Consider an individual for whom Y is initially

£100 and U(Y) = Ya

, offered a bet on the toss of a fair coin at a price of £5. For each of the payouts A and B, calculate the expected value of the Y outcome, the individual’s expected utility, certainty equivalent and cost of risk bearing, for a taking the values 0.9, 0.95, 0.99. 0.999 and 1.0. In situation A, the individual gets £15 if he or she calls the way the coin falls correctly, and nothing if he or she gets it wrong. In B, the pay-out on a correct call is £10. Note that A is actuarially a very good bet, while B is actuarially fair, and identify the circumstances in which the individual would take the bet.

Note also that from equation 13.4 the certainty equivalent is expected utility raised to the power 1/a.