Tomorrow evening, I plan to tackle this problem during class. In order to solve this problem, one must use various concepts from the reading; specifically, expected value, expected utility, and certainty equivalent. If you have time between now and then to work on it, that’d be great. If not, not to worry. For a nicely formatted PDF version of this class problem, click here.
Blanche has identified a risky venture opportunity. This venture will have one of two possible outcomes: It will be a flop, or it will be successful. If it is a flop, it will make $0. If it is successful, it will make $120,000. There is an 80% chance it will be a flop, and a 20% chance that it will be successful. It does not cost Blanche anything to undertake this venture.
Blanche has initial wealth of $40,000, and a utility function
U(W) = W0.5
where W is her wealth.
[Note: Carry all calculations to at least two decimal places in this problem]
(a) What is Blanche’s certainty equivalent for this risky venture opportunity?
Blanche’s certainty equivalent is: ________________________
Now Blanche hits upon another idea. She finds 10 members of her MBA cohort, and decides to try to “sell” the opportunity to invest in this venture for $2,000 per investor. Each of the 10 cohort members that Blanche approaches with this investment offer has an initial wealth of $90,000, and a utility function U(W) = W0.5, where W is the cohort member’s wealth.
If a cohort member invests $2,000 with Blanche, then:
- If the venture is successful, Blanche keeps the investor’s $2,000 and pays the cohort member 1/10th of the upside (that is, $12,000). This means the investor enjoys a net gain of $10,000, and a final wealth level of $100,000.
- If the venture is a flop, however, then Blanche will keep the investor’s $2,000 and pay the investor nothing in return. The investor suffers a net loss of $2,000, and a final wealth of $88,000.
(b) I-Banker Joe is one of the ten cohort members Blanche approaches. What is Joe’s certainty equivalent for the deal that Blanche is offering? If Joe’s only two options are either to accept Blanche’s offer, or to maintain his initial wealth of $90,000 for sure, will Joe accept Blanche’s offer?
Joe’s certainty equivalent if he invests with Blanche is ___________________________
Joe ( will, will not ) accept Blanche’s offer because:__________________________
(c) Is Blanche better off selling-off her investment opportunity to 10 cohort members (under the terms described above), or is she better off taking the investment opportunity herself?
Blanche should ( sell off the opportunity, take the opportunity herself )