Question 3. {2f} marl-rs} This question deals with decision making under uncertainty. [1} State precisely what we mean by a decision maker's preferences over a space of simple lotteries satisfying the independence axiom and explain in the context of lotteries over three consequences why continuity and the independence axiom would imply that the in difference curves are parallel straight. lines. [It] marks] [2} Consider a decision maker who when confronted with a choice be- tween a lottery that would give her $1,0[l for sure and a lottery that would give her $111m with probability 0.39, nothing with probability Hill, and $5,, with probability {1.10 would pre- fer the rst lottery; and when confronted with a choice between a lottery that would give her nothing with probability $.89 and $1,U,flfl with probability [Lil and a lottery that would give her nothing with probability 0.91} and $51m with probability Ill would prefer the second lottery. Show that these preferences violate the independence axiom. {If} marks]