What price an A?

An economist at a large state university mentioned to a student that he pays his teaching assistants $5 each if someone gets 90 percent or more correct on the final exam. The economist had previously paid off only twice in 29 years of teaching large introductory sections (total enrollment about 15,000 students over the years). The student pointed out very cleverly that any student who does well creates a positive externality (the dollars paid to the teaching assistants), so students in the class should be subsidized to give them the proper incentives to study hard. Who should offer the subsidy, the teaching assistant or the teaching economist? Identify and explain the underlying principle at work here.

Stock market strategies

You have been collecting data on the behavior of a particular stock over many years. You notice that every Friday the 13th, the stock drops substantially, only to come back up over the next few weeks. Your conclusion is that superstitious stockholders sell their stock in anticipation of bad luck. What can you do to make use of this information? What effect does your action have? Suppose more people notice the behavior of the stock and react accordingly--what is the effect?

Congratulations to Kaitlin Gossard for providing a reasoned explanation of the likely consequences of the above problem.

Damaged Goods: Another Guessing Game

Jackie and Greg, returning from a Las Vegas, find that the airline has damaged the identical antiques that each had purchased. An airline manager says that he is happy to compensate them but is handicapped by being clueless about the value of these strange objects. Simply asking the travelers for the price is hopeless, he figures, for they will inflate it.

Instead he devised a more complicated scheme. He asks each of them to write down the price of the antique as any dollar integer between 2 and 100 without conferring together. If both write the same number, he will take that to be the true price, and he will pay each of them that amount. But if they write different numbers, he will assume that the lower one is the actual price and that the person writing the higher number is cheating. In that case, he will pay both of them the lower number along with a bonus and a penalty—the person who wrote the lower number will get $2 more as a reward for honesty and the one who wrote the higher number will get $2 less as a punishment. For instance, if Jackie writes 46 and Greg writes 100, Jackie will get $48, and Greg will get $44.

What numbers will Jackie and Greg write? What number would you write?