To determine the price that a company would pay for perfect information, we compare the maximum expected profit that the company could achieve with perfect information with the best expected profit that could be achieved if they had 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. Therefore, given that for each level of demand the company will choose the best supply alternative, the expected value is $68 [($0 × .1) + ($40 × .3) + ($80 × .4) + ($120 × .2)]. Without having perfect information, if the company provided a supply of 0 units, its expected profit would be 0. If it supplied 2 units, the expected profit would be $28 [(?$80 × .1) + ($40 × .9)]. If it supplied 4 units, the expected profit would be $20 [(?$160 × .1) + (?$40 × .3) + ($80 × .6)]. If it supplied 6 units, the expected profit would actually be a loss of $36 [(?$240 × .1) + (?$120 × .3) + ($120 × .2)]. So, without perfect information the best that the company can do is an expected profit of $28. Since perfect information would provide an expected profit of $68 and the best the company can do without perfect information is $28, the company would pay $40 (the difference) for the perfect information.
This is the expected profit with perfect information minus the expected profit from supplying 4 units, the demand level with the highest probability of occurring. See the correct answer for a complete explanation.
This is the amount of expected profit with perfect information. This is not the price one is willing to pay for the perfect information. See the correct answer for a complete explanation.
This is the difference between the expected profit with perfect information and the expected loss at the supply level of 6 units, the lowest expected payoff without perfect information. See the correct answer for a complete explanation.
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The price one is willing to pay for perfect information is
