fin-401-08fa

# fin-401-08fa - 1 6th December 2008 Instructions Answer 7 of...

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1 6th December 2008 Instructions : Answer 7 of the following 9 questions. All questions are of equal weight. Indicate clearly on the f rst page which questions you want marked. 1. Assume some consumer chooses bundle x j at prices p j , j =1 , 2 , 3 , where p 1 =( 1 , 1 , 2) ; x 1 =(5 , 19 , 9) p 2 =( 1 , 1 , 1) ; x 2 =(12 , 12 , 12) p 3 =( 1 , 2 , 1) ; x 3 =(27 , 11 , 1) . Show these data satisfy WARP. Is there an intransitivity in the revealed prefer- ences? Justify your answer. ANSWER Cost of these bundles at these prices 1 2 3 Deductions 1 42 48 40 Bundle 1 is revealed preferred to 3 2 33 36 39 Bundle 2 is revealed preferred to 1 3 52 48 50 Bundle 3 is revealed preferred to 2 These preferences are consistent with WARP but clearly they violate transitivity. 2. Consider the two-state world of Andy and Brian. In the good state each has awea ltho f 80 ;inthebadstateeachhasawea ltho f 40 , assuming they do not trade with each other. Let the probability of the good state be 3 / 4 . The only way in which they di f er is Andy is risk averse and Brian is risk neutral. Describe as precisely as you can the Pareto e cient allocations for these two people. Now suppose there are many Andys and an equal number of Brians. Describe as precisely as you can the competitive equilibrium of this economy. ANSWER Draw an Edgeworth rectangle with wealth in the good state along the horizontal

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2 risk averse so his indi f erence curves are convex to his origin. Brian is risk neutral so his indi f erence curves are straight lines; in fact, they have a numerical slope equal to the probability of the good state over the probability of the bad state, which is 3 / 4 over 1 / 4 or 3 . The tangencies trapped between the Andy and Brian indi f erence curves through their endowment points form the core – that is, the Pareto e cient allocations where neither person is worse o f . As in earlier general equilibrium examples in class the o f er curves will intersect on Brian’s indi f erence curve through his endowment point. In the competitive equilibrium each Brian will completely insure each Andy. The equation for a line with a slope of 3 , passing through (80 , 40) is w A b =280 3 w A g . We know that when the Andys are o f ered fair insurance they will choose to insure completely ± w A b = w A g ² so solving these two equations in the competitive equilibrium w A b = w A g = 280 4 =70 w B g =1 6 0 70 = 90 w B b =8 0 70 = 10 P w g P w b
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## This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.

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fin-401-08fa - 1 6th December 2008 Instructions Answer 7 of...

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