Legal disputes and the gains from settling out of court

Litigation versus settlement as a bargaining situation

Let us return to the example from Chapter 3 involving the factory and the residents. We will use the bargaining framework outlined in the previous section in this chapter to illustrate the gains from settling out of court. Suppose that the factory's production of Q units is currently causing harm to the residents, but the residents enjoy a property right to clean air. That is, the residents have the legal right to prevent the factory from polluting, and so could enforce Q = 0 in a court of law and avoid the costs that they are currently incurring from the factory's production. To try to enforce this right, suppose that the residents file a lawsuit against the factory. The residents then become the plaintiffs and the factory becomes the defendant in this legal dispute. Suppose that the parties have identical quasi-linear preferences and that it is efficient for the factory to produce Q* = Q /2 units. Prior to trial, the parties may engage in pre-trial negotiation in the hope of arriving at a settlement which would result in the factory making a payment of T > 0 to the residents in exchange for the right to produce.

We assume that neither party knows the court's ruling with certainty. Remember that the factory's utility is increasing in Q, whereas the residents' utility is increasing in Q - Q, the absence of production. Let p be the (commonly perceived) probability that the residents will win in court. If the residents win, they enjoy utility of u(Q). On the other hand, if they lose, they receive nothing. If the factory wins, they receive u(Q), but nothing if they lose. Finally, let:

CR = the resident's (fixed) costs of going to trial

CF = the factory's costs of going to trial

T = amount that defendant must plaintiff if they settle

Nr = the residents' costs of settling/negotiating

Nf = the factory perceived costs of settling/negotiating

There are only two states of the world here: the state of the world in which the residents wins, and the state of the world in which they lose. Notice also that the costs of going to trial and of settling are assumed to be fixed. Thus, the expected benefits for the residents from going to trial are:

and the expected benefits for the factory are:

On the other hand, suppose that the parties settle out of court. Let T be the transfer that the factory makes to the residents. When the parties settle, they agree that the factory should produce the efficient level of production. The payoff to the residents from settling out of court is:

whereas the payoff to the factory from settling out of court is:

The residents will be willing to settle out of court as long as they gain from doing so, which requires:

or:

On the other hand, the factory will be willing to settle out of court as long as they gain from doing so, which requires:

or:

Thus, the gains from settlement will be positive as long as both inequalities are satisfied:

or:

The interpretation of this condition is straightforward. The left-hand side is the size of the joint surplus that is available to the parties if they negotiate out of court and agree to implement the efficient level of production. The right-hand side is the size of the joint surplus that is available to the parties if they go to court. The gains from settlement will be positive as long as the former exceeds the latter. Notice that in Q ( Q ^

our formulation, since — is the efficient outcome, 2u — must exceed

_ 2 l2

u (Q). Further, for each it is reasonable to assume that the costs of settling are less than the costs of going to court. Under these assumptions, equation (11.14) will always hold: in this framework, if any agreements between the parties can be implemented, then the parties will never go to court, and trials will never be observed.

 
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