Cardinal Utility Function

A Cardinal Utility Function is an objective utility function that ...

• • …
• Counter-Example(s):
  • Ordinal Utility.
• See: Preferences, Affine Transformation, Expected Utility Theory, Intertemporal Choice, Consumer Choice.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/cardinal_utility Retrieved:2015-4-4.
  • In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine transformations. Two utility indices are related by an affine transformation if for every value [math]\displaystyle{ u(x_1) }[/math] of one index u, occurring at quantity [math]\displaystyle{ x_1 }[/math] of the goods bundle being evaluated, the corresponding value [math]\displaystyle{ v(x_1) }[/math] of the other index v satisfies a relationship of the form : [math]\displaystyle{ v(x_1) = au(x_1) + b\! }[/math] , for fixed constants a and b. Thus the utility functions themselves are related by : [math]\displaystyle{ v(x) = au(x) + b. }[/math] The two indices differ only with respect to scale and origin. The idea of Cardinal utility is considered outdated except for specific contexts such as decision making under risk, utilitarian welfare evaluations, and discounted utilities for intertemporal evaluations where it is still applied. Elsewhere, such as in general consumer theory, ordinal utility is preferred.

1953

• Harsanyi, John C. “Cardinal utility in welfare economics and in the theory of risk-taking.” In: The Journal of Political Economy 61, no. 5 (1953): 434.
  • QUOTE: … to do with each other: “It is entirely unnecessary to identify the quantity that individuals are interpreted as maximizing [in the case of choices involving risk] with the quantity that should be given special importance in public policy.”2 In effect, the cardinal utility function has to be …

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