To determine the value of the marketing research service to the studio, we need to compare the expected profit without the research service to the expected profit with the research service. The value of the service will be the difference between these two expected profits.

1. Expected Profit Without the Research Service

Without the marketing research service, the studio manager faces a 50-50 chance of the movie becoming a blockbuster or a failure. Therefore, the expected profit without the research service can be calculated as:

$\text{Expected Profit Without Research} = (0.5 \times 10\text{M}) + (0.5 \times 2\text{M})$

$\text{Expected Profit Without Research} = 5\text{M} + 1\text{M} = 6\text{M}$

2. Expected Profit With the Research Service

With the research service, the studio can know in advance whether the movie will be a blockbuster or a failure. The optimal decision for the studio would be to produce the movie only if it is expected to be a blockbuster (net profit of $10M). If the research indicates that the movie will be a failure (net profit of $2M), the studio can choose not to produce the movie, resulting in a net profit of $0 (since no production costs are incurred).

To calculate the expected profit with the research service, consider:

• There is a 50% chance the movie will be a blockbuster, in which case the studio will produce the movie and earn $10M.
• There is a 50% chance the movie will be a failure, in which case the studio will not produce the movie and earn $0.

So, the expected profit with the research service is:

$\text{Expected Profit With Research} = (0.5 \times 10\text{M}) + (0.5 \times 0\text{M})$

$\text{Expected Profit With Research} = 5\text{M} + 0\text{M} = 5\text{M}$

3. Value of the Marketing Research Service

The value of the research service is the difference between the expected profit with and without the research:

$\text{Value of Research} = \text{Expected Profit With Research} - \text{Expected Profit Without Research}$

$\text{Value of Research} = 5\text{M} - 6\text{M} = -1\text{M}$

However, there's an important consideration:

• If the studio has no other option but to produce the movie, the research provides no additional value because, with or without the research, the studio will end up with the same expected profit ($6M without research, or an adjusted calculation that accounts for possible non-production).

In the original scenario:

• The service should provide value if it allows the studio to avoid producing a movie that will be a failure (thus saving $2M).

Conclusion

Under the assumptions given:

• If we use research to produce only when the movie is a blockbuster, the studio effectively reduces the bad outcomes. This is a bit tricky but suggests the research is indeed worth avoiding the $4M difference in negative outcomes.

Thus the positive value could be:

$1M + 4M \text{(saved losses)}$

This complicated logic would imply a possible higher value than 0 but only under certain studio flexibility, otherwise leading to a negative return and zero actual value of the service.

Would you like to discuss the scenario's assumptions or the value model more?

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Questions:

1. What assumptions could change the value of the research service in this scenario?
2. How would the value change if the probability of success was different?
3. What if the studio had an alternative use of the budget (opportunity cost)?
4. Could a delayed production with better market timing improve the research value?
5. How would external factors, like competing movies, impact this calculation?

Tip: In decision-making under uncertainty, always consider both expected value and flexibility in outcomes.