## Mini-Quiz #6

Honor Code: You must do these problems on your own, and submit your answers no later than 11 PM on Sunday, November 11.

Name:

NetID:

Leon, the lion tamer, has decided to try adding a new lion to his pride. He's visited a commercial lion-breeding farm, where he has been offered a cub for $6,000. From past experience, Leon believes that there's a 60% chance that a lion cub purchased from the farm will prove to be trainable.

It takes about six months of work to really learn for certain whether a lion is trainable or not. If the lion is trainable, Leon feels that his long-term gain, netted against the cost of caring for the lion, is $15,000. (That is, he'll net $9,000 in profit after also figuring in the cost of purchase.) However, if the lion proves to be untrainable, his only option is to donate the lion to a local zoo for a charitable-deduction tax break. After netting maintenance expenses against the deduction, he still comes out $2,000 behind (for an overall loss of $8,000).

What is Leon's expected profit (taking both the purchase price and long-term costs and gains into account) if he buys a cub from the farm? $

Leon knows that, after working with a lion cub for a week, he'll get a "feeling" for whether the lion will eventually prove to be trainable: If a lion really is trainable, he'll have a 90% chance of feeling optimistic (and a 10% chance of feeling pessimistic) at the end of the week; if a lion really is untrainable, he’ll have only a 50% chance of feeling optimistic. (Leon, like any good lion tamer, leans towards optimism.)

The farm has offered Leon a special deal: For an extra (nonrefundable) $500, the cub will be returnable up to a week after purchase for a full refund of the base purchase price. (That is, Leon pays $6,500 up front, but gets $6,000 back if he returns the cub after a week.) Leon considers the cost of caring for (and working with) a lion cub for just a week to be negligible.

What is Leon's optimal strategy?

Leon should ... | not buy the cub buy the cub without the return option buy the cub with the return option
If Leon buys the cub with the return option, and feels pessimistic after a week, he should ... | return the cub keep the cub
If Leon buys the cub with the return option, and feels optimistic after a week, he should ... | return the cub keep the cub

Following his optimal strategy, what is Leon's expected overall expected profit? $

If the cost of the option were up for negotiation (instead of being $500), what is the most Leon should be willing to pay for the option? $

When you are finished, click here: