Question

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.

Answer 1

Given that the payoffs associated with a booming, stagnating, and deteriorating macroeconomic environment are $600, $200, and $100 and  the probabilities are p(B)=0.3, p(S)=0.5, and p(D)=0.2, respectively.

a) Payoff with current image= $350

The expected payoff from the new mainstream brand image = (600*0.3)+(200*0.5)+(100*0.2)

=$300

Therefore, the expected payoff from the current mainstream brand image is higher than from the new one

b) Given that, U(Payoff)=sqrt(Payoff)

the expected utility from the current mainstream brand image = sqrt (350)

=175

the expected utility from the new mainstream brand image= sqrt(300)

=150

Therefore, the expected utility from the current mainstream brand image is higher than from the new one.

So, Both a and b are correct