Caplan says that Rothbard did not understand the position he was attacking, because microeconomic theorists go to great pains to show that their results hold for any monotonic transformation of an ordinal utility function, and do not entail cardinal utility.
22.
Note the difference between CES utility and isoelastic utility : the CES utility function is an ordinal utility function that represents preferences on sure consumption commodity bundles, while the isoelastic utility function is a cardinal utility function that represents preferences on lotteries.
23.
In mathematics, a homothetic function is a monotonic transformation of a function which is homogeneous; however, since ordinal utility functions are only defined up to a monotonic transformation, there is little distinction between the two concepts in consumer theory.
24.
If the number of bundles is infinite, one option is to start by ignorning the randomness, and assess an ordinal utility function v ( x _ 1, . . ., x _ n ) which represents the person's utility on " sure " bundles.
25.
Pareto was the first to realize that cardinal utility could be dispensed with and economic equilibrium thought of in terms of ordinal utility that is, it was not necessary to know how much a person valued this or that, only that he preferred X of this to Y of that.
26.
When ordinal utilities are used, differences in utils ( values taken on by the utility function ) are treated as ethically or behaviorally meaningless : the utility index encodes a full behavioral ordering between members of a choice set, but tells nothing about the related " strength of preferences ".
27.
For instance, having ordinal utilities of 4, 3, 2, 1 for alternatives a, b, c, d, respectively, is the same as having 1000, 100.01, 100, 0, which in turn is the same as having 99, 98, 1, . 997.
28.
The theory was developed so that analysis of economic choices could be based upon preferences which can be observed and compared ( "'ordinal utility "'), rather than the older concept of utility which was based on the unrealistic assumption that the satisfaction derived from economic choices could be measured ( "'cardinal utility "').
29.
Caplan says that Rothbard did not understand the position he was attacking, because microeconomic theorists go to great pains to show that their results are derived for any monotonic transformation of an ordinal utility function, and do not entail cardinal utility . " it would appear that there may be an endemic problem with the topic that straddles the fringe issue insofar as there are two distinct and disparate factions associated with the Austrian School.
30.
He is particularly well known for the demand theory with the earlier ordinal utility approach of Eugene Slutsky and Sir John Hicks, by showing that demand functions satisfy his Strong Axiom if and only if they can be generated by maximising a set of preferences that are " well-behaved " in the sense that they satisfy the axioms of choice theory, that is, they are reflexive, transitive, complete, monotonic, convex and continuous essentially the conditions required for a Hicksian approach to demand theory.
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