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Unformatted text preview: Problem Set 3 Due Thursday, Oct. 15th, by 10pm 1. Andrew and Daniel consume bionicles ( x 1 ) and superhero costumes ( x 2 ). Andrew starts off with 10 bionicles while Daniel starts off with 10 costumes. Andrews utility function is u A = 5 ln( x A 1 ) + x A 2 while Daniels utility function is u D = x D 1 x D 2 (a) Draw an Edgeworth box that represents their current endowments. Be sure to label all relevant points. (b) Derive Andrew and Daniels demands as a function of p 1 /p 2 . For Andrew, e A 1 = 10 so the lagrangian is: L = 5 ln( x A 1 ) + x A 2 + (10 p 1 x A 1 p 1 x A 2 p 2 ) Taking FOC and solving the system leads to the demands: x A 1 =5 p 2 p 1 x A 2 =10 p 1 p 2 5 if p 1 p 2 > 1 / 2 =0 otherwise 1 For Daniel, e D 2 = 10 so the lagrangian is: L = x D 1 x D 2 + (10 p 2 x D 1 p 1 x D 2 p 2 ) Taking FOC and solving the system leads to the demands: x D 1 = 5 p 2 p 1 x D 2 = 5 (c) Find the market clearing price. To find the equilibrium price ratio we need to find the one that clears the market for both goods: x A 1 + x D 1 = 10 = 5 p 2 p 1 + 5 p 2 p 1 = 10 = p 2 p 1 = 1 x A 2 + x D 2 = 10 = 10 p 1 p 2 5 + 5 = 10 = p 1 p 2 = 1 So the market clearing price ratio is p 1 p 2 = 1 with x A = (5 , 5) and x D = (5 , 5) (d) Find two points that are Pareto efficient Two Pareto efficient points are 1) if we...
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This note was uploaded on 05/13/2010 for the course ECON 105D taught by Professor Cur during the Fall '09 term at Duke.
 Fall '09
 CUR
 Microeconomics, Utility

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