Rubinstein2005-page95

Rubinstein2005-page95 - “concrete terms.” DeFne: CV ( p...

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October 21, 2005 12:18 master Sheet number 93 Page number 77 Choice over Budget Sets and the Dual Problem 77 b. Check the properties of the indirect utility function (homogeneity of degree zero, monotonicity, continuity and quasi-convexity). c. Calculate the indirect utility function for the case in which A ={ a , b } and V a > V b > 0 . Problem 4. ( Moderate ) Show that if the utility function is continuous, then so is the Hicksian de- mand function h ( p , u ) . Problem 5. ( Moderate ) A commodity k is Giffen if the demand for the k -th good, x k ( p , w ) , is in- creasing in p k . A commodity k is inferior if the demand for the commodity decreases with wealth. Show that if a commodity k is Giffen in some neigh- borhood of ( p , w ) , then k is inferior. Problem 6. ( Moderate ) One way to compare budget sets is by using the relation % as deFned in the text. According to this approach, the comparison between ( p , w ) and ( p 0 , w ) is made by comparing two numbers u ( x ( p , w )) and u ( x ( p 0 , w )) , where u is a utility function deFned on the space of the bundles. ±ollowing are two other approaches for making such comparisons using
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Unformatted text preview: “concrete terms.” DeFne: CV ( p , p , w ) = w − e ( p , u ) = e ( p , u ) − e ( p , u ) where u = u ( x ( p , w )). This is the answer to the question: What is the change in wealth that would be equivalent, from the perspective of ( p , w ) , to the change in price vectors from p to p ? DeFne: EV ( p , p , w ) = e ( p , u ) − w = e ( p , u ) − e ( p , u ) where u = u ( x ( p , w )). This is the answer to the question: What is the change in wealth that would be equivalent, from the perspective of ( p , w ) , to the change in price vectors from p to p ? Now, answer the following questions regarding a consumer in a two-commodity world with a utility function u : a. ±or the case u ( x 1 , x 2 ) = x 1 + x 2 , calculate the two “consumer surplus” measures....
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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.

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