Question

Consider a group of individuals A, B and C and the relation as wealthy as as in A is as wealthy as B. Does this relation satisfy the completeness and transitivity properties? If the relation of the same group of individuals as above was strictly wealthier than, would this relation be transitive?

Answer 1

Answer-To answer the question, let us first understand the concepts of completeness and transitivity.

COMPLETENESS refers to the property that when consumers face a choice between any two bundles of goods, they can always rank them according to their preferences i.e. individuals must have a preference relationship between any goods. Consider two goods A and B, the consumer in either he/she must weakly prefer A to B, or that he/she weakly prefer B to A, or both (indifference).

TRANSITIVITY refers to the property of preference relationships that if one bundle (bundle A) is preferred to another (bundle B), and that bundle is preferred to a third (bundle C), then the first bundle must be preferred to the third. If we consider three bundles- A, B and C, then, by the rule of transitivity, relationship between the first and the third bundles will be governed by the strongest preference relationship in the set; if A is strictly preferred to B and B is weakly preferred to C then A is strictly preferred to C.

In the question, ' A is as wealthy as B' do satisfy the completeness property because here A and B are compared and ranked as both equally preferable (i.e. indifferent). Here both groups are compared and ranked so it is complete.

If the relation of the same group of individuals as above was strictly wealthier than, then this relation would be- C is strictly wealthier than B, B is strictly wealthier than A. It implies C is strictly wealthier than A.In this form, the relationship would have been transitive because it is based on the strongest preference relationship.