Steve gets happiness from money according to the utility function U($) = $. This

Question

Steve gets happiness from money according to the utility function U($) = $. This means that $25 worth of money gives him 25 units of happiness and $50 worth of money gives him 50 units of happiness. Suppose a casino lets him bet on the spin of a roulette wheel. He can bet $10 on black and will win $10 if the ball falls in a black bin, or lose his $10 if the ball falls in either a red or green bin. Suppose further that there are are 24 possible black bins, 24 red bins, and two green bins. How much would we expect playing this game would impact happiness?

Explanation / Answer

Answer

If he wins he will get $20 and

probability of winning = Probability of getting black(p1) = 24/(24 + 24 + 2) = 24/50.

If he looses he will get $0 and

probability of loosing(p2) = Probability of getting green or red = (24+2)/(24 +24+2) = 26/50.

Expected utiity = p1u(winning($)) + p2u(loosing($))

= (24/50)*20 + (26/50)*0

= 9.6

If he doesnt played the game then his utility = 10

Hence we expect his happiness to decrease by 10 - 9.6 = 0.4 units

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.