midtermsolutions_winter2009

# midtermsolutions_winter2009 - Econ 51: Midterm Solutions...

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February 9, 2009 1. Short questions (42 points) with probability 0.99, and pays nothing with probability 0.01. If you are su±ciently risk loving, you should buy the ticket. (3 points) True of false? (4 points) Explain using at most two sentences (third sentence and on will not be read). so as long as v ( x ) is increasing in x , you should not buy the ticket, regardless of your risk preferences. (b) (7 points total) You have a vNM utility function of v ( x ) = log( x ). You have income as experiment 1). You would pay \$8 to participate in this lottery. (3 points) True of false? (4 points) Explain using at most two sentences (third sentence and on will not be read). True. You would pay for this lottery any amount x that satis²es log(10) < 1 2 log(15 ± x ) + 1 2 log(25 ± x ). The left-hand-side is equal to 2.3. Substitute x = 8 in the right- hand-side, and you get 2.39. (c) (6 points) There are four goods ( a , b , c , and d ). Rob’s utility function is u R ( a; b; c; d ) = a + b ± c . Tom’s utility function is u T ( a; b; c; d ) = a + b ± d . There are 10 units of each good. Describe the set of all Pareto e±cient allocations. (You can use words or math, but it has to be precise). Any allocation that gives no c to Rob and no d to Tom is Pareto e±cient. (d) (6 points) Consider the same setting as in part (c) above, but suppose now that there is also a ²rm that can transform each unit of c to ²ve units of d , that is Y = f ( c; d ) j c ² 0 ; d = ± 5 c g . Describe the set of all Pareto e±cient allocations. (You can use words or math, but it has to be precise). Any allocation and any production plan of the ²rm is Pareto e±cient, as long as (as in part (c)) Rob gets no c and Tom gets no d: Note that the ²rm remaining idle is only one possible Pareto e±cient allocation. (e) (6 points) Rob and Tom have the same utility function u R ( x; y ) = u T ( x; y ) = log( x ) + log( y ). There is an initial endowment of both x and y . Firm A can transform one unit of x to one unit of y . Firm B can transform one unit of y to one unit of x . There is no way that both ²rms can be operative in equilibrium. True of false? Explain using at most two sentences (third sentence and on will not be read). 1

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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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midtermsolutions_winter2009 - Econ 51: Midterm Solutions...

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