fin-401-08fa

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

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

View Full Document Right Arrow Icon
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
Background image of page 1

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

View Full DocumentRight Arrow Icon
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
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 8

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online