Prof.
Bryan Caplan
bcaplan@gmu.edu
http://www.bcaplan.com
Econ
812
HW
#4 (please type all answers)
1. Suppose two players play the following games,
in order:
Game
#1:


Player 2 

Player 1 

Coop 
Don't 
Coop 
5,5 
1,6 

Don't 
6,1 
2,2 
Game
#2:


Player 2 

Player 1 

Left 
Right 
Left 
5,1 
0,0 

Right 
0,0 
1,5 
Does
playing Game #2 make cooperation in Game #1 sustainable if players do not
discount future payoffs (b=1)? Why or why not? If a cooperative equilibrium is possible,
would you expect it to be likely? Why or
why not?
2. Suppose you are playing an
infinitelyrepeated PD game with payoffs from the Week 34 notes. The game ends each turn with probability p,
and players discount the future by b. Under what conditions can trigger
strategies sustain cooperation?
3. In an infinitelyrepeated reputation game
(with the payoffs from the Week 5 notes), imagine customers only punish a turn
of Cheat with 50% probability of not buying the next turn. Solve for the seller's critical value of b.
4. Analyze the expected efficiency properties of
the MSNE where two firms simultaneously incur sunk costs. Use the notation from the notes (V.I.) for
the firms; designate maximum consumers surplus as CS_{max},
consumers surplus under monopoly as CS_{mon}, and note that if a good
is not produced then consumers surplus is 0.
Under what conditions is contestability with simultaneous sunk costs
welfaredominated by simple monopoly?
5. How does cost heterogeneity affect the
welfare equivalence of perfect competition and Bertrand oligopoly? How much is this likely to matter in the real
world? Use diagrams to illustrate your
answer. (one
paragraph)
6. Analyze the incentive for firms to increase
their productive efficiency under Bertrand oligopoly. Use diagrams to illustrate your answer. (one paragraph)
7. Suppose that there are 4 Cournot competitors
with MC=0 and no fixed costs. Prove that
at least one of these firms would like to split into two firms; i.e., that 2*P(5)>P(4).
8. Suppose Cournot firms have a fixed cost, K,
but 0 MC. If P=20Q, solve for the free
entry value of N as a function of K.
Briefly explain why the firstbest outcome sets N=1.