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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 646649.
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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 Winter '08
 Burbidge,John
 Microeconomics

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