Question

Consider an agent's preferences satisfy rationality, convexity, continuity, and local non-satiation. Suppose he is indifferent between the consumption bundles he chose at (p1,w1) and (p2,w2), which is x(p1,m1)~x(p2,m2). Let p3 = 0.6*(p1+p2) and w3 = 0.6*(w1+w2), assume that p1≠p2 and m1≠m2. Is it correct, incorrect, or unknown that x(p3,w3) is strictly preferred to x(p1,w1)? Please explain.

Answer 1

If p3 = 0.6*(p1+p2) and w3 = 0.6*(w1+w2), then p3 is higher than the average of p1 and p2, and w3 is higher than average of w1 and w2. So, it is incorrect that x(p3,w3) is strictly preferred to x(p1,w1).