# Exercises

1. Return to the analysis of Chapter 3, where the factory and the residents have

Q

the same quasi-linear utility function. The efficient level of production is — .

(a) What are the payoffs to the parties in any bargaining procedure which implements the efficient outcome?

(b) Write down the expression for the Nash bargaining solution in this situation. Find the solution, and show that the final payoffs to the parties are:

for the factory, and: for the residents.

2. Consider the differing perceptions model of litigation and settlement that

was examined in this chapter. Let:

- •
*p*plaintiff's perceived probability of winning at trail._{P}= - •
*p*defendant's perceived probability that the plaintiff will win at trial._{D}= - •
*C*plaintiff's costs of going to trial._{P}= - •
*C*defendant's costs of going to trial._{D}= - •
*N*plaintiff's costs of settling out of court._{P}= - • N
_{d}= defendant's costs of settling out of court - •
*J*_{P},*J*are the plaintiff's and defendant's common perceived dollar value of judgment if plaintiff wins at trial._{D}

Suppose that the parties are risk neutral.

- (a) Define the
*English Rule*and the*American Rule*for the allocation of legal costs. What is the plaintiff's expected utility under each of these rules if a trial goes ahead? What is the defendant's expected utility under each of these rules if a trial goes ahead? - (b) Let
*S >*0 be the amount that the parties agree to settle for. Under which conditions which settlement possibilities exist under each cost allocation rule? - (c) Now consider the following
*hybrid*cost allocation rule: if the case goes to trial, the loser must pay a fraction*q*of the winner's legal costs, where 0 <*в <*1. Suppose that if settlement possibilities exist, the parties split any settlement surplus equally. How does the settlement rate depend on q? Are cases more likely to settle if*q*is higher or lower?