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_iD+a*c_jD, 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.