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he ever-flamboyant chanteuse Lady Gaga is considering changing her style in fashion and music. She reckons...

he ever-flamboyant chanteuse Lady Gaga is considering changing her style in fashion and music. She reckons that if she adopts a new look and sound the probability of a hit record is ϕ and the payoff from a hit would be $16 million—including tour and merchandising revenues. However a flop would leave her with only $160 thousand after expenses.

Alternatively, if she sticks with her previous formula, her chances of striking a chord and having a big hit are only .05. However in the event that she does not have a hit, she is assured of revenues of $1 million dollars from sales to her faithful followers.

a. If Lasy Gaga’s expected utility function is U(ch, cf)= phch0.5+pfcf0.5, where h refers to a hit, f to a flop, what does the probability of a hit from a change in style have to be for a change in style to be optimal? WHY?

b. If Lasy Gaga’s expected utility function is U(ch, cf)= phch+pfcf, where h refers to a hit, f to a flop, what does the probability of a hit from a change in style have to be for a change in style to be optimal? WHY?

c. If Lasy Gaga’s expected utility function is U(ch, cf)= phch2+pfcf2, where h refers to a hit, f to a flop, what does the probability of a hit from a change in style have to be for a change in style to be optimal? WHY?

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