(This problem foreshadows the topic of Chapter 19; it is well worth trying.

If you have problems with the exponential utility function, please see the discussion in the Online Supplement.)

Jan MBA has the opportunity to take a gamble that will net her either a gain of $50,000 or a loss of $25,000, each with probability 1/2. Jan chooses among gambles to maximize her expected utility, with utility function u(y) = −e−0.0000211y, where y is Jan’s net proceeds from the various deals she is currently contemplating.

(a)Will Jan choose to take this gamble, if the alternative is a sure thing of $0?

(b) Suppose Jan could securitize this gamble, which means she prints up 100

“shares” in the gamble, each of which gives a 1/2 chance at a gain of $500 and a 1/2 chance of a loss of $250. Suppose Jan has 99 friends, each of whom has precisely the same utility function as Jan. Would one of those 99 friends be willing to pay Jan $100 for a 1% share of the gamble?