Two neighbors, Sempronius and Caus, have the same initial wealth of 10, which is subjected to the risk of a potential loss equal to 8.

Two neighbors, Sempronius and Ca¨ıus, have the same initial wealth of 10, which is subjected to the risk of a potential loss equal to 8. However, they greatly differ in the probability of occurrence of the loss. For Sempronius the loss has a probability of 0.40, while it is much higher for Ca¨ıus and amounts to 0.95.

Both Sempronius and Ca¨ıus have the opportunity to buy a safety device that costs 1 but reduces the probability of occurrence of the loss by 0.15.

(a) Show that if both Sempronius and Ca¨ıus are risk neutral they should both buy the device. Explain why.

(b) Iftheyareequallyriskaversewithautilityfunctionu(w) = w−0.04w2 identical for each of them, show that their opinion about the interest of the safety device will diverge.

(c) Once you have done the computations in (b), explain the results intu itively. In other words, why is Ca¨ ıus now reluctant to buy the safety device?