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601-t1a-09f

# 601-t1a-09f - Econ 601 Test 1 1 Prove that the following...

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Econ 601 Test 1 1 . Provethatthefo l low ingtwode f n it ionso ftheW eakAx iomo fRevea ledPre ference are equivalent. (A) WARP holds in some choice structure ( B ,C ( · )) if: B,B ± B , { x, y } B, { x, y } B ± : x C ( B ) ,y C ( B ± ) x C ( B ± ) . (B) WARP holds in some choice structure ( B ,C ( · )) if: B,B ± B , { x, y } B, { x, y } B ± : x C ( B ) ,y C ( B ± ) { x, y } C ( B ) and { x, y } C ( B ± ) . ANSWER (A) (B) The only thing to prove is that y C ( B ) . Try rewriting (A) with B,B ± and x, y interchanged: B ± ,B B , { y,x } B ± , { y,x } B : y C ( B ± ) ,x C ( B ) y C ( B ) Now note that the material before the implication symbol is the same, except for order, as the material in (A), which we are assuming is true. So y C ( B ) hastobetrue . (B) (A). The material before the implication symbols is the same in both (A) and (B) and { x, y } C ( B ±

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601-t1a-09f - Econ 601 Test 1 1 Prove that the following...

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