Decision Analysis - Mainstream Image vs. Luxury Brand Image

A car company is considering a campaign to change its image from a mainstream to a luxury brand. If it decides to "create a" new image, the success will depend on the macroeconomic environment, which can be either booming (B), stagnating (S), or deteriorating (D).

• The payoffs associated with a booming, stagnating, and deteriorating macroeconomic environment are $600, $200, and $100, respectively.
• The car company evaluates the probabilities of a booming, stagnating, and deteriorating economy at p(B)=0.3, p(S)=0.5, and p(D)=0.2.
• If the company decides to go with its current image, its payoff is $350, regardless of the macroeconomic environment.

Question 16(1 point)

Saved

Which statement is true?

Question 16 options:

The expected payoff from the current mainstream brand image is higher than from the new one.

Assuming risk aversion with U(Payoff)=sqrt(Payoff), the expected utility from the current mainstream brand image is higher than from the new one.

Both a. and b. are correct.

None of the above is correct.

Question 17(1 point)

The expected payoff from the new luxury brand image is

Question 17 options:

250

300

350

400

Question 18(1 point)

Measured by payoffs (risk neutrality), what is the expected value of perfect information?

Question 18 options:

415

420

425

430

Question 19(1 point)

Measured by payoffs (risk neutrality), what is the maximum willingness to pay for perfect information?

Question 19 options:

25

50

75

100

Question 20(1 point)

Measured by utility [assuming U(Payoff)=sqrt(Payoff)], what is the expected utility of perfect information?

Question 20 options:

20.44

24.40

26.14

29.31

Question 21(1 point)

Measured by utility [assuming U(Payoff)=sqrt(Payoff)], what is the expected willingness to pay for perfect information?

Question 21 options:

147.76

356.64

417.97

None of the above.

Question 22(1 point)

Which statement is true? The willingness to pay for perfect information under the assumption of risk neutrality

Question 22 options:

is smaller than under the assumption of risk aversion.

is greater than under the assumption of risk aversion.

is the same as under the assumption of risk aversion.

is indeterminate from the given information.

Assume next that the car company consults a market research company. The market research company cannot provide the car company with perfect information, but it can tell the car company whether the image campaign has a high (H) or low (L) potential. The car company then updates its expectations about the macroeconomic environment as follows:

P(High | Boom) = 1.0, P(Low | Boom) = 0.0

P(High | Stagnating) = 0.6, P(Low | Stagnating) = 0.4

P(High | Deteriorating) = 0.0, P(Low| Deteriorating) = 1.0

This means, for example, the car company thinks that if a booming state of nature reveals itself to the marketing research company, then there is an 100% chance that the marketing research company concludes "High Potential" [P(High | Boom) = 1.0].

Question 23(1 point)

After the car company updated its probabilities, what is the probability that the car company gets a verdict of high potential, p(High)

Question 23 options:

0.3

0.4

0.6

0.7

Question 24(1 point)

After the car company updated its probabilities, what is the probability that the car company gets a verdict of low potential, p(Low)

Question 24 options:

0.3

0.4

0.6

0.7

Question 25(1 point)

Assume the marketing research company comes back with a verdict that the outlook is "high potential." What's the car company's updated probability that the economy is booming, given that the marketing research company finds high potential, p(B | H)?

Question 25 options:

0.0

0.25

0.5

0.75

Question 26(1 point)

Assume the marketing research company comes back with a verdict that the outlook is "high potential." What's the car company's updated probability that the economy is stagnating, given that the marketing research company finds high potential, p(S | H)?

Question 26 options:

0.0

0.25

0.5

0.75

Question 27(1 point)

Assume the marketing research company comes back with a verdict that the outlook is "high potential." What's the car company's updated probability that the economy is deteriorating, given that the marketing research company finds high potential, p(D | H)?

Question 27 options:

0.0

0.25

0.5

0.75

Question 28(1 point)

What is the updated expected payoff of launching the new campaign if the marketing research company finds "high potential?"

Question 28 options:

375

400

425

450

Question 29(1 point)

Assume the marketing research company comes back with a verdict that the outlook is "low potential." What's the car company's updated probability that the economy is booming, given that the marketing research company finds low potential, p(B | L)?

Question 29 options:

0.0

0.25

0.5

0.75

Question 30(1 point)

Assume the marketing research company comes back with a verdict that the outlook is "low potential." What's the car company's updated probability that the economy is stagnating, given that the marketing research company finds low potential, p(S | L)?

Question 30 options:

0.0

0.25

0.5

0.75

Question 31(1 point)

Assume the marketing research company comes back with a verdict that the outlook is "low potential." What's the car company's updated probability that the economy is deteriorating, given that the marketing research company finds low potential, p(D | L)?

Question 31 options:

0.0

0.25

0.5

0.75

Question 32(1 point)

What is the updated expected payoff of launching the new campaign if the marketing research company finds "low potential?"

Question 32 options:

150

175

200

225

Question 33(1 point)

Assume that the car company is risk neutral, what is the maximum willingness to pay for the marketing research company's services?

Question 33 options:

10

20

30

40

Question 34(1 point)

Assume that the car company is risk averse, what is the maximum willingness to pay for the marketing research company's services?

Question 34 options:

20.69

26.90

29.60

60.29

Question 35(1 point)

If the marketing research company charged $25 for its services, which statement is true?

Question 35 options:

Both a risk neutral and a risk averse management would consult the marketing research company.

Only a risk neutral management would consult the marketing research company.

Only a risk averse management would consult the marketing research company.

Neither a risk neutral nor a risk averse management would consult the marketing research company.