Question A

A manufacturer is considering buying a used machine in an auction. If the machine is in a good condition, then the manufacturer expects an extra income of 100,000$; otherwise, when the machine is in a bad condition, she would incur a loss of 50,000$. There is a 90% chance that the machine is in a good condition.

a) How high should the bid go?

b) What is the value of perfect information?

The manufacturer can hire an expert. When the machine is in a good condition, there is an 80% chance that the expert would recommend buying. When it is in a bad condition, there is a 30% chance he would recommend buying.

c) How much would you recommend paying the expert?

Question B

After its recent failures in the financial sector, Citigroup decided to change course and look for new investment opportunities. It can invest in one of the following:

(1) Oil drilling in the North Sea. An investment of 4M$ is required. The possible outcomes:

A1 = Success - 10%. Expected revenue 20M$.

A2 = Failure. Expected revenue 1M$.

(2) Diamond mining in South America. An investment of 5M$ is required. The possible outcomes:

B1 = Success - 30%. Expected revenue 15M$.

B2 = Failure. Expected revenue 3M$.

(3) Producing a new Angelina Jolie movie. An investment of 5M$ is required. The possible outcomes:

C1 = Success - 60%. Expected revenue 11M$.

C2 = Failure. Expected revenue 2M$.

In addition, there is a 10% chance of a revolution in South America. In that case, any investment there is lost (even if diamonds are found).

Calculate the EMV.

How much would the company be willing to pay for perfect information on A only?

Diana Diamondcan predict success in diamond mining. Her recommendations are YES (success) or NO (failure). It is known that:
P(YES|B1) = 0.9; P(NO|B2) = 0.8

How much would the company be willing to pay Diana for her recommendation?