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A plant manager wants to know how much she should be willing to pay for perfect market research. Currently there are two states of nature facing her decision to expand or do nothing. Under favorable market conditions the manager would make $100,000 for the large plant and $5,000 for the small plant. Under unfavorable market conditions the large plant would lose $80,000 and the small plant would make $0. If the two states of nature are equally likely, how much should she pay for perfect information

Respuesta :

Answer:

She should pay $25,000 for perfect information.

Explanation:

Since it is assumed that the two states of nature are equally likely, we therefore have:

P1 = Probability favorable market condition = 50%, or 0.5

P2 = Probability of unfavorable market condition = 50%, or 0.5

For large plant, we have:

Amount to make under favorable market condition = $100,000

Amount to make unfavorable market condition = -$50,000

Therefore, we have:

Expected value of the amount to make from large plant = (P1 * $100,000) + (P2 * (-$50,000)) = (0.5 * $100,000) + (0.5 * (-$50,000)) = $25,000

For small plant, we have:

Amount to make under favorable market condition = $5,000

Amount to make unfavorable market condition = $0

Therefore, we have:

Expected value of the amount to make from small plant = (P1 * $5,000) + (P2 * $0) = (0.5 * $5,000) + (0.5 * $0) = $2,500

Decision

Expected value of the amount to make from large plant = $25,000

Expected value of the amount to make from small plant = $2,500

Since the expected value of the amount to make from large plant of $25,000 is larger than the expected value of the amount to make from small plant of $2,500, this implies that the maximum the plant manager can make is $25,000.

Therefore, she should pay $25,000 for perfect information.

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