Mises Daily – February 11, 2011

February 11, 2011

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What Can the Law of Diminishing Marginal Utility Teach Us?
by Thorsten Polleit on February 11, 2011

The law of diminishing marginal utility is at the heart of the explanation of numerous economic phenomena, including time preference and the value of goods; and it also plays a crucial role in showing that socialism is economically and ethically inferior to capitalism.

The law of diminishing marginal utility, as developed by Carl Menger (1840–1921), is axiomatic in nature; that is, it is irrefutably true. In mainstream economics, however, this fundamental economic law is typically interpreted as resting on psychology, namely the law of satiation of wants.

Such an interpretation, however, does not actually conceive the law of diminishing marginal utility as a fundamental economic law — which has truth value irrespective of time and place — but as a fleeting explanation of certain economic phenomena, which may or may not hold in a given situation.

Given the importance of the law of diminishing marginal utility for economic theory and policy, it is important to keep advertising that the law of diminishing marginal utility is irrefutably true — because it follows from the axiom of human action. For ignoring this truth leads to fallacious and erroneous conclusions, and eventually to false economic theory and economic policies.

The Axiom of Human Action

Ludwig von Mises (1881–1973) reconstructed economics as an axiomatic science, which he called praxeology: the science of the logic of human action. The central element of praxeology is the axiom of human action.[1]

The axiom of human action basically says that human beings act. This may sound trivial at first glance. However, at second glance it becomes obvious that Mises’s axiom of human action and its implications are far from being trivial:

To start with, an axiom is a (set of) proposition(s) presumed to be true on the basis of logical necessity; it serves as presenting different subject matters as formal and coherent theories, all of which are propositions which can be deduced from the axiom. For instance, Pythagoras’s theorem is deducible from the axioms of Euclidian geometry.

The axiom of human action is of a special nature: It represents a synthetic a priori proposition, to use the terminology of Immanuel Kant (1724–1804). A synthetic a priori proposition is knowledge that (1) cannot be denied without running into an intellectual contradiction, and (2) is derived from reflection rather than observation.

The axiom of human action cannot be denied without running into an insoluble contradiction. This is because denying the axiom of human action implies human action — that is the human act of denying. Arguing that humans cannot act is thus a contradiction in itself, an absurdity.

Further, the axiom of action is derived from human reflection: it is independent of experience. This is because one cannot observe humans making an action per se. In order to know what “action” means, one has to know what action is — which implies that knowledge about action exists prior to action.

That said, the axiom of human action fulfills both of Immanuel Kant’s requirements for qualifying as an a priori synthetic proposition: it is self-evidently true, and it is derived from reflection. That said, logical deductions from the axiom of human action must be also absolutely, or apodictically, true as well.

By developing praxeology, Mises showed that economic theory is the formal logic of the irrefutably true axiom of human action. According to Mises, economic theory is not concerned with psychology, but with the implications of the axiom of human action.

The Law of Diminishing Marginal Utility

The law of diminishing marginal utility can be logically deduced from the axiom of human action. To show this, let us start with some remarks on utility.

Utility is a subjective concept. It denotes “satisfaction” (or “happiness” or “contentment”). It rises if and when an individual increases his or her state of satisfaction. Conversely, if and when someone considers himself in a worse state of affairs, his utility decreases.

What is more, utility is an ordinal concept, meaning that utility cannot be measured in terms of higher or lower utility from the viewpoint of an individual; and changes in utility among different people cannot be measured. All one can say is that utility is higher or lower from the viewpoint of an individual.

Rothbard explained why this is:

In order for any measurement to be possible, there must be an eternally fixed and objectively given unit with which other units may be compared. There is no such objective unit in the field of human valuation. The individual must determine subjectively for himself whether he is better or worse off as a result of any change.[2]

Marginal utility means the utility of increments of goods; it means the utility of enjoying an additional good. Marginal utility does not mean increments of utility — which would imply measurability of utility.[3] So what does the law of diminishing marginal utility say?

The law says, first, that the marginal utility of each (homogenous) unit decreases as the supply of units increases (and vice versa); second, that the marginal utility of a larger-sized unit is greater than the marginal utility of a smaller-sized unit (and vice versa). The first law denotes the law of diminishing marginal utility, the second law the law of increasing total utility.

These two dimensions of the law of diminishing marginal utility follow directly from the axiom of human action; they can be logically deduced from it, and they do not in any way depend on psychology or any behavioral assumption. This will be shown in what follows.

The A Priori Nature of the Law of Diminishing Marginal Utility

A priorism denotes a theory that yields true propositions without the need to take recourse to empirically derived knowledge: its truth value can be established a priori, independent of (sensual) experience.

Praxeology, resting on the axiom of human action, asserts something about reality and can be validated without taking recourse to experience; it is an a priori science. Furthermore, the law of diminishing marginal utility follows logically from the irrefutably true axiom of human action, and as such it is also a priori true; this conclusion doesn’t have anything to do with psychology.

To show this, we must remind ourselves of the obvious and less-obvious implications of the axiom of human action.

The axiom of human action implies that humans act, and that human action is purposeful, aiming at certain ends. Human action is distinguishable from those types of human behavior that are purposeless or purely reflexive. To assume the contrary would result in an insoluble intellectual contradiction.[4]

The axiom of human action implies substituting a more satisfactory state of affairs for a less satisfactory one. For if there were perfect contentment (and thus full satisfaction), no human action would result — which is, as noted earlier, unthinkable.

Human action implies employing means to the fulfillment of ends, and the axiom of human action implies that means are scarce. For if they were not scarce, means would not serve as objects of human action; and if means were not scarce, there would be no action — and that is unthinkable.

Because means are scarce — with respect to the ends that they could possibly serve — they must therefore be economized. As a result of scarcity, the actor has to allocate scarce means to serve the most desired ends, and so certain ends will have to remain unsatisfied. From this it follows that the larger the supply of means is, the more ends can be satisfied.

As means are scarce, human action implies that individual actors must rank their alternative ends. Human action is therefore indicative of judgment and valuation — or, as Rothbard said, demonstrated preferences: the highest-ranking ends are those which the actor values most highly.

Against this backdrop it becomes obvious that the law of diminishing marginal utility follows from the axiom of human action.

First, the greater the supply of a good is, the lower is the utility of an additional unit: the more goods are available, the more of the less-urgent ends can be satisfied. People thus value goods at the margin: If, for instance, someone has to give up one of his goods serving the fulfillment of his ends, he will give up the lowest ranking end, that is, the marginal unit. It is the latter that determines the good’s valuation from the viewpoint of the actor.

Second, the total utility of a greater supply of goods is always greater than the utility of a smaller supply of goods — as the former allows the satisfaction of more ends than the latter.

Mises summarizes the law of diminishing marginal utility succinctly:

In treating marginal utility we deal neither with sensuous enjoyment nor with saturation and satiety. We do not transcend the sphere of praxeological reasoning in establishing the following definition: We call that employment of a unit of a homogeneous supply which a man makes if his supply is n units, but would not make if, other things being equal, his supply were only n-1 units, the least urgent employment or the marginal employment, and the utility derived from it marginal utility. In order to attain this knowledge we do not need any physiological or psychological experience, knowledge, or reasoning. It follows necessarily from our assumptions that people act (choose) and that in the first case acting man has n units of a homogeneous supply and in the second case n-1 units. Under these conditions no other result is thinkable. Our statement is formal and aprioristic and does not depend on any experience.[5]

Three Applications of the Law of Diminishing Marginal Utility

Finally, let us consider three economic aspects in which the irrefutably true law of diminishing marginal utility plays an important role — something, however, that is all too often ignored by mainstream economics. Such faulty economics thereby support — intentionally or unintentionally — destructive policies.

(1) A rise in the money stock. A rise in the money stock must, for logical reasons, reduce the exchange value of a money unit. This is because the additional money unit can be used to satisfy an additional end that is necessarily less urgent than the satisfaction of the preceding end. A rise in the money stock will thus necessarily lead to a decrease in the marginal utility of the money unit (compared to the situation in which the money stock had remained unchanged).

As a result, a rise in the money stock can never be “neutral” in economic terms. It necessarily leads to a decline in its exchange value — when compared with a situation in which the money stock had remained unchanged; and it should also be noted here that a rise in the money stock affects different market agents differently (the “Cantillon Effect”).

A monetary policy of increasing the money supply is therefore never “neutral”: It necessarily lowers the exchange value of the money unit, and it necessarily benefits some people (namely the first receivers of the new money) at the expense of others (namely the late receivers of the new money).

(2) A lowering of the market interest rate. The pure market interest rate reflects societal time preference — which, in turn, is also implied in the axiom of human action. Time preference means that market agents value goods available today (present goods) more highly than goods available in the future (future goods).

And the more that present goods (out of current income) are exchanged against future goods (as is typically illustrated by the positive slope of the savings schedule in the savings/investment and interest-rate space), the higher will be the valuation assigned to present goods relative to future goods — and this is a result of the irrefutably true law of diminishing marginal utility. The pure rate of interest is thus expressive of the relation between the valuations of present goods and the valuations of future goods.

If government intervenes in the time market — by, for instance, increasing the supply of bank circulation credit and fiat money — it necessarily causes a deviation of the market interest rate from the pure interest rate (namely pushing the market interest rate below the pure market interest rate), which subsequently must lead to malinvestment and boom-and-bust.

(3) Violating individuals’ property rights.[6] Violations of individual property rights (for instance through government taxation, regulations, etc.) will make property owners value present goods increasingly more highly than future goods — a conclusion which follows from the law of diminishing marginal utility.

Violations of individual property rights thus raise peoples’ time preference, increasing consumption at the expense of savings and investment, thereby reducing (or even reverting) the pace of capital accumulation. An interventionist-socialist societal order will therefore necessarily lead to impoverishment relative to a free market societal order, in which there are no systematic violations of individuals’ property rights.

Thorsten Polleit is Honorary Professor at the Frankfurt School of Finance & Management. Send him mail. See Thorsten Polleit’s article archives.

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[1] For an in-depth explanation, see Hoppe, H.-H. (2007 [1995]), “Praxeology and Economic Science,” in Economic Science and the Austrian Method, Ludwig von Mises Institute, pp. 7–48.

[2] See Rothbard, M. N. (2007 [1962]), Man, Economy, and State, Scholar’s edition, Ludwig von Mises Institute, pp. 21–33.

[3] See in this context Rothbard, M. N. (1959), “Towards a Reconstruction of Utility in Welfare Economics,” originally published in On Freedom and Free Enterprise: The Economics of Free Enterprise, May, Sennholz, H. F., ed., Princeton, N.J: D. Van Nostrand, 1956; reprinted in The Logic of Action One: Method, Money, and the Austrian School by Murray N. Rothbard, London: Edward Elgar, 1997, pp. 211–255.

[4] Mises, L. (2007 [1957]), Theory and History, Ludwig von Mises Institute, p. 3, notes: “it would simply be silly to deny the fact that man manifestly behaves as if he were really aiming at definite ends. Thus the denial of purposefulness in man’s attitudes can be sustained only if one assumes that the choosing both of ends and of means is merely apparent and that human behavior is ultimately determined by physiological events which can be fully described in the terminology of physics and chemistry.

Even the most fanatical champions of the ‘Unified Science’ sect shrink from unambiguously espousing this blunt formulation of their fundamental thesis. There are good reasons for this reticence. So long as no definite relation is discovered between ideas and physical or chemical events of which they would occur as the regular sequel, the positivist thesis remains an epistemological postulate derived not from scientifically established experience but from a metaphysical world view.”

[5] Mises (1996), Human Action, 4th ed., Fox & Wilkes, San Francisco, p. 124.

[6] See in this context, for instance, Hoppe, H.-H. (2010), Theory of Socialism and Capitalism, Ludwig von Mises Institute.