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Microeconomics FHS Problem Set 7 Sketch Solutions
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Sketch solutions for select questions in the Microeconomics FHS Problem Set 7: Adverse Selection, Signalling & Screening
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UNIVERSITY OF OXFORD Last updated: September 16, 2013Department of Economics
Undergraduate - Microeconomics
Tutorial/Class 7: Adverse Selection, Signalling & Screening
Sketch solutions
FOR USE BY TUTORS ONLY
DO NOT CIRCULATE, ESPECIALLY TO STUDENTS
, Problems and Multipart Questions
1. Lemons & Peaches
Four qualities of a certain brand of car are produced in equal numbers. There are
two groups of potential consumers, none of whom wants to own more than a single
car. Three times as many are type X as are type Y . The two types place di↵erent
values on each grade of car, summarised in the table below. The price of a new car
is £16,000, and in the eyes of each consumer no depreciation occurs in the first six
months after the car has left the factory.
Quality Type X value Type Y value
(£,000) (£,000)
A 21 18
B 18 17
C 15 16
D 11 12
(a) Who buys new cars, assuming that they discover the grade only after purchase?
Assume there are 12n type X consumers and 4n type Y .
Expected value of a car to type X is 65/4 = 16 14 > 16.
Expected value of a car to type Y is 63/4 = 15 34 < 16.
So all type X’s buy new cars, and no type Y ’s do.
Therefore there are 12n cars bought, 3n of each quality.
(b) Analyse the market for six month resales, continuing to assume that consumers
are able to judge the quality of a specific car only after purchase, but that they do
know the average quality of used cars traded – i.e. if potential buyers o↵er a price
of £20,000, they know that any type Y owner would sell, but that the type X
owners would sell only if their car was grade B, C, or D. (Each potential trader
decides whether or not to trade a single used car at the prevailing price and no
later resales are possible.)
Draw supply and demand curves.
If p 21, owners with cars of all qualities will sell, supply is 12n, expected
value to type Y is 15 34 , demand is 0.
If 18 p < 21, owners with cars of qualities B, C, D will sell, supply is 9n,
expected value to type Y is 14 23 , demand is 0.
If 15 p < 18, owners with cars of qualities C, D will sell, supply is 6n,
expected value to type Y is 13, demand is 0.
If 11 p < 15, owners with cars of quality D will sell, supply is 3n, (expected)
value to type Y is 12, demand is ...?
...0 if p > 12, and 4n if p is between 11 and 12.
Excess demand forces the price up to 12.
So, only the 3n quality D cars are traded, and the sellers are each better off
by £1,000.
1
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