Some home builders in recent years are moving towards condominium/townhouse complexes because of the rising cost of detached homes. Jell Inc. a new builder, must decide if to produce small, medium or large size complexes. The decision is complicated by the state of nature (demand for this type of housing), which can be quite unpredictable. Jell Inc. consulted a financial analyst who constructed a payoff table (in thousands of dollars) to reflect the alternatives available to the builder:

Complex Size

Demand Large Medium Small

High 1560 1060 870

Moderate 960 1060 870

Low -40 710 870

The probabilities associated with each state of nature are as follows:

P (high) = P (H) = 0.28; P (moderate) = P (M) = 0.43; P (Low) = P (L) = 0.29

Required:

1. What is the most the builder should pay for information about the state of nature?
2. The builder plans to employ a team of consultants with the following track record to better predict the state of nature.

P(I₁\H) = 0.78 P(I₁\M) = 0.20 P(I₁\L) = 0.02

P(I₂\H) = 0.14 P(I₂\M) = 0.70 P(I₂\L) = 0.28

P(I₃\H) = 0.08 P(I₃\M) = 0.10 P(I₃\L) = 0.720

Where

I₁ market research indicates high demand

I₂ market research indicated medium demand

I₃ market research indicates low demand.

Assuming that the consultant indicates a high demand for the product, revise the probabilities (to three decimal places) for high, moderate, and low demand

1. Does the prediction of a high demand by the consultant change the decision about plant size in part a? Show your calculations