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The price that Stan Berry would pay for perfect information is the difference between the expected profit with perfect information and the expected profit without perfect information. See the correct answer for a complete explanation.
To determine the maximum amount that a company would pay for perfect information, we compare the maximum profit that the company could achieve with perfect information with the best profit that would be available if we needed to choose one level when demand is not known. With perfect information the company would be able to choose the correct level of supply for each of the levels of demand. For example, if he knew the demand would be for 20 bags, Stan Berry would bring 20 bags and his profit would be $20. If he knew the demand would be 30 bags, he would bring 30 bags and the profit would be $30. And so on. However, he would be paying for this "perfect information" in advance, before he knows what the information will be. So to determine what he is willing to pay for the information in advance, he will calculate the expected value of his profit, assuming he will be able to bring exactly the right number of bags once he knows what the demand will be. He will use the various probabilities of demand as the weights in calculating this expected value. Therefore, given that for each level of demand the company will choose the best supply alternative, the expected value of the profit with perfect information is $33 [($20 × .2) + ($30 × .4) + ($40 × .3) + ($50 × .1)]. Without perfect information, Stan Berry would choose to stock 40 bags, because the expected profit for stocking 40 bags is $30.40, and that is higher than the expected profits for any of the other three potential supply levels. Since perfect information would provide an expected profit of $33.00 while the expected profit without the perfect information is $30.40, Stan Berry would pay a maximum of $2.60 (the difference between $33.00 and $30.40) for the perfect information.
The price that Stan Berry would pay for perfect information is the difference between expected profit with perfect information and expected profit without perfect information. This answer is the difference between the highest expected profit he could earn without perfect information ($30.40) and the second highest expected profit he could earn, also without perfect information ($29.60).
The price that Stan Berry would pay for perfect information is the difference between expected profit with perfect information and expected profit without perfect information. This is the difference between the highest expected profit he could earn without perfect information ($30.40) and the lowest expected profit he could earn, also without perfect information ($20.00).