sábado, 27 de novembro de 2004

Utilidade Ordinal II

"Rothbard contributed two major advances beyondthe standards set by Mises’s Human Action.

First, Rothbard provided systematic clarification of the theory of marginal utility, and then advanced a new reconstruction of welfare economics and, entirely absent in Mises’s system, an economic theory of the state.

Building on the foundations of a strictly ordinalist interpretation of marginal utility laidout by Mises as early as 1912 in his Theory of Money and Credit,6 Rothbard explainedthat the word “marginal” in marginal utility does not refer to increments of utility (which would imply measurability), but rather to the utility of increments of goods (and thus has nothing to do with measurability).

The good to which utility is attached, and theincrements in its size, can be described in physical terms. The good and its incrementextend in space, and thus can be measured and counted as unitary quantitative addition.In distinct contrast, the utility attached to a physical good and its unitary physicalincrements is a purely intensive magnitude. It does not extend in space, and hence isimmeasurable and intractable by unitary counting and the rules of arithmetic.

Allattempts to construct a cardinal measure of utility are in vain. Qua intensive magnitude,utility can be treated only ordinally; that is, as a rank order on a one-dimensional individual preference scale (and every economic phenomenon, in particular monetary calculation and “objective” cost accounting, must ultimately be reducible to and explained as the simple outcome of ordinal individual rank order judgments).

Apart fromtheir placement on one-dimensional individual preference scales, no quantitativerelationship between different goods and different quantities of the same good exists. In particular, no such thing as total utility—conceived of as the addition or integration ofmarginal utilities—exists. Rather, “total” utility is the marginal utility of a larger-sized quantity of a good, and, Rothbard explained,

[t]here are, then two laws of utility, both following from the apodictic conditions ofhuman action: first, that given the size of a unit of a good, the (marginal) utility of eachunit decreases as the supply of units increases; second, that the (marginal) utility of alarger-sized unit is greater than the (marginal) utility of a smaller-sized unit. The first isthe law of diminishing marginal utility. The second has been called the law of increasingtotal utility. The relationship between the two laws and between the items considered inboth is purely one of rank, i.e., ordinal.

Graphically, Rothbard illustrated, the relationship can be represented thus:

Ranks in Value

-3 eggs

-2 eggs

-1 egg

-2nd egg

-3rd egg

The higher the ranking on this individual value scale for eggs, the higher the value. Bythe second law, 3 eggs are valued more highly then 2 eggs and 2 eggs more highly thanone. By the first law, the 2nd egg will be ranked below the first on the value scale, andthe 3rd below the 2nd.

No mathematical relationship exists between, for instance, the marginal utility of 3 eggs and the marginal utility of the 3rd egg except that the former is greater than the latter.

As Lionel Robbins, influenced by Wicksteed and Mises, had first brought home to mainstream economics, from the ordinal character of utility it follows logically that everyinter-personal as well as intra-personal comparison of utility must be regarded asimpossible (unscientific), and hence every social welfare proposal involving any suchcomparison is arbitrary.

While mainstream welfare economics was thrown into disarray upon full realization of this conclusion, Rothbard provided a radically new strictly ordinalist reconstruction of welfare economics based on the twin concepts of individual self-ownership and demonstrated preference."


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