Michael, is a prospect theory maximizer. Michael can choose between two risky prospects, ˜p and ˜q. Each of them is expressed here in terms of the changes with respect to Michael’s reference point:
p˜ = (0.1, ?4; 0.5, ?1; 0.3, +1; 0.1, +9) q˜ = (0.5, ?2; 0.5, +3)
Michael’s underlying value function over changes relative to his reference point is given by v(x) = ( x^0.6 if x ? 0 ?2(|x|)^0.6 if x < 0
where |x| denotes the absolute value of x.
a) Assuming Michael does not distort the probabilities of different outcomes, calculate the overall value of each prospect and determine which one he would prefer.
b)Now suppose that Michael uses the following probability weighting function, which differs depending on whether the outcome that the probability refers to is a gain or a loss; ?(px) = ( (px)^2 if x ? 0 (px)^0.5 if x < 0 .
That is, if x is a gain, then the decision weight used by Michael for x will be its probability squared, (px)^2 (note that this makes the decision weight smaller than the probability). In contrast, if x is a loss, the decision weight used by Michael will be the square root of the probability, (px)^0.5 (note that this makes the decision weight larger than the probability). Recalculate the overall value of each prospect using the decision weights from the probability weighting function.
