Question

Consider a relation R=" is at least as old as." Does this relation satisfy the three axioms if consumer theory?

Answer 1

Yes, the relation 'is at least as old as' satisfies the three axioms that are as follows:

Complete: This means that between two bundles the consumer is capable of fo deciding which one is preferable to others and rank them. Between two bundles, A and B, either A is as old as B or B is as old as A or both (if A=b). Thus, the consumer can always rank based on the relation given.

Reflexive: This means that the bundle is at least as good as itself. Now of course, a bundle A is at least as old as A. so the relation is reflexive.

Transitive: This means that if A is preferred to B and B is preferred to C, we must have A is preferred to C. Now if A is at least as old as B and B is at least as old as C, it follows that A is at least as old as C. Thus, transitivity holds.