601-test1qnew-09f

601-test1qnew-09f - E 601 1 Sample test 1 questions cfw_a,...

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E frqrplfv 601 1 Sample test 1 questions 1. 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 } ² 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 } ( { b, c } { b } , and C ( { c, a } { c } . (a) Does C ( · ) satisfy WARP? WARP holds in some choice structure ( B ( · )) if: B,B ± B , { x, y } B, { x, y } B ± : x C ( B ) ,y C ( B ± ) x C ( B ± ) . The only way to contradict WARP here is for some problem to arise with budget sets that don’t contain d. But there is none of these with two or more elements in common, so the supposition in the de f nition of WARP is not satis f ed and thus WARP must be true. Remember, anything is true of the empty set. (b) Is there a rational preference relation which rationalizes C ( · ) on B ? No, because a " b " c but c " a, so transitivity doesn’t hold. (c) If { a, b, c } were another budget set could C ( · ) satisfy WARP? Defend your answers to (a), (b) and (c) carefully. Try C ( { a, b, c } { a } ; but C ( { c, a } { c } so WARP is violated. C ( { a, b, c } { b } ; but C ( { a, b } { a } so WARP is violated. C ( { a, b, c } { c } ; but C ( { b, c } { b } so WARP is violated. So the only way to satisfy WARP is to set C ( { a, b, c } the empty set, which is not allowed. 2. You are given the following information about a consumer’s purchases. Goods 1and2aretheon lygoodsconsumed . Year 1 Year 2 Quantity Price Quantity Price Good 1 100 100 120 80 Good 2 100 100 ? 100
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E frqrplfv 601 2 Forwhatva lueso fgood2consumedinyear2wou ldyouconc lude : (a) that the consumer’s consumption bundle in year 1 is revealed preferred to that in year 2? Denote the consumption of good 2 in year 2 by x 2 2 . If the consumer’s consumption bundle in year 1 is revealed preferred to that in year 2 then the year 2 bundle must be a f ordable with year 1 prices and income. So (100) (100) + (100) (100) (100) (120) + (100) x 2 2 or x 2 2 80 . (b) that the consumer’s consumption bundle in year 2 is revealed preferred to that in year 1? If the consumer’s consumption bundle in year 2 is revealed preferred to that in year 1 then the year 1 bundle must be a f ordable with year 2 prices and income. So (80) (120) + 100 x 2 2 (80) (100) + (100) (100) or x 2 2 84 . (c) that her/his behaviour contradicts the weak axiom? This requires that the inequalities in (a) and (b) both hold, but it is impossible for x 2 2 80 and x 2 2 84 so there is no violation of the weak axiom for any value of x 2 2 . (d) that good 1 is an inferior good somewhere for this consumer (assume WARP holds)? No value of x 2 2 . (e) that good 2 is an inferior good for this consumer (assume WARP holds)? No value of x 2 2 .
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E frqrplfv 601 3 3. Consider a price-taking consumer in a two-good world. Let w denote money income, ( p 1 ,p 2 ) prices, x j ( p 1 2 ,w ) Marshallian demands, h j ( p 1 2 ,u ) Hicksian de- mands, V ( p 1 2 ) the indirect utility function and e ( p 1 2 ) the expenditure func- tion. Fill in the following tables, and verify the Slutsky equation for the e f ect of changing the price of good 1 on the demand for good 2, for someone whose prefer- ences are represented by: u = x 1 x 2 .
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601-test1qnew-09f - E 601 1 Sample test 1 questions cfw_a,...

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