An automobile manufacturer must make an immediate decision on the car size which should account for the majority of the firm's production two years from now. The firm perceives three possible states of nature at that time: S₁, gasoline will be rationed; S₂, gasoline will be readily available at close to current prices; and S₃, gasoline will be readily available, but at much higher prices. The firm has determined the following profit payoff table (in $l,000s).
a.An economist at the auto company has advised the firm that the probabilities of the states of nature are P(S₁) = .2, P(S₂) = .5, and P(S₃) = .3. Find the expected value for the three decisions.
b.Which decision should be chosen under the expected value criterion?
c.Determine the expected value of perfect information.

Question

An automobile manufacturer must make an immediate decision on the car size which should account for the majority of the firm's production two years from now. The firm perceives three possible states of nature at that time: S₁, gasoline will be rationed; S₂, gasoline will be readily available at close to current prices; and S₃, gasoline will be readily available, but at much higher prices. The firm has determined the following profit payoff table (in $l,000s).

a.An economist at the auto company has advised the firm that the probabilities of the states of nature are P(S₁) = .2, P(S₂) = .5, and P(S₃) = .3. Find the expected value for the three decisions.
b.Which decision should be chosen under the expected value criterion?
c.Determine the expected value of perfect information.

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The Answer of An automobile manufacturer must make an immediate decision on the car size which should account for the majority of the firm's production two years from now. The firm perceives three possible states of nature at that time: S₁, gasoline will be rationed; S₂, gasoline will be readily available at close to current prices; and S₃, gasoline will be readily available, but at much higher prices. The firm has determined the following profit payoff table (in $l,000s). a.An economist at the auto company has advised the firm that the probabilities of the states of nature are P(S₁) = .2, P(S₂) = .5, and P(S₃) = .3. Find the expected value for the three decisions. b.Which decision should be chosen under the expected value criterion? c.Determine the expected value of perfect information.

An Automobile Manufacturer Must Make an Immediate Decision on the Car