Of all the programs picked 25% turn out to be hits. This is same as the probability of any given program picked turns out to be a hit is 0.25
P(hit)=0.25 with a payoff of $18 millions
Of all the programs picked 75% turn out to be flops. This is same as the probability of any given program picked turns out to be a flop is 0.75
P(flop)=0.75 with a payoff of -$8 millions
If the program is actually going to be a hit, there is a 75% chance that the market researchers will predict hit. This is same as the conditional probability of market researchers predict hit given that the program is actually going to be a hit is 0.75
If the program is actually going to be a flop, there is only a 30% chance that the market researchers will predict hit. This is same as the conditional probability of market researchers predict hit given that the program is actually going to be a flop is 0.30
Using these, we calculate the following
We calculate the following conditional probabilities
We prepare the following decision tree, ignoring the cost C of market research
Node 6: chance node
The expected value at node 6 is
Node 7: chance node
The expected value at node 7 is
Node 8: chance node
The expected value at node 8 is
Decision node 3:
Chose between 2 alternatives
The optimum decision is to pick the program
EV(3)=$3.817
Decision node 4:
Chose between 2 alternatives
The optimum decision is to not pick the program
EV(4)=$0
Decision node 5:
Chose between 2 alternatives
The optimum decision is to not pick the program
EV(5)=$0
chance node 2:
The expected value is
a) Using the above, we get the following
The expected value with sample(the market research) information is
The expected value without sample(the market research) information is
The expected value of sample(the market research) information is
This is the maximum value C that the network should be willing to pay the market research firm
ans: $1,575,000 (when using unrounded probabilities)
b) If the network knows exactly (has the perfect information) if the program being picked is going to be a hit, it will pick the program at a payoff of $18 million. If it knows that if the program being picked is going to be a flop, it will not pick the program at a payoff of $0 million
The expected value with perfect information is
The expected value without perfect information is the expected value at node 5
The expected value of perfect information is
ans: EVPI=$4,500,000
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