Let I = [0, 1] be an interval of monetary outcomes, and let L denote the set of all lotteries

over I with finite support. This means each p L is a function p : I [0, 1] such that

supp(p) := {x I : p(x) > 0} is finite and xI sum of p(x) = 1. Let denote a preference

relation over L represented by the function

U(p) = u(xp) + (1 )u(xp)

where 0 < < 1, u : I R is continuous, concave, and strictly increasing and, for every p,

xp and xp are the max and min elements of supp(p), respectively.

(a) Provide an interpretation of these preferences. Explain, in words, what the parameter

represents, and why an agent might have such preferences.

(b) For each of the following claims, determine whether the claim is true or false. Support

your answers with proofs or counterexamples.

(i) is completely and transitive.

(ii) satisfies the Independence axiom.

(iii) satisfies the Continuity axiom.

(iv) is risk averse