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MT2answer420KSpring08 - MT2 answer Part 1 Spring 08 Q1(d...

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MT2 answer, Spring 08 Part 1 Q1 : (d) Q2 : (c) Q3 : (a) Q4 : (b) Q5 : (a) Q6 : (a) Q7 : (d) Q8 : (c) Q9 : (b) Q10 : (e) Q11 : (c) Q12 : (e) Q13 : (d) Part 2 Q1 : (i) Notice that if A’s consumption is perfectly insured, denoted by ( c, c ) let’s say, then B’s allocation is perfectly insured as well, which is given by (10 - c, 10 - c ). Let πv A ( x A 1 ) + (1 - π ) v A ( x A 2 ) be the representation of A’s preference in the ex- pected utility form, and πv B ( x B 1 ) + (1 - π ) v B ( x B 2 ) be the representation of B’s preference, where π denotes the probability of state 1. Then, at any allocation like above, MRS A = πv 0 A ( c ) πv 0 A ( c ) = π 1 - π MRS B = πv 0 B (10 - c ) πv 0 B (10 - c ) = π 1 - π Hence A and B have equal MRS, and the allocation is Pareto efficient. (ii) Since π = 1 3 , π 1 - π = 1 2 , which corresponds to the equilibrium price ratio. Thus p 1 p 2 = 1 2 . The allocation is obtained by taking the intersection of the line with slope - 1 2 that passes though the endowment point and the certainty line. Let t be the amount of contingent good 1 which A buys, then the final consumption of A is given by (4 + t, 7 - 1 2 t ). Since A’s consumption is perfectly insured in equilibrium,
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