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# PS12 - Intermediate Microeconomics Winter 2008 Problem Set...

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Intermediate Microeconomics, Winter 2008 Problem Set No 12 due: Wednesday, March 5; Thursday, March 6 Q1. For the following utility functions and total endowments: Calculate the contract curve. To calculate the contract curve, °nd the points at which the marginal rates of subtitutions are identical, if the MRS is de°ned, see solved problem 10.3. Draw the Edgeworth box corresponding to this economy and draw the contract curve in it. Illustrate the set of allocations that are individually rational for both persons. If person A is chosen to be the dictator, which bundle would she choose? If person A is chosen to be the proposer in a simple bargaining game, which bundle would she propose? 1. (a) U A ( q 1 ; q 2 ) = U B ( q 1 ; q 2 ) = q 1 q 2 . e A = (20 ; 20) ; e B = (100 ; 60) (b) U A ( q 1 ; q 2 ) = q 1 2 1 + q 2 , U B ( q 1 ; q 2 ) = q 1 2 1 + q 2 . e A = (20 ; 20) ; e B = (100 ; 60) : (c) U A ( q 1 ; q 2 ) = q 1 + q 2 , U B = 1 2 q 1 2 1 + 1 2 q 1 2 2 , e A = (20 ; 20) ; e B = (20 ; 60) (d) U A ( q 1 ; q 2 ) = min f q 1 ; q 2 g , U B ( q 1 ; q 2 ) = q 1 q 2 , e A = (20 ; 20) ; e B = (20 ; 60) (e) U A ( q 1 ; q 2 ) = q a 1 q 2 , U B ( q 1 ; q 2 ) = q 1 q 2 , a > 1 . e A = (20 ; 20) ; e B = (20 ; 20) (f) U A ( q 1 ; q 2 ) =

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PS12 - Intermediate Microeconomics Winter 2008 Problem Set...

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