Question 1 a) Consider the following four lotteries: Lottery L: 50% chance of winning 80; 10% chance of winning 50, 0 otherwise Lottery M: 30% chance of winning 80; 40% chance of winning 50, 0 otherwise Lottery N: 40% chance of winning 80; 40% chance of winning 50, 0 otherwise Lottery P: 20% chance of winning 80; 70% chance of winning 50, 0 otherwise If an individual prefers lottery L to lottery M, and prefers lottery N to lottery P; prove rigorously whether or not their preferences conform with the Independence Axiom of Expected Utility Theory. [50%] b) Critically evaluate the claim that the Allais paradox fatally undermines Expected Utility Theory. [50%] Question 1 a) Consider the following four lotteries: Lottery L: 50% chance of winning 80; 10% chance of winning 50, 0 otherwise Lottery M: 30% chance of winning 80; 40% chance of winning 50, 0 otherwise Lottery N: 40% chance of winning 80; 40% chance of winning 50, 0 otherwise Lottery P: 20% chance of winning 80; 70% chance of winning 50, 0 otherwise If an individual prefers lottery L to lottery M, and prefers lottery N to lottery P; prove rigorously whether or not their preferences conform with the Independence Axiom of Expected Utility Theory. [50%] b) Critically evaluate the claim that the Allais paradox fatally undermines Expected Utility Theory. [50%]