The following is a payoff table giving profits for various s

The following is a payoff table giving profits for various situations

                                                        STATES OF NATURE

                                                                   DEMAND

ALTERNATIVES                 LOW                   MEDIUM                        HIGH

Alternative 1                         80                          120                                140

Alternative 2                         90                            90                                  90

Alternative 3                         50                            70                                150

The probabilities for states of nature Low, Medium, and High are 0.25, 0.55, and 0.2, respectively. If a perfect forecast of the future were available, what is the expected value of perfect information (EVPI)?

Solution

maximum pay off under low nature= 90

maximum pay off under medium nature =120

maximum pay off under low nature    =150

required probability given are for low =.25 ,mdium=.55   high =.2

exprected pay off with perfect information=.25*90+120*.55+150*.2

                                                                =118.5

now,EVPI=expected pay off with perfect information-expected payoff without experimantation

              from the bayes theorem,expected pay off without experimantation is 100

               =118.5-100

                 =18.5