Solutions_Spring2004

Solutions_Spring2004 - Econ 51 Final Answer Key 1 Walrasian...

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Econ 51: Final Answer Key 1 Walrasian Equilibrium and Pareto E ciency (23 points) (a) (5 points) Apples and bananas are perfect substitutes for both Rob and Tom. Tom likes more apples, Rob likes more bananas. Therefore, a Pareto e cient allocation assigns all the apples and some bananas to Tom, or all the bananas and some apples to Rob. In math: { ( a R ,b R ): b R =40 , 0 a R 100 } (the upper side of the Edgeworth box) or { ( a R ,b R ): a R =0 , 0 b R 40 } (the left side of the Edgeworth box). (b) (7 points) Because the f rms can transform one-to-one, any Pareto e cient allocation should assign all bananas to Rob and all apples to Tom. To see why, suppose for example that Rob has some apples. He can use the f rms to transform those apples to bananas. This will make him happier, without a f ecting anyone else in the economy. Given that Rob gets all bananas and Tom gets all apples, any production plan is Pareto e cient. In math: { ( a R ,b R ,a T ,b T ): a R =0 ,b T =0 ,a R + b T =140 } . (c) (7 points) Normalize p a =1.If p b 6 = p a one of the f rms can make in f nite pro f ts, so we cannot have an equilibrium. Therefore, in equilibrium it must be that p b =1 . W ith these prices, Rob would spend all his income on bananas, and Tom would spend all his income on apples. Therefore, consumption will be c R =(0 , 100) and c T =(40 , 0). To make this feasible, f rm 2 will transform 60 apples to 60 bananas. (d) (4 points) The answers to parts (b) and (c) are unchanged. Firms 3 and 4 are less e cient than f rms 1 and 2. For part (b): it is easy to see that it is not e cient to use them for production; their inputs can produce more if used by the other f rms. For part (c): if either f rm 3 or 4 produces, one of the other f rms will have in f nite demand, so this cannot be an equilibrium. 2 Externalities (22 points) (a) (8 points) Normalize p m =1 .C lear ly ,the f rm produces in equilibrium, so we must have p c = 1. Rob’s demand is given by MRS R = 3 c R = p c p m = 1, i.e. c
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This note was uploaded on 03/19/2011 for the course ECON 51 taught by Professor Tendall,m during the Winter '07 term at Stanford.

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Solutions_Spring2004 - Econ 51 Final Answer Key 1 Walrasian...

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