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# PS13 - Intermediate Microeconomics Winter 2008 Problem Set...

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Intermediate Microeconomics, Winter 2008 Problem Set No 13 due: Monday, March 10; Tuesday, March 11 Q1. For the following utility functions and total endowments: Find the market clearing price(s) and the competitive allocation. Hint: You can set one price equal to one. 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 ) = Aq 1 + q 2 , U B ( q 1 ; q 2 ) = Bq 1 + q 2 , A > B . e A = (20 ; 20) ; e B = (20 ; 20) (g) U A ( q 1 ; q 2 ) = min f q 1 ; q 2 g , U B ( q 1 ; q 2 ) = q a 1 q 2 , e A = (20 ; 20) ; e B = (20 ; 20) . Q2. Choose three of the examples from before. Take some interior Pareto e¢ cient allocation that is not a competitive allocation given the initial endow- ment. Find a di/erent endowment such that it is a competitive allocation for some price vector. (Recall the Second Welfare Theorem: For every Pareto
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