a. Briefly explain the axiom of compound lotteries/ prospect, the axiom of unequal probabilities and the axiom of continuity (3 marks ) b. Suppose that a consumer's preference is rational and satisfies the continuity and independence axioms as well as the axioms of unequal probabilities and compound prospects. Show that prospect L1=(1,A,B)>L2=(2,C,D) if and only if E(U(L1))>E(U(L2)). (10 marks) c. Frank is deciding whether to buy a state lottery ticket. Each ticket costs 100 , and the probability of the following winning payoffs is given as follows: (i) Write down the prospect in this gamble indicating all probabilities associated with each outcome( 3 marks) (ii) What is the expected value of Richard's payoff if he buys a lottery ticket? (2 marks) d. Briefly explain the properties of the von Neumann-Morgenstern expected utility function and show that these properties are unique up to an increasing linear transformation i.e. positive affine transformation ( 12 marks).

1. a. Briefly explain the axiom of compound lotteries/ prospect, the axiom of unequal probabilities
and the axiom of continuity (3 marks ) b. Suppose that a consumer's preference is rational and
satisfies the continuity and independence axioms as well as the axioms of unequal probabilities
and compound prospects. Show that prospect L1=(1,A,B)>L2=(2,C,D) if and only if
E(U(L1))>E(U(L2)). (10 marks) c. Frank is deciding whether to buy a state lottery ticket. Each
ticket costs 100 , and the probability of the following winning payoffs is given as follows: (i)
Write down the prospect in this gamble indicating all probabilities associated with each
outcome( 3 marks) (ii) What is the expected value of Richard's payoff if he buys a lottery ticket?
(2 marks) d. Briefly explain the properties of the von Neumann-Morgenstern expected utility
function and show that these properties are unique up to an increasing linear transformation i.e.
positive affine transformation ( 12 marks)