Question

A machine shop owner is attempting to decide whether to purchase a new drill press, a lathe, or a grinder. The return from each will be determined by whether the company succeeds in getting a government military contract. The profit or loss from each purchase and the probabilities of each contract outcome are shown in the following payoff table: Contract No contract Purchase P(C) = .4 P(NC) = 6 Drill Press 30,000 Minus 10,000 Lathe 20,000 4,000 Grinder 12,000 10,000 a) What is the expected value of perfect information? b) Say the owner is a risk neutral person. Also say she is wondering about the probability of the contract. Over what range of values of the probability of a contract would each purchase have the highest expected utility?

Answer 1

a)

Expected value of perfect information

Exp of Drill Press = 30000 x 0.4 + (-10,000) x 0.6 = $ 6000

Exp of Lathe = 20000 x 0.4 + 4000 x 0.6 = $ 10,400

Exp of Grinder = 12000 x 0.4 + 10000 x 0.6 = $ 10,800

The maximum of these expectations is the type of purchase we will make. As we do not know whether or not we will be awarded the contract and only know the probability, we expect the highest return.

Expected value of perfect information is $ 10,800