# Problems with Rothbard’s marginal utility analysis

Just the day before yesterday I wrote a post in which I said that among the major economic insights of Murray Rothbard is the first clear Austrian formulation of the principle of marginal utility. But now that I am thinking of the idea I fail to see its usefulness for economic theory.

The principle of marginal utility is relatively simple. Suppose that there is a person who has to abandon one unit of good X. She uses Y units of such good, each for one of Y goals, ranked in importance from 1 to Y. Which unit will she abandon? The answer that Rothbard gives is that she will abandon the unit of good X which is used for achievement of goal with rank Y because this goal is the least important.

The problem with this principle is that if it is correct it is merely a tautology and if it is supposed to be predictive it is false, or at least inconsistent with the Austrian treatment of choice and value.

Let us start from the latter. The Austrian approach to economic analysis presupposes that value scales exist only within (as constituent elements of) particular choices. Thus, only as a result of a choice can alternatives be ranked in importance. Thus, the only prediction that can be made with respect to which unit of good X will be abandoned is that it will be the unit which is used for the achievement of a goal (out of the set of Y goals) which the person will rank as the least important. However, when talking about marginal utility in Man, Economy, State (MES) Rothbard seems to contradict what he has written several pages earlier:

Let us now consider a supply from the point of view of a possible decrease, rather than an increase. Assume that a man has a supply of six (interchangeable) horses. They are engaged in fulfilling his wants (emphasis added). Suppose that he is now faced with the necessity of giving up one horse. It now follows that this smaller stock of means is not capable of rendering as much service to him as the larger supply. This stems from the very existence of the good as a means.[23] Therefore, the utility of X units of a good is always greater than the utility of X – 1 units. Because of the impossibility of measurement, it is impossible to determine by how much greater one value is than the other. Now, the question arises: Which utility, which end, does the actor give up because he is deprived of one unit? Obviously, he gives up the least urgent of the wants which the larger stock would have satisfied. Thus, if the individual was using one horse for pleasure riding, and he considers this the least important of his wants that were fulfilled by the six horses, the loss of a horse will cause him to give up pleasure riding.

The contradiction seems to arise from the words which I put in bold. Rothbard seems to imply that a certain ranking exists for goals that are being simultaneously pursued by an acting person which in principle allows an economist to make a prediction about which of them will have to be abandoned if the person has to abandon one unit of the good in the hypothetical example. Of course, this interpretation does not follow unambiguously from Rothbard’s discussion of marginal utility in MES. He might have just meant a tautological assertion that the unit of the good which will be abandoned will be the unit serving the goal which will be abandoned as a result of the relevant future choice.

But if the principle of marginal utility is a mere tautology, it is superfluous and cannot be useful for explaining anything in beyond what its corollary is used to explain. However, Rothbard assigned to the principle of marginal utility separate explanatory power. In particular, he claimed that it is needed to explain the inverse relationship between the price and the quality demanded. But is it really?

It is only needed for this purpose if we need to prove that the law of demand is apodictically certain, i.e. that it always holds true that if the price of good X rises then the quantity demanded falls. But obviously no serious student of economics would want to make such a claim in view of lots of available counterexamples from economic reality, including the ones where increases in price lead to increases in the quantity demanded.

So what economists actually need to prove is that the increase in price creates a tendency towards decrease in consumption and spell out the factors that may countervail this tendency. It is not the task of this blog post to provide such a formulation because serious theoretical work is needed. In particular what is needed is a serious investigation into the essence of the value scales formation within particular choices. I can just point out here that the fact that a value scale only exists within a particular act of choice does not mean that conceptualizations of alternatives in different choices may not be identical, unless we are ready to succumb into radical subjectivism of the Schackle-Lachmann variety. If I am correct this may be used for formulating the right ceteris paribus condition. In any case, the problems I uncovered in this post seem to show that a serious and thorough restatement of the foundations of Austrian economic analysis is in order.