Question 1.11. For the insurance problem: max(1-p)u(Ii)+pu(I2) t.(1-)l1+l2 where I>0 is the loss, p E(0, 1)is the probability of the bad event, T E(O, 1) is the price of insurance, w is initial wealth, I1=W-T, and I2=w-1+(1-q (a) If the insurance market is not competitive and the insurance company makes a posi- tive expected profit: Tq-pq>0, will the consumer demand full-insurance('=l) under-insurance(q"<I, or over-insurance(q">0)? Show your answer (b) Show the above solution on a diagram Question 1.12. There are two consumers A and B with utility functions and endow- ments ua(rA, ra)=aIn A+(1-a)In a, VA=(0 uB(aB, B)=min(=B, 3), Calculate the equilibrium price(s) and allocation(s Question 1. 13. Consider a two-consumer, two-good economy. Both consumers have the same Cobb-Douglas utility functions u;(ai 2)=In. +In There is one unit of each good available. Calculate the set of Pareto efficient allocations and illustrate it in an edgeworth box. Question 1. 14. Consider an economy with two firms and two consumers. Denote g the number of guns, b as the amount of butter, and a as the amount of oil. The utilit functions for consumers are u1(,b)=94b06, u2(g,b)=10+0.5lng+0.5lnb Each consumer initially owns 10 units of oil: i1=i2= 10. Consumer 1 owns firm 1 which has production function g=2 r; consumer 2 owns firm 2 which has production function b=3 r. Find the competitive equilibrium 3Question 1.11. For the insurance problem: max (1 − p)u(I1) + pu(I2) s.t. (1 − π)I1 + πI2 = w − πl where l > 0 is the loss, p ∈ (0, 1) is the probability of the bad event, π ∈ (0, 1) is the price of insurance, w is initial wealth, I1 = w − πq, and I2 = w − l + (1 − π)q. (a) If the insurance market is not competitive and the insurance company makes a posi￾tive expected profit: πq − pq > 0, will the consumer demand full-insurance (q∗ = l), under-insurance (q∗ < l), or over-insurance (q∗ > l)? Show your answer. (b) Show the above solution on a diagram. Question 1.12. There are two consumers A and B with utility functions and endow￾ments: uA(x1 A, x2 A) = a ln x1 A + (1 − a) ln x2 A, WA = (0, 1) uB(x1 B, x2 B) = min(x1 B, x2 B), WB = (1, 0) Calculate the equilibrium price(s) and allocation(s). Question 1.13. Consider a two-consumer, two-good economy. Both consumers have the same Cobb-Douglas utility functions: ui(x1 i , x2 i) = ln x1 i + ln x2 i , i = 1, 2. There is one unit of each good available. Calculate the set of Pareto efficient allocations and illustrate it in an Edgeworth box. Question 1.14. Consider an economy with two firms and two consumers. Denote g as the number of guns, b as the amount of butter, and x as the amount of oil. The utility functions for consumers are u1(g, b) = g0.4 b 0.6 , u2(g, b) = 10 + 0.5 ln g + 0.5 ln b. Each consumer initially owns 10 units of oil: x¯1 = ¯x2 = 10. Consumer 1 owns firm 1 which has production function g = 2x; consumer 2 owns firm 2 which has production function b = 3x. Find the competitive equilibrium. 3