final_Winter2007

final_Winter2007 - Econ 51: Final Exam March 23, 2007...

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Econ 51: Final Exam March 23, 2007 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. Please write on each blue book the number of the question, your name, and your section number (or section time and TA). Always remember: think before you do the math . intelligently. Question 3.d is a potential bonus of 4 points, so your grade could be as high as 104. Good luck! 1. General Equilibrium (27 points) Consider an economy with two goods, apples ( a ) and bananas ( b ), and N agents (1 ; 2 ; :::; N ). Each agent has an initial endowment of 10 apples and 5 bananas. a. Suppose that all agents have identical utility functions: u i ( a i ; b i ) = log a i + log b i ii. (3 points) Solve for the Walrasian Equilibrium prices and allocations. How does your answer depend on N ? Explain. b. Suppose now that there is a ±rm with a technology that can transform one apple to one banana, that is Y = f ( y a ; y b ) : y a ± 0 ; y b = ² y a g : ii. (3 points) Solve for the Walrasian Equilibrium prices and allocations (as initial endowments use those given at the beginning of the question, not those derived in part a.ii). How does you answer depend on N ? Explain. iii. (2 points) How would your answer to parts b.i and b.ii above change if there were two ±rms with identical technologies? Explain. 1
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iv. (2 points) How would your answer to parts b.i and b.ii above change if there was Y 2 = f ( y a ; y b ) : y b & 0 ; y a = ± y b g ? Explain. c. Suppose now that there are no &rms, but that agents’ preferences are di±erent (en- dowments are the same as before). Agent i ’s utility is given by: u i ( a i ; b i ) = (2 i ± 1) log a i + log b i Note : 2 i means 2 to the power of i . i. (4 points) Solve for the Walrasian Equilibrium prices and allocations when N = 2. ii. (4 points) Solve for the Walrasian Equilibrium prices and allocations when N = 3.
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final_Winter2007 - Econ 51: Final Exam March 23, 2007...

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