final_Spring2004

final_Spring2004 - Econ 51: Final Exam June 7, 2004...

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Econ 51: Final Exam June 7, 2004 Instructions: This is a closed book, closed-notes exam. You are allowed to use a hand-held calculator (i.e. no laptop). You have 180 minutes. Please answer all 5 questions. Please use a separate blue book for each question. Always remember: think before you do the math. Most questions start easy and get more di cult, so make sure you organize your time intelligently (5.d may be particularly hard). Good luck! 1 Walrasian Equilibrium and Pareto E ciency (23 points) Consider an economy with two goods, apples ( a ) and bananas ( b ), two agents (Rob and Tom). Rob’s utility is given by: u R ( a R ,b R )= a R +2 b R Tom’s utility is given by: u T ( a T ,b T )=2 a T + b T Aggregate endowments are e a = 100 and e b =40 . (a) (5 points) Describe the set of all Pareto E cient allocations in this economy. Suppose now that this economy also has two f rms, 1 and 2. Firm 1 can transform one apple to one banana, i.e. Y 1 = { ( y a ,y b ): y a 0 ,y b = y a } . Firm 2 can transform one banana to one apple, i.e. Y 2 = { ( y b ,y a ): y b 0 ,y a = y b } . (b) (7 points) Describe the set of all Pareto E cient allocations in this new economy with production .
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(c) (7 points) Suppose that Rob is endowed with all apples and no bananas, and Tom is endowed with all bananas and no apples, i.e. e R =(100 , 0) and e T =(0 , 40). Compute a Walrasian equilibrium: prices, consumption by Rob and Tom, and production plans for the f rms. (d) (4po ints)Twonew f rms enter the market ( f rms 1 and 2 are still around). Firm 3 can transform two apples to one banana, i.e. Y 3 = { ( y a ,y b ): y a 0 , 2 y b = y a } .F i rm 4 can transform two bananas to one apple, i.e. Y 4 = { ( y b ,y a ): y b 0 , 2 y a = y b } . Repeat parts (b) and (c). 2 Externalities (22 points) Consider an economy with two agents (Rob and Tom) and two goods, cigarettes ( c )and money ( m ). A f rm can transform one unit of money to one cigarette, i.e. Y = { ( y m ,y c ): y m 0 ,y c = y m } . Rob and Tom both enjoy smoking, but su
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final_Spring2004 - Econ 51: Final Exam June 7, 2004...

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