Beth’s preferences over her payment can be represented by the utility function (P) = √P. She
works in sales and can choose between two different payment options: (A) flat rate, or (B)
percentage of sales. With option A, Beth earns $49/hour. With option B, there is a 25% chance
of a high sales scenario in which Beth earns $144/hour and a 75% chance of a low sales scenario
in which she earns $16/hour.
Calculate Beth’s expected value and expected utility when she chooses option B. That is, E(PB)
and E[(PB)]. Which of the following alternatives is correct?
(a) E[(PB)] = √144 × 0.50 + √16 × 0.50 = 8
(b) E[(PB)] = √144 × 0.25 + √49 × 0.75 = 8.25
(c) E(PB) = 144 × 0.50 + 16 × 0.5 = 80
(d) E(PB) = 144 × 0.25 + 16 × 0.75 = 48