Value of perfect information/uncertainty

The expected value with perfect information will always be higher than the expected value without it - it must be. If the expected value with and without perfect information is negative in both cases then we would not go ahead with anything (although with perfect information is bound to be less negative than without perfect information).

It is not what I ask, I ask, if the loss occurs in one of the occasions. Value of perfect information, would it be the amount of loss x probability? Or is it the highest amount, that could be chosen, if the demand is predictable x probability?I noticed that in some answers about perfect information, there was just amount of loss taken and x probility? But what If there are several demand rows, and we could predict also the higest profit? Thanks.

Where there is perfect information, then for each possible outcome we choose the best course of action (i.e. that giving the highest return). Then we calculate the expected value of those highest returns. In general, when calculating expected values then a loss is included in the normal way - just as a negative figure. With perfect information, then if for one possible outcome all courses of action result in a loss, then the best course of action would be to do nothing - so a return of zero. (Unless of course the question said that you had to take a course of action, in which case you would select the one giving the smallest loss.)

Yes, this is true, do nothing, but given we know that the loss could be predicted, we have to pay for this information. And this is a value of all lossess for all possible outcomes multiplied by probability. Correct?

No - the maximum we will be prepared to pay for the information will be the difference between the expected value with the information, and the expected value without the information. I don't know if you have looked at the example in our free course notes (the answer to it is at the back of the notes), but it might be helpful. At the moment there is no lecture on the perfect information part of the example, but all being well I will be recording one within the next couple of weeks.