Question

State and explain five assumptions of Cardinal utility

Answer 1

Cardinal utility analysis introduced by Alfred Marshall is based on the following assumptions. These assumptions are known as the axioms of cardinal utility.

1) comparability ( sometimes called completeness.)

For the entire set ,S, of uncertain alternatives, an individual can say either that outcome x is preferred to outcome y or y is preferred to x or the individual is indifferent as to y and x

2) Transitivity ( sometimes called consistency)

If an individual prefers x to y and y to z, then x is preferred to z.lf an individual is indifferent as to x and y and also indifferent as to y and z, then he or she is indifferent as to x and z.

3) Strong independence.

Suppose we construct a gamble where an individual has a probability of receiving outcome x and a probability of. ( 1- ) of receiving outcome z. We shall right this gamble as G(x,z:) . Strong independence says that if the individual is indifferent as to x and y, then he or she will also be indifferent as to a first gamble, set up between x with probability and a mutually exclusive outcome z, and a second gamble, set up between y with probability and a mutually exclusive outcome,z.

4) Measurability

If outcome y is preferred to less than x but more than z, then there is a unique ( a probability) such that the individual is indifferent between y and a gamble between x with probability a and z with probability (1-) .

5) Ranking.

If alternatives y and u both lie somewhere between x and z and we can establish a gamble between x ( with probability 1) and z, while also indifferent between u and a second gamble, this time between x ( with probability 2) and z , then 1 is greater than 2 , y is preferred to u.