Calculating the utility derived from each bet

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Reference no: EM131093133

Rosco has a utility function over money = log(I) where log is base 10 and I is money. His initial income (I) is $1000. Suppose he must accept one of three bets:

Bet (I): Win $100 with probability 1⁄2; lose $100 with probability 1⁄2

Bet (II): Win $100 with probability 3⁄4; lose $300 with probability 1⁄4

Bet (III): Win $100 with probability 9/10; lose $900 with probability 1/10

(a) Graph each of these of a utility-of-income graph with income on the horizontal and utility on the vertical axis, calculating the utility derived from each bet.

(b) Show that each of these bets are fair bets.

Reference no: EM131093133

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