Question

how do you compute the total surplus in this question?

The context of the question is: Abe gave Beth a ring. They started fighting later and eventually Abe, broke off the relationship and asked for the return of his ring. Beth replied that it was a gift to her and she was not about to return it. He answered that he had only loaned it to her to wear for the duration of their friendship. Abe and Beth are now involved in a legal dispute over the ring. Beth possesses the ring and she declares that she intends to sell it. Abe threatens to sue her. If Abe wins at trial, the court will require Beth to return the ring to him. The ring is worth $1,000 to Abe. If Beth wins at trial, the court will allow her to keep the ring. She would then sell the ring for $600 to an acquaintance. (The acquaintance does not know Abe and will not resell the ring to him.) In the event of a trial, each one expects to win with probability 0.5. A trial will cost Abe $250 and it will also cost Beth $250. Abe and Beth start negotiating to reach a settlement and avoid a trial. The costs of settling out of court are nil. Assume that these numbers are common knowledge for all parties.

What I don't understand is the efficient allocation of property rights and how to compute the corresponding total surplus.

I would say that the efficient allocation of property rights is to let Abe have the ring because it is more valuable to Abe and the corresponding surplus would be $400 because he values it $400 dollars more than Beth. However, I am not sure if I understand the concepts.

Answer 1

There are two people involved - Abe and Beth The ring is worth $1000 to Abe and $600 to Beth The probability of winning at the trial is 0.5 for both of them The cost of the trial is also $250 for both of them Begin by calculating the expected value of fighting the trial. Calculate the expected value of the trial to Abe and Beth as follows: EA=0.5(1000 – 250)+0.5(-250) =0.5(750)– 125 = 375-125 = $250

Ez = 0.5(600 – 250)+0.5(-250) = 0.5(350)-125 =175-125 = $50 As Abe's expected value of the trial is higher than that of Beth, that means Abe attaches a higher value to the ring. Therefore, the efficient allocation would be to assign the property rights of the ring to Abe. Further, when there is no trial and the settlement is done outside, then the total surplus would be $1000 as that is the maximum value attached to the ring and either of the parties will need to compensate to the other. When there is a trial in court, the total surplus would be $250 + $50 = $300.