Prof.
Bryan Caplan

bcaplan@gmu.edu

http://www.bcaplan.com

Econ
812

**HW
#5 (will NOT be collected or graded)**

1. Determine the critical value of b
for Bertrand collusion enforced by punishments of just ONE turn of Nash
reversion.

2. Determine the critical value of b
for Cournot collusion enforced by punishments of just ONE turn of Nash
reversion.

3. Consider the voluntary donation game in part
II of the Week 6 notes. Determine the
critical value of b required to sustain the socially optimal
donation level using trigger strategies.

4. Suppose there are 2 players deciding whether
to contribute to a public good. The
public good is discrete: it is produced at the optimal level so long as 1
person contribute. Contributing costs
the individual who contributes C, and 0 otherwise. If the public good is produced, everyone gets
a benefit of B; otherwise they get a benefit of 0. B>C.
Calculate and explain the PSNE of this game. Informally, what would the MSNE look like?

5. Characterize the PSNE of the game in problem
4 if there are N players and (N-k) people must contribute to create the public
good.

6. Diagram a situation where there are large
externalities but laissez-faire still yields a perfectly efficient result. Suggest a real-world example.

7. Suppose you have a 2-player version of problem
#3, with one difference: Each agent cares somewhat about the other, so they
maximize U_{i}=c_{i}D+a*c_{j}D, with 0<a<1. How does your answer to #3 change, and
why? (__Hint:__ You have two
symmetric equations in two unknowns).

8. Present and explain a novel application of:

a. Coordination games

b. Hawk/Doves games

9. Where are you most likely to see full
rent-dissipation? When are you least
like to see it?

10. Carefully explain and diagram the welfare
properties of the "worse-case" of monopoly, where there is
allocative, productive, AND lobbying inefficiency.