ProblemSet7_2009

# ProblemSet7_2009 - u 1 x 1,x 2,x 3 = min x 1,x 2 e 1 =(1 0...

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Econ 6202, Fall 2009 Dmitry Shapiro Problem Set 7 Due Tuesday November 17 1. Consider the following Edgeworth box economy. The consumers have iden- tical preferences given by u 1 ( x 1 ,x 2 ) = u 2 ( x 1 ,x 2 ) = min { x 1 ,x 2 } . There are 20 units of good 1, and 10 units of good 2. Characterize the set of Pareto-eﬃcient allocations. 2. Consider a two-consumer, two-good exchange economy. The consumers have identical preferences given by u 1 ( x 1 ,x 2 ) = u 2 ( x 1 ,x 2 ) = x 1 x 2 . Their initial endowments are e 1 = (1 , 1) ,e 2 = (1 , 3). Compute the Walrasian equilibrium price and allocations. 3. (JR 5.19) An exchange economy has three consumers and three goods. Consumers’ utility functions and initial endowments are as follows:
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Unformatted text preview: u 1 ( x 1 ,x 2 ,x 3 ) = min { x 1 ,x 2 } e 1 = (1 , , 0) , u 2 ( x 1 ,x 2 ,x 3 ) = min { x 2 ,x 3 } e 2 = (0 , 1 , 0) , u 3 ( x 1 ,x 2 ,x 3 ) = min { x 1 ,x 3 } e 3 = (0 , , 1) . Find the Walrasian equilibrium price and allocation. 4. Compute the Walrasian equilibria of the following two-consumer, two-good economy [HINT: there is more than one equilibrium.] u 1 ( x 1 ,x 2 ) = " ( x 1 )-2 + ± 12 37 ¶ 3 ( x 2 )-2 #-1 e 1 = (1 , 0) , u 2 ( x 1 ,x 2 ) = " ± 12 37 ¶ 3 ( x 1 )-2 + ( x 2 )-2 #-1 e 2 = (0 , 1) . 1...
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