Question

consider a world off to good x and y and consider the following preferences defined over all bundles of positive quantities of these two goods

(Xa,Ya)>=(Xb,Yb) if and only if Xa>Xb or Xa=Xb and Ya>=Yb

in other words this consumer always prefers the bundle that has more x. If two bundles have the same amount of X, then the consumer rephrase the one with more y

1) show that this preference violates one of the axioms of rational choice

Answer 1

Ans.

In Microeconomics, according to the Axioms of Rationality, the preferences should hold following axioms. They are:

a) Axiom of Completeness - This implies that a consumer can order his preferences, like if bundle A is preferred over bundle B, and B is preferred over A. then they both are equally attractive.

b) Axiom of Transitivity - This means if there are three bundles A, B and C, then if A is preferred to B, and B is preferred to C, then A must be preferred to C.

c) Axiom of Continuity - This means if A is preferred over B, then if there exist a bundle which is having some amount more than B, say bundle C, then according to the continuity axiom, bundle A should be preferred over bundle C. Also, Monotonicity property implies that 'more is better', i.e. a bundle shouldd be preferred such that it must be having more of good 1 and no less of good 2.

But, according to the preferences given in the question, it seems good X is more dearer to the consumer, because he can sacrifice the amount of good Y to have more of good X. For eg,

There exist 3 bundles A, B and C as

A(2,4), B(1,3) and C(3,2)

Then according to the preference of the consumer as described in the question, he is willing to prefer A over C, which violates monotonicity property as bundle B gives more of good X but less of good Y, that clearly violates the axioms of rational choice.