Midterm Exam
(You may leave any complete question or questions blank for 20%)

1. Your employer, the Prudent Bank and Trust Co., is being sued by GetRichQuick.com, an online investment company that bought a substantial quantity of mortgage based securities from PBT and lost quite a lot of money on them.

After a preliminary investigation you conclude that without substantial evidence of misrepresentation they have zero chance of prevailing. Unfortunately, several of your employees engaged in extensive email correspondence with GRQ employees prior to the transactions, and there is some risk, you think about 20%, that somewhere in that email there is something that could be interpreted by a court as misrepresentation, raising their chance of prevailing to 10%. If they do prevail you expect them to be awarded \$10,000,000. Hiring someone to do a careful search through the accumulated email will cost \$50,000. GRQ has offered to accept \$250,000 to settle their claims and you  believe this is their final offer. You estimate your trial costs if the case is not settled at \$100,000.

Draw a decision theory diagram for the problem on the back of page 3 and use it to decide what to do with regard to deciding both whether to search and whether to accept the settlement offer or go to trial. Explain if necessary.    (10 points)

The first choice is whether to search or not.

If you don't search, the next choice is to settle (\$250,000 cost) or go to trial (\$100,000). If you go to trial there is a .02 chance of losing (.2 chance there is evidence x .1 chance if there is evidence that you will lose--I could have shown this as two separate die rolls but didn't bother) and a .98 chance of winning. Winning costs you nothing, losing costs \$10,000,000, so .02 chance of losing costs \$200,000. That plus the \$100,000 trial cost is more than the cost of settling, so if you don't search you settle, making the cost of that branch \$250,000

If you do search, you find evidence (p=.2) or don't (p=.8). If you do you can settle for \$250,000 or go to trial. Trial costs \$100,000, a .1 chance of losing costs \$1,000,000, so total cost is \$1,100,000, so if there is evidence you settle. If you don't find evidence trial costs you only the \$100,000 trial cost, since you are sure to win, and that's lower than the \$250,000 settlement cost. So if you don't find evidence you go to trial.

So you have a .2 chance of finding evidence, cost \$250,000, a .8 chance of not finding it, cost \$100,000, total expected cost \$130,000. Add to that the \$50,000 search cost and the expected cost if you look for the evidence is \$180,000, which is less than the expected cost if you don't. So you look for evidence, settle if you find it, go to trial if you don't.

2. Consider the previous problem from the standpoint of Lenny Litigator, GRQ’s attorney, who agrees with you about the facts of the situation. Lenny is deciding what his settlement demand should be; his costs if the case goes to trial are \$50,000.

A. Use game theory—specifically, subgame perfect equilibrium—to decide whether he (and his client) are better off demanding \$250,000 or \$100,000. Assume all parties are risk neutral. Draw any necessary diagrams on the back of page 2.

We have already analyzed what happens if he demands \$250,000. The defendants pays for a search, settles if there is evidence (p=.2), goes to trial if there isn't (p=.8). From Lenny's standpoint that means a .2 chance of \$250,000 in settlement, a .8 chance of paying \$50,000 for a trial and getting nothing, for an expected return of \$50,000-\$40,000 = \$10,000

If he demands \$100,000, settling is cheaper than search+either settling or paying for a trial, so the defendant will settle, giving Lenny \$100,000.

So better to demand \$100,000.

B. Can you think of any reason why the assumptions of subgame perfect equilibrium might not hold in this situation?    (10 points)

The defendant might want to go to trial even with the lower demand, in order to lower the plaintiff's return and so discourage future plaintiffs.

3. The diagram shows the "put to bed/tantrum" game discussed in class; the parent's payoffs are black, the child's blue. The same game can also be described using a strategy matrix, shown below. Define the strategies and fill in the cells with the payoffs to each player.

ParentStrat1: Put to bed

ParentStrat2: Don't put to bed (let stay up)

ChildStrat1: Never throw a tantrum, whether or not put to bed

ChildStrat2: Always throw a tantrum, whether or not put to bed

ChildStrat3: Throw a tantrum only if put to bed

ChildStrat4: Throw a tantrum only if not put to bed

(5 points)

 Child's Strategies ChildStrat1 ChildStrat2 ChildStrat3 ChildStrat4 Parent's Strategies ParentStrat1 (10,-5) (-10,-10) (-10,-10) (10,-5) ParentStrat2 (-5,10) (-15,0) (-5,10) (-15,0)

4. The Law School has decided to offer every graduating student a free Bar prep course in the hope of raising its Bar passage rate. It is negotiating with PaBar, a small but well respected firm that produces such courses. The central issue being considered is how to determine how much PaBar is paid. Should it be based on the number of students who choose to take the course, the number of student hours spent in class, the number of students who, after taking the course, pass the Bar Exam on their first try, or the percentage of graduating students (including those who do not take the course) who pass the Exam on their first try?

A second issue is where the courses are to be given. Should PaBar find its own facilities, and if so who should pay for them? Alternatively, should PaBar be offered the use of university classrooms, if available, and on what terms?

Briefly describe several possible contracts, the problems each might raise and how they should be dealt with, and recommend the one you think best.  You may use the back of page 1.    (15 points)

Compensation: With cost plus, PaBar's only incentive to keep costs down is the hope of future business. Since it is presumably running some other courses, there might be problems measuring cost--PaBar would have an incentive to try to allocate as many costs as possible to its university courses--overpay teachers there with the understanding that they would work for lower wages in its other courses, for instance.

Fixed payment has two problems. One is that Paybar, as a small firm, may not want to bear the risk of higher costs. But the only element that one would expect to be unpredictable is the number of students, and the fixed payment could be made on a per student basis.

The other problem is the incentive to lower quality in order to save money. Which brings us to …

Giving Pabar an incentive to do a good job. The simplest way would be to make the compensation in part depend on how many students pass the bar--not entirely because PaBar is probably risk averse. This raises some further problems, however.

If the bonus is per student who passes, PaBar has an incentive to try to encourage students likely to pass to enroll and to discourage students unlikely to pass--still more so if it's based on the percentage of students who taking the PaBar course who pass the bar. What the school wants is to maximize the fraction (or equivalently the total number) of its graduating students who pass. So it could base the bonus on that number, counting both students who have and students who have not enrolled in PaBar. That way Pabar has no incentive to try to cherry pick the students who would pass anyway. Instead it will invest its efforts in whatever gives the greatest increase in bar passage rate per dollar spent.

So far as facilities, the school, having agreed on a fixed rate per student plus bonus compensation plan, should offer its facilities to PaBar at cost, and leave it free to rent outside facilities if that costs less.

Contract 1: Cost plus a bonus for each student who enrolls in PaBar. No incentive to keep cost down, and an incentive to try to attract students whether or not the added course will increase their chance of passage.

Contract 2: Per student payment, bonus based on percent of students taking the course who pass. Incentive to cherry pick the students who would probably pass anyway.

Contract 3. Per student payment, bonus based on total number of graduating students who pass (meaning in each case pass at the first try), including those who didn't enroll. Best alternative of the three for reasons sketched above.

A further point one student made was that if the contract does not provide an adequate incentive to maintain quality, the law school might want to monitor the teaching in an attempt to measure quality--although it's not clear what the school can do if it isn't satisfied.

[This question didn't have a single right answer--what I wanted to see was how well you could analyze the problem.]

5. High-Brow Decorators sells furnishings for fancy offices, specializing in an old English library look.. One of its most popular furnishings is a "wall" of 1000 old books. In its inventory, the company has three "walls" of old books. The first it purchased for \$100; the next it purchased for \$300 and the third it purchased for \$500. The price of old books varies based on the scrap value of used books at the time of purchase. One of High-Brow's customers – Joan Lawyer – who just became a partner in a fancy law firm orders one wall of books for \$2000; the firm delivers the books and bills Joan.

Show the T-accounts for the three purchases and the sale. What is the combined result of the series of transactions on the firm’s total assets, liability and equity?

Assets go up by \$1900 (FIFO) or \$1500 (FIFO). Liability unaffected. Equity up by the same amount as assets.

Draw a final set of T-accounts to show what happens when Joan pays the bill. How does that affect the firm’s total assets, liabilities and equity?

(5) in the T-accounts above. Assets, liabilities and equity are unchanged--one asset (account receivable) has been converted into another (cash).

State any assumptions you are making about the firm’s accounting practices.    (10 points)

The T Accounts assume FIFO--with LIFO item 4 would be \$500.