Question

Arthur alleges that Betty borrowed a valuable kettle and broke it, so he sues to recover its value, which is $300. The facts are very confusing. Betty contends that she did not borrow a kettle from Arthur; even if it is proved that she borrowed a kettle from Arthur, she contends it is not broken; even if it is proved that she borrowed a kettle from Arthur and that it is broken, she contends that she did not break it.

Assume that because the facts in the case are so unclear, Arthur and Betty independently believe that the chances of either side’s winning in court are an even 50 percent. Further assume that litigation in small claims court will cost each party $50 and that the costs of settling out of court are nil. So, cooperation in this case is a matter of settling out of court and saving the cost of a trial. Noncooperation in this case means trying the dispute.
This involves Arthur, Betty and the kettle. But assume that the value of the kettle is $350 and assume that the cost to each party of going to small claims court is $60. The cost of settling is nil. Note that the question has parts a through f. Show your work.

QUESTIONS:

a. What is Arthur’s threat value?

b. What is Betty’s threat value?

c. If Arthur and Betty cooperate together in settling their disagreement, what is the net cost of resolving the dispute?

d. What is the cooperative surplus?

e. A reasonable settlement would be for Betty to pay Arthur _____.

f. Suppose that instead of both sides believing that there is an even chance of winning, both sides are optimistic. Specifically, Arthur thinks that he will win with probability 2/3, and Betty thinks that she will win with probability 2/3.

1. What is Arthur’s putative threat value (what he believes he can secure on his own without Betty’s cooperation)?

2. What is Betty’s putative threat value (what she believes she can secure on her own without Arthur’s cooperation)?

3. The putative cooperative surplus equals _____.

4. Describe the obstacle to settlement in a few words.

Answer 1

1) :-Arthur's threat value is his expected net gain from trial. Because the value of the kettle is $300, because he has a 50 percent probability of winning, and because the trial will cost him $50, the expected net value of a trial is $300(0.5) - $50 = $100.

2) :-Betty's threat value is her expected loss from trial. Because the value of the kettle is $300, because she has a 50 percent probability of losing, and because the trial will cost her $50, the value to her of a trial is -$300(0.5) - $50 = -$150 - $50 = -$200.

3) :-The cost to Arthur and Betty of cooperatively resolving their dispute without trial is $0 because the transaction costs of settling are, by assumption, zero.

4) :-The surplus from cooperating (i.e., from settling the dispute rather than litigating) is $100, which is the sum of the two parties' costs of litigating.

5) :-A reasonable settlement would be for Betty to pay Arthur $150.

Thus, Arthur gets his threat value ($100) plus half the surplus ($50). And so does Betty: -$200 (her threat value) + $50 (the saving in litigation costs) = -$150.

6):-Assuming that the cost of litigating is still $50, Arthur's net expected gain from litigating is $300(2/3)-$50 = $150.

2( :-Betty believes that the probability of her losing the case and having to pay for the kettle is 1/3. Her probability of winning the case and not having to pay for the kettle is 2/3. Thus, Betty's threat value is (-$300)(1/3) - $50 = -$150.

3) :-The putative cooperative surplus is 0.

The actual cooperative surplus from settling rather than litigating is still $100 but because of their optimism, the parties both anticipate doing better from litigating than from cooperating. If the actual cooperative surplus is $100 and each party anticipates a reasonable split of that surplus, then Arthur anticipates receiving $200 from cooperating with Betty in settling the dispute: $150 (his threat value) + $50 (his share of the cooperative surplus) = $200. Betty expects to lose $150 from going to trial; with her share of the cooperative surplus, she would be willing to offer Arthur $100 to settle: -$150 (her threat value) + $50 (her share of the cooperative surplus) = -$100. What Arthur expects from cooperation ($200) is much greater than what Betty is prepared to offer for cooperating ($100). Thus, neither party prefers cooperating to litigation.

4):-Neither party anticipates a surplus from cooperating because each party is optimistic about winning the trial