In this chapter, we have put the emphasis on the axioms underlying the alter native models, sothat it can beseenascomplementarytoChapter1.However, individual or collective decisions can also be analyzed with the help of the alternative models, which may produce interesting results and predictions.

The main purpose of this exercise is to illustrate this claim.

A decision maker has a wealth W0 subjected to a potential loss ˜ x described by a binary random variable (−x,p;0,1−p), where x

P =(1+λ)pβx

(a) What is the distribution of final wealth?

(b) Express the agent’s welfare if the adopts the axioms of Yaari’s dual theory with the function f(p)= p2.

(c) Showthat his optimal decision will be either β∗ = 0orβ∗ = 1 depend ing upon the values of p and λ. In fact you must obtain that β∗ = 1ifλ

is “not too high” for a given p.

(d) Convince yourself that β∗ = 1 may be optimal even if the loading is strictly positive. Contrast this result with the one obtained under EU.