Suppose that Warren Buffett is considering buying Mysterious Practices, Inc. (MPI). Due to financial distress unrelated to MPI's operations, MPI's current ownership has fallen on hard times and is considering selling the company. As it turns out, Buffett is the only potential buyer for MPI before it is eventually liquidated.

Buffett can make a single take-it-or-leave-it offer to MPI, and he judges that there are four possible scenarios for the technology MPI is currently using. Each scenario is equally likely. Moreover, suppose that (for now, at least) there is nothing Buffett can do to distinguish between the four possible scenarios.

(in billions)

Buffett's valuation. Current owner's valuation

Cutting-edge technology $3.0 $2.0

Efficient technology $2.0 $1.5

Average technology $1.5 $1.0

Antiquated technology $0.5 $0.2

You can assume that MPI's current owners would accept an offer equal to their valuation, and that they know what the state of their technology is.

(a)Suppose Buffett offers a price of $1 billion. What is the probability that this offer is accepted? And what are Buffett's expected profits (taking into account the possibility of rejection) from this offer?

(b)Suppose Buffett offers a price of $2 billion. What is the probability that this offer is accepted? And what are Buffett's expected profits (taking into account the possibility of rejection) from this offer?

(c)What price would you advise Buffett to offer, assuming that you have no more information than he does? What would his profits be? Be sure to fully explain your reasoning.

(d)A consulting firm offers to determine the state of MPI's technology. Suppose that Buffett trusts that the consultant's information will reveal the true state of MPI's technology, but Buffett has to pay for the information in advance (before learning which state will be revealed). What price would Buffett be willing to pay for this information? Explain.