PS 22 moral hazard

PS 22 moral hazard - Intermediate Microeconomics, Winter...

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Intermediate Microeconomics, Winter 2008 Problem Set No 22 We will discuss the problem set next week but it will not be collected. Reading: "Tourist Trap Model," pp 646-649. Q1. Adverse Selection and Buying Stocks. Reconsider the problem of buying stocks. Suppose the value of the stock can be either high, medium, or low. Each of the three values is equally likely (i.e., 1 3 ). Values and costs are as follows V alue v c High 100 90 Medium 90 80 Low 80 70 So this is the same setup as in the lecture, but with three possible values instead of two. Again, the buyer makes a price o/er p and the seller accepts if p c j . a) Calculate the expected utility of the buyer if he o/ers p = 90 ;p = 80 ;p = 70 . b) The three prices from before are the only candidates for optimal o/ers. Why? c) Which of the three prices is actually the optimal o/er? d) Challenging. Suppose, the stock can have 11 possible values. For each value, the buyer is willing to pay more than the opportunity cost of the seller: Value V 1 V 2 V 3 V 4 V 5 V 6 V 7 V 8 V 9 V 10 V 11 Buyer v 100 90 80 70 60 50 40 30 20 10 0 Seller c 90 80 70 60 50 40 30 20 10 0 0 The probability of each of these values is the same, i.e., prob [ V i ] = 1 11 . What to compare the expected payo/ from the candidate prices p 2 f 0 ; 10 ; 20 ;::::; 90 g . (You will not really need to calculate the exact numbers. But to give you an idea, if the buyer o/ers p = 50 , all sellers with costs equal to or below 50 accept
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PS 22 moral hazard - Intermediate Microeconomics, Winter...

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