G w utility construction

In economics, a cardinal utility function or scale is a utility index that preserves preference orderings uniquely up to positive affine g w utility construction. The two indices differ only with respect to scale and origin. Thus if one is concave, so is the other, in which case there is often said to be diminishing marginal utility. Thus the use of cardinal utility imposes the assumption that levels of absolute satisfaction exist, so that the magnitudes of increments to satisfaction can be compared across different situations.

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The first one to theorize about the marginal value of money was Daniel Bernoulli in 1738. He assumed that the value of an additional amount is inversely proportional to the pecuniary possessions which a person already owns. Since Bernoulli tacitly assumed that an interpersonal measure for the utility reaction of different persons can be discovered, he was then inadvertedly using an early conception of cardinality. Bernoulli assumed that “a poor man generally obtains more utility than a rich man from an equal gain” an approach that is more profound that the simple mathematical expectation of money as it involves a law of moral expectation.

Early theorists of utility considered that it had physically quantifiable attributes. They thought that utility behaved like the magnitudes of distance or time, in which the simple use of a ruler or stopwatch resulted in a distinguishable measure. Utils” was the name actually given to the units in a utility scale. In the Victorian era many aspects of life were succumbing to quantification.

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