401-samplequest1a

401-samplequest1a - E 401 1 Answers to sample questions 1...

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E frqrplfv 401 1 Answers to sample questions 1 1. (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 ± ) . 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) No, because a " b " c but c " a, so transitivity doesn’t hold. (c) Try C ( { a, b, c } )= { a } ; but C ( { c, a } { c } so WARP is violated. Try 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. (a) 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) 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 (100) (120) + 80 x 2 2 (100) (100) + (80) (100) or x 2 2 75 . (c) This requires that the inequalities in (a) and (b) both hold, so 75 x 2 2 80 . (d) x 2 2 < 75 . (e) 80 <x 2 2 100 .
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E frqrplfv 401 2 3. x 1 ( p 1 ,p 2 ,w ) x 2 ( p 1 2 ) V ( p 1 2 ) Range 1 2 w p 1 1 2 w p 2 1 4 w 2 p 1 p 2 p 1 2 > 0 0 h 1 ( p 1 2 ,u ) h 2 ( p 1 2 ) e ( p 1 2 ) Range p 1 / 2 1 p 1 / 2 2 u 1 / 2 p 1 / 2 1 p 1 / 2 2 u 1 / 2 2 p 1 / 2 1 p 1 / 2 2 u 1 / 2 p 1 2 > 0 0 Slutsky equation: from the duality between the UMP and the EMP we know x 2 ( p 1 2 ,e ( p 1 2 )) = h 2 ( p 1 2 ) . Di f erentiate this with respect to p 2 and use the envelope theorem to obtain x 2 p 1 + x 1 x 2 w = h 2 p 1 LHS =0+ 1 2 w p 1 1 2 1 p 2 But w = e ( p 1 2 )=2 p 1 / 2 1 p 1 / 2 2 u 1 / 2 , so = 1 2 p 1 / 2 1 p 1 / 2 2 u 1 / 2 = RHS 4.
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This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.

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401-samplequest1a - E 401 1 Answers to sample questions 1...

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