Question

. Film scenario. A Hollywood film producer named John Mogul is evaluating a script for a potential film. Mogul estimates that the probability of a film based on that script being a hit is .10 and probability of it being a flop is .90. The studio accounting department estimates that if a hit, the film will make $25 million in profit, but if a flop, will lose $8 million. Before deciding whether or not to produce a film based on that script, Mogul needs to decide whether or not to hire film critic Dick Roper to evaluate the script. Over many reviews of scripts in the past, Roper film would be a hit (of the scripts) for 70% of the films (based on the scripts) that turned out to be hits, and had predicted film was a flop (of the scripts) for 80% of the films (based on the scripts) that turned out to be flops. [adapted from Taylor (2004)]

(a) Assuming Roper would not charge for his review services, determine the optimal strategy based on the expected value criterion, and state its expected value (Draw and solve the Decision Tree below).

(b) Determine EVSI (with Roper regarded as the sample information).

(c) If Roper were to charge $100,000 for his review, what would be the optimal strategy and its expected value?

Answer 1

We know the following probabilities

the probability of a film based on that script being a hit is .10. The profit if a hit is $25 million

and probability of it being a flop is .90. The profit if a flop is -$8 million (we show the loss as negative profit)

Roper had predicted film would be a hit (of the scripts) for 70% of the films (based on the scripts) that turned out to be hits.

This is same as the probability that Roper predicts a hit given that the film is a hit is 0.70

and had predicted film was a flop (of the scripts) for 80% of the films (based on the scripts) that turned out to be flops.

This is same as the probability that Roper predicts a flop given that the film is a flop is 0.8

the probability that Roper predicts a hit is

the probability that Roper predicts a flop is

the probability that film is a hit given that Roper predicts a hit is

the probability that film is a flop given that Roper predicts a hit is

the probability that film is a flop given that Roper predicts a flop is

the probability that film is a hit given that Roper predicts a flop is

(a) Assuming Roper would not charge for his review services, determine the optimal strategy based on the expected value criterion, and state its expected value (Draw and solve the Decision Tree below).

Create the following tree

Moving from the right to the left

Node 6: chance node

The expected value is

Node 7: chance node

The expected value is

Node 8: chance node

The expected value is

Node 3: Decision Node

Decide between the 2 choices

• Produce the film at an expected value of $1.24 million
• Do not produce the film at an expected value of $0

Since Produce the film has a higher expected value, the optimum decision at node 3 is to produce the film

The expected value at node 3 is

EV(3)=1.24

Node 4: Decision Node

Decide between the 2 choices

• Produce the film at an expected value of -$6.68 million
• Do not produce the film at an expected value of $0

Since do not Produce the film has a higher expected value, the optimum decision at node 4 is to do not produce the film

The expected value at node 4 is

EV(4)=0

Node 5: Decision Node

Decide between the 2 choices

• Produce the film at an expected value of -$4.7 million
• Do not produce the film at an expected value of $0

Since do not Produce the film has a higher expected value, the optimum decision at node 5 is to do not produce the film

The expected value at node 5 is

EV(5)=0

Node 2: Chance node

The expected value is

Node 1: Decision Node

Decide between the 2 choices

• Hire Roper to critic: The expected value is $0.31 million
• Do not hire Roper: The expected value is $0

The optimum decision is to hire Roper

ans: the optimal strategy based on the expected value criterion is hire Roper to evaluate the script, and its expected value is $0.31 million

(b) Determine EVSI (with Roper regarded as the sample information).

The expected value with sample information is the expected value when we hire Rope

The expected value without sample information is the expected value when we do not hire Roper

The expected value of Sample information is

ans: EVSI = $0.31 million

(c) If Roper were to charge $100,000 for his review, what would be the optimal strategy and its expected value?

The expected value of Roper evaluating the script is EVSI=$310,000

If Roper charges $100,000 the expected value would be $310,000-100,000=$210,000

Since this expected value is positive, it makes sense to hire Roper

ans: The optimal strategy would be to hire Roper to evaluate the script at $100,000. The expected value would be $210,000