Simon Fraser University
ECON 302
Spring 2016
S. Lu
Problem Set 9
Due on March 30, at 2:30pm
Remember to show your work on all questions.
1. Consider a market for used cars with risk-neutral participants, like we did in lecture. Suppose
there are three qualities for cars: Excellent (E), Good (G) and Bad (B). Let the sellers’
valuation for the three qualities be cE>cG>cB, and let the buyers’ be vE>vG>vB. Assume that
there is an equal number of cars in each of the three categories.
a) Suppose everyone observes the quality of each car. What is the condition for sales of
excellent cars to be feasible? Good cars? Bad cars? In each case, what is the feasible
price range?
b) Suppose no one observes car quality. What is the condition for car sales to be feasible?
What is the feasible price range?
c) Suppose only sellers know the quality of each car. What is the condition for sales of
excellent cars to be feasible? Good cars? Bad cars? [Caution: Be careful when answering
the latter two cases!] In each case, what prices could you observe?
2. There are two types of people in the world: brave and wimpy. Brave people incur a disutility
of 200 from bungee jumping, while wimps incur a disutility of 300. 70% of people are wimps.
Bungee jumping creates no social value.
Kelly has a partner Sam, and is trying to determine how assertive to be in the relationship.
Let a be the degree of Kelly’s assertiveness, which can be any nonnegative number. Kelly’s
utility is –a2 if Sam is brave, and –(a-1)2 if Sam is a wimp.
Suppose that Sam incurs disutility 400a, where a is Kelly’s assertiveness. Therefore, Sam’s
overall utility is u(a,e) = -400a-200e if brave and u(a,e) = -400a-300e if wimpy, where e=1
if Sam bungee jumps and e=0 otherwise. Also assume that Kelly and Sam love each other so
much that both would incur infinite disutility from breaking up.
a) Find Kelly’s optimal assertiveness if Sam is wimpy with probability p.
b) Does there exist an equilibrium where Kelly can determine Sam’s type with certainty by
giving Sam the choice of bungee jumping or not? Explain.
c) Does there exist an equilibrium where Kelly gains no information from whether Sam
bungee jumps? If so, find all such equilibria. If not, explain.
d) Does there exist an equilibrium where Kelly gains some information from whether Sam
bungee jumps? If so, find all such equilibria. If not, explain.
e) In which equilibrium is Kelly best off? Brave Sam? Wimpy Sam?