\The Market for Lemons" (Akerlof, 1970) is the rst article that proposes
a formal model for adverse selection. Akerlof considered a stylized model of
the used car market. You learned during lecture that in extreme cases, adverse
selection might lead to no exchange at all in this market. In this exercise, you
will work on a slightly modi ed version of Akerlof's model.
Suppose there is a potential supply of nS used cars indexed by a quality
parameter q that is uniformly distributed between 1 and 5, i.e., Q U[1; 5].
a) Find the supply of used cars S(p) as a function of ns and p.
b) Find the average quality E(Q) as a function of p.
c) For which price(s) is S(p) = nS ? What is its associated average quality?
Assume there are two types of buyers. For a car of quality q, low intensity
buyers are willing to pay 3
2 q and high intensity buyers are willing to pay 2q.
Furthermore, assume there exist nL low intensity buyers and nH high intensity
buyers. Also, each buyer buys at most one car.
d) Find the reservation price of the low intensity buyers.
e) Find the reservation price of the high intensity buyers.
f) Find the demand of used cars D(p) as a function of nL, nH, and p (Hint : it
is a piecewise-de ned function).
