7.6 If there is a 25 per cent probability that Amy will lose €1000 of her cash on the safari, what is the safari’s expected utility?

Suppose that Amy can buy insurance against losing the €1000 (say, by purchasing traveller’s cheques) at an ‘actuarially fair’ premium of

€250. Show that her expected utility is higher if she purchases this insurance than if she faces the chance of losing the €1000 without insurance.

What is the maximum amount that Amy would be willing to pay to insure her €1000?

In deciding to sell a counterfeited product illegally, an indi vidual knows that the probability of getting caught by the police is p and that the fine the individual will have to pay if apprehended is

f. Suppose that all individuals are risk averse

(i.e., U

″(W

) < 0, where W is the individual’s wealth).

Will a proportional increase in the probability of being caught or a proportional increase in the fine be a more effec tive deterrent to illegal trade? Hint: Use the Taylor series approximation U

(W − f

) = U

(W

) − fU

′(W

) +

(f 2/2)U″(W

).