Question

Wilhelms Cola Company plans to market a new lime-flavored cola this summer. The decision is whether to package the cola in returnable or non-returnable bottles. Currently, the legislature is considering eliminating nonreturnable bottles. The CEO of Wilhelms has discussed the problem with state legislators and established that there is a 50-50 chance that returnable bottles will be eliminated. The following table has been created to show estimated monthly profits in returnable vs nonreturnable bottles.

	Law Passed (s1)	Law Not Passed(s2)
Returnable Bottles	80	40
Non Returnable Bottles	25	60

1. Compute the expected opportunity loss for returnable bottles.  Round to one decimal.

2. Compute the expected opportunity loss for non-returnable bottles.  Round to one decimal.

3. Compute the expected value of perfect information.  Round to one decimal

Answer 1

First we will calculate the regret in both the cases where law is passed and where law is not passed.

So in case the law is passed (s1) the best expected payoff is in case of returnable bottles which is 80 and the regret for non returnable bottles will be 80 - 25 = 55. For returnable bottles it will be 80 - 80 = 0.

In case of the law is not passed (s2) the best expected payoff is in case of non returnable bottles which is 60 and the regret for returnable bottles is 60 - 40 = 20. For non returnable bottles it will be 60 - 60 = 0.

1. So now we have both regrets for returnable bottles and the probability is 50% or 0.5 for both the scenarios. Hence EOL for returnable bottles = (0.5 * 0) + (0.5 * 20) = 10.

2. So now we have both regrets for non returnable bottles also and the probability is 50% or 0.5 for both the scenarios.  Hence EOL for non returnable bottles = (0.5 * 55) + (0.5 * 0) = 27.5.

3. The formula for expected value of perfect information is

EVPI = Expected value with perfect information -  Expected value without perfect information

now we have already calculated the value without information which is best at 27.5. However the first part of EVwPI is not known and it will the best outcome subject to probability so in case law is passed it is 80 in case of returnable bottles and 60 in case of returnable bottles; the probability is 0.5.

So EVwPI = (0.5 * 80) + (0.5 * 0.6) = 40 + 30 = 70.

Hence EVPI =  EvwPI - EVwoPI = 70 - 27.5 = 42.5