(a) Find Amit's optimal demand for insurance for each price p > 0. Assume that Amit cannot sell insurance, so that he must choose q ≥ 0. Solution: The optimal demand is 4(1-P) if p ≤ 1 and 0 otherwise. (b) Suppose that trade is determined according to the following sequential game. Barbara first chooses the price p> 0 at which she offers insurance to Amit. Amit then chooses the quantity q ≥ 0 of insurance to buy at the offered price. Find a subgame perfect equilibrium of this game. Solution: Using backward induction, the optimal strategy for Amit is to use the demand from part (a). Given this strategy, Barbara's expected profit is maximized by choosing p=1/√2. Hence the SPE is (p=1/√√2,q(p) = max{4(1-p)/p,0}). (c) Now suppose instead that first Amit offers a price p > 0 and quantity q 20 of insurance to buy. After hearing his offer, Barbara chooses whether to accept it or reject it. If she accepts the offer, then the proposed trade occurs, and if she rejects it then there is no trade. Find a subgame perfect equilibrium of this game (Note: you only have to find one equilibrium, not every equilibrium).

(a) Find Amit's optimal demand for insurance for each price p > 0. Assume that Amit cannot sell insurance, so that he must choose q ≥ 0. Solution: The optimal demand is 4(1-P) if p ≤ 1 and 0 otherwise. (b) Suppose that trade is determined according to the following sequential game. Barbara first chooses the price p> 0 at which she offers insurance to Amit. Amit then chooses the quantity q ≥ 0 of insurance to buy at the offered price. Find a subgame perfect equilibrium of this game. Solution: Using backward induction, the optimal strategy for Amit is to use the demand from part (a). Given this strategy, Barbara's expected profit is maximized by choosing p=1/√2. Hence the SPE is (p=1/√√2,q(p) = max{4(1-p)/p,0}). (c) Now suppose instead that first Amit offers a price p > 0 and quantity q 20 of insurance to buy. After hearing his offer, Barbara chooses whether to accept it or reject it. If she accepts the offer, then the proposed trade occurs, and if she rejects it then there is no trade. Find a subgame perfect equilibrium of this game (Note: you only have to find one equilibrium, not every equilibrium).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.5P

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