Question

5-6. You are considering three investment alternatives for some spare cash: Old Reliable Corporation stock (A1), Fly-By-Nite Air Cargo Company stock (A2), and a federally insured savings certificate (A3). You expect the economy will either “boom” (N1) or “bust” (N2), and you estimate that a boom is more likely (p1=0.6) than a bust (p2=0.4). Outcomes for the three alternatives are expected to be (1) $2,000 in boom or $500 in bust for Old Reliable Corporation; (2) $6,000 in boom, but $5,000 (loss) in bust for Fly-By-Nite; and (3) $1,200 for the certificate in either case. Set up a payoff table (decision matrix) for this problem, and show which alternative maximizes expected value.

5-7. If you have no idea of the economic probabilities pj in Question 5-6, what would be your decision based on uncertainty using (a) maximax, (b) maximin, (c) equally likely, and (d) minimax regret assumptions?

Answer 1

Decision making environment There are following three types of decision making environment, i.e., the different states under which a decision can be made:

1) Decision making under uncertainty

2) Decision making under risk

3) Decision making under certainty

Decision making under risk

In this condition, for each possible state of nature (Nj), there exists a known or assumed probability of occurring such nature. For e.g., probability of nature X can be assumed as 0.8 while the probability of nature Y will be 0.2. These states of nature are evaluated for different alternatives, (Ai)

Decision matrix for the given conditions and three alternatives as mentioned in the question can be formulated as follows:

Calculate for the maximized expected value as follows:

The alternative with the highest expected value is FBN. Thus, investment should be made in FBN