A person's value function is v(x) = ./x!1. for gains and v{x) = -2Jixi for losses. The person is facing the choice between a sure $2 and a 50-50 gamble that pays $4 if she wins and $0 if she loses.

(a) Show algebraicaJly that this person is loss averse, in the sense that she suffers more when she loses $-l than she benefits when she receives $4.

(b) If the outcomes are coded as gains, meaning that she will take the worst possible outcome as her reference point, what is the value of (i) the sure amount and (ii) the gamble? Which would she prefer?
(c} If the outcomes are coded as losses, meaning that she will take the best possible outcome as her reference point. what is the value of (i) the sure amount and (ii) the gamble? Which would she prefer?