2021 S2 ECON8039/3004 HEALTH ECONOMICS TUTORIAL WEEK 9 Q1: TB CH8 Q11 11 Suppose a local car dealership is offering an inspection service that can perfectly deter- mine the quality of any car on the market. The dealership is trying to determine how much it will be able to charge for this procedure. Review the original assumptions about the Akerlof model. Specifically, we assume the buyer and seller utilities from equation (8.1), that car quality X is distributed uniformly from 0 to 100, and that the prevailing price P = 50. a Due to adverse selection, only some of the cars remain on the market (S2(P)). How are these cars distributed, and what is their average quality? only cars with quality X = P = 50 will re the market . Thus, Xu unit [0. 50 ) Their average quality is E (XIX =50 ] =- 1 = 0,50 = 2, b Suppose a buyer picks a car i at random from the cars still available on the market, and thinks about whether to purchase it. What is her expected change in utility from this transaction? Recall that buyer's utility function is : N/a . Ex - 1 . if not purchase if purchase . Buyer's expected utility from purchase : E [ H ] = { } | X | X = 5 . ] - P : ? : 25 -50 = - 12.5 c Even though her expected change in utility is negative, there is a possibility that she picked a relatively high-quality car and that her actual change in utility would be positive. What is the lowest value of X, such that this will happen, and what is the probability that X; is at least this high? . Buyer's utility from purchasing the product with quality Xi ? X; - 50 = 0 == > xi = 1° Thus the lowest value of Xi such that buyers derive positive utility from purchasing is igo . Since Xn unif [0, 50] Pr ( x = 1; ) = 50 = 115 > Pr ( X > 1; ) = 1 - j 1 = 3
d Now suppose the local car dealership decides to offer this buyer its inspection service for free, before she decides whether to purchase the car. She resolves to purchase car i if it will increase her utility, and refrain from purchasing it if it will not increase her utility. Now, what is her expected change in utility from this trans- action, considering that we do not yet know whether the car will be good enough to purchase? How does this differ from your answer in Exercise 11(b)? The inspection will help to exclude X < 100 3 from the market . From c) : 1 (1 1 x > 1;0 ) = } Pr 1 X = {0 } = {} as if there is a minimum guaranteed quality . - recall lec . Thus the buyer's expected utility is : ;