A person’s value function is v (x) = √x/2 for gains and v (x) = −2√|x| 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 algebraically that this person is loss averse, in the sense that she suffers more when she loses $4 than she benefits when she receives $4.

(b) If she takes the worst possible outcome ($0) as her reference point, what is the value of the sure amount and the gamble? Which would she prefer?

(c) If she takes the best possible outcome ($4) as her reference point, what is the value of the sure amount and the gamble? Which would she prefer?