Problem 1. When Abe graduated from Texas A&M, he bought adiamond ring with a golden insignia to impress his high schoolfriends. The person most impressed was his old sweetheart, Beth.They grew so fond of each other that Abe asked Beth to wear hisring. Then the quarreling began. The relationship deteriorateduntil, in a fit of anger, Beth enrolled as a student at Universityof Texas. Abe, naturally, broke off the relationship and asked forthe return of his ring. Beth replied that it was a gift to her andshe was not about to return it. He answered that he had only loanedit to her to wear for the duration of their friendship. Abe andBeth are now involved in a legal dispute over the ring. Bethpossesses the ring and she declares that she intends to sell it.Abe threatens to sue her. If Abe wins at trial, the court willrequire Beth to return the ring to him. The ring is worth $1,000 toAbe. If Beth wins at trial, the court will allow her to keep thering. She would then sell the ring for $600 to an acquaintance.(The acquaintance does not know Abe and will not resell the ring tohim.) In the event of a trial, each one expects to win withprobability 0.5. A trial will cost Abe $250 and it will also costBeth $250. Abe and Beth start negotiating to reach a settlement andavoid a trial. The costs of settling out of court are nil. Assumethat these numbers are common knowledge for all parties.
Abe's expected value from going to trial is:
Beth's expected value from going to trial is:
The bargaining surplus over which the two are negotiatingis:
If Abe and Beth were to split the bargaining surplus evenly,what kind of exchange (ring and currency) should take place?
A) Abe should let Beth keep the ring in exchange of her givinghim $200.
B) Beth should give Abe the ring in exchange of him giving her$600.
C) Beth should give Abe the ring in exchange of him giving her$400.
D) Beth should give Abe the ring in exchange of him giving her$250.
E) Abe should let Beth keep the ring in exchange of her givinghim $1000.
