A consumer purchased the bundle (x1,y1 ) = (5; 2) at prices P1 x, P1y = (2; 2).

Question

A consumer purchased the bundle (x1,y1 ) = (5; 2) at prices P1 x, P1y = (2; 2). On another occasion, the consumer bought bundle (x2,y2 ) = (6,0) at prices P2 x, P2 y = (1; 1). Assuming he has rational preferences, but not knowing his wealth on those different occasions, can we infer with certainty that his preferences changed between t = 1 and t = 2? (Hint: Consider whether, when bundle 1 was chosen, bundle 2 would have been a§ordable to him, and vice versa. Choices are consistent, reáecting the same rational preference, if the following is true. Suppose the consumer is observed to choose bundle i when he could also have chosen bundle j. Then, whenever he can afford both bundles, he should never choose bundle j. This is known as the "Weak Axiom of Revealed Preference.")

Explanation / Answer

From above information we know that the cost of the Bundle (5, 2) at Prices (2, 2) = 5*2+2*2 = 14

The cost of bundle (6, 0) at prices (1,1) = 6*1+0*1 = 6

the cost of bundle (5,2) at Prices (1, 1) = 5+2 = 7

the cost of bundle (6, 0) at prices (2, 2) = 6*2+2*0 = 12.

Thus at prices (2, 2) the bundle (6 0) are affordable but at prices (1,1 ) when (6, 0) was purchased the bundle (5, 2) is not affordable. Thus the prefernces have not changes between t=1 and t = 2.

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