{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

final_Spring2004

# final_Spring2004 - Econ 51 Final Exam June 7 2004...

This preview shows pages 1–3. Sign up to view the full content.

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 fi 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 . 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
(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 fi rms. (d) (4 points) Two new fi rms enter the market ( fi 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 } . Firm 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 fi 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 ff er when the other is smoking. In particular, Rob’s utility is given by u R ( c R , c T , m R ) = 3 log( c R ) log( c T ) + m R and Tom’s utility is given by u T ( c T , c R , m T ) = 3 log( c T ) log( c R ) + m T (as always, logs are natural logarithm, i.e. base e ). Rob and Tom are each endowed with 20 units of money and no cigarettes.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}