Consider the case of an accident involving an injurer and a victim. The victim has suffered a harm of 10,000. The law holds the injurer liable to fully compensate the victim if and only if the former was negligent. However, the victim believes that he can prove negligence on the part of the injurer with probability Pp, where 0 ≤ Pp ≤ 100%; the injurer has identical belief about his probability of being held negligence, i.e., Pd = Pp. The litigation costs for the victim (plaintiff) and the injurer (defendant) are Cp and Cd, respectively. There are no hurdle to pre-trail negotiations between the parties. Moreover, if the litigation happens, each party will bear its litigation costs. Answer the following:
(a) Find the ‘range of the settlement’ payment, i.e., the minimum and the maximum payment that can possibly be made by the Defendant. Does the range depend on the litigation costs?
(b) Now assume that if there is litigation, the court will adopt the ‘cost-shifting rule’, i.e., if a party looses a case it will have to pay for the litigation expenses of the winner. Find out the ‘range of the settlement’. Is the victim’s higher than his payoff under (a) above?