - who developed the utility function approach went out of their way to avoid the use of cardinal utility.[7] Let a neoclassical theorist say "bundle one offers utility of 8, while bundle two offers utility of 7," and Rothbard concludes that he believes in cardinal utility. But the language here is technical; to parse it, you must return to the underlying definitions. Upon doing so, you will find that the meaning of "bundle one offers utility of 8, while bundle two offers utility of 7" is nothing more or less than "bundle one is preferred to bundle two." A utility function is just a short-hand summary about an agent's ordinal preferences, not a claim about "utils."[8] This is why neoclassicals say that the utility function is uniquely defined up to a monotonic transformation. You can rescale any utility function however you like, so long as you re-scale it monotonically.[9]

What about the theorem - that Rothbard dismissed - which claims that utility-maximizing individuals equalize the marginal utilities of goods consumed divided by their prices? Doesn't this show that neoclassicals believe in cardinal utility? No, it does not; statements made in technical jargon often sound absurd if you forget the underlying definitions. A utility function just uses numbers to summarize ordinal rankings; it doesn't commit us to belief in cardinal utility. Deriving the marginal utility of individual goods from this function commits us to nothing extra.[10]

Rothbard's rejection of the utility function approach led him to make strange ad hoc concessions to it elsewhere in his writings. Using his value scale approach, Rothbard was able to derive the laws of demand and supply as theorems.[11] But then inexplicably in his later discussion of labor and land, Rothbard conceded the theoretical possibility of "backward" bending supply curves.[12] Furthermore, in his discussion of the economics of taxation, Rothbard admits the theoretical possibility that greater taxation of labor income could induce an increase in labor supply - even going so far as to mention a "substitution" and an "income" effect which his initial treatment of utility theory and demand utterly failed to mention.[13] What is interesting is that Rothbard was unable to derive the substitution and income effects from his value scale approach. Rather, he borrowed it from the standard utility function analysis, which shows that there are two different channels by which a price change induces a change in the quantity demanded. Thus, not only does Rothbard inappropriately dismiss the neoclassical approach to utility theory, but deemed it sufficiently fruitful that he borrowed its implications on an ad hoc basis.

To sum up, Rothbard falsely accused neoclassical utility theory of assuming cardinality. It does not. There is nothing actually wrong with Rothbard's value scale approach, but because the neoclassical assumptions are in some ways less restrictive than Rothbard's[14], neoclassicals made the important discovery that price changes have both income and substitution effects - a discovery Rothbard was unable to derive from his own postulates but conceded without explanation.[15]