601-sampleq1

601-sampleq1 - E frqrplfv 601 1 Sample questions 1 1. MWG,...

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Unformatted text preview: E frqrplfv 601 1 Sample questions 1 1. MWG, 1.B.3 and 1.B.4. 2. Let X = { a, b, c, d } , B = { a, b } , { a, c } , { a, d } , { b, c } , { b, d } , { c, d } , { d, b, c } , { a, b, d } , { a, c, d } and ( B , C ( )) be a choice structure. Suppose C ( ) is such that d is the best choice whenever d is available and C ( { a, b } ) = { a } , C ( { b, c } ) = { b } , and C ( { c, a } ) = { c } . (a) Does C ( ) satisfy WARP? (b) Is there a rational preference relation which rationalizes C ( ) on B ? (c) If { a, b, c } were another budget set could C ( ) satisfy WARP? Defend your answers to (a), (b) and (c) carefully. 3. Answer both parts. (a) What does it mean to say that a utility function, u ( ) , represents a preference relation on some choice set X ? Prove that if u ( ) represents preference relation , this preference relation must be complete and transitive. (b) Now suppose X = R 2 + and ( x 1 1 , x 1 2 ) " ( x 2 1 , x 2 2 ) when x 1 1 > x 2 1 , or x 1 1 = x 2 1 and x 1 2 > x 2 2 . Is this preference relation complete, transitive and continuous? Defend your answers. 4. You are given the following information about a consumers purchases. Goods 1 and 2 are the only goods consumed....
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601-sampleq1 - E frqrplfv 601 1 Sample questions 1 1. MWG,...

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