Peter evaluates risky alternatives based on prospect theory. For positive values of X (up to $7,500), his valuation function is V(X) = 30,000X - 2X2. For negative values of X (closer to zero than - $7,500), it's V(X) = 60,000X - 2X2. Peter's probability weighting function is Z (P) = 0.05 + 0.9P. Do these functions fit the assumptions of prospect theory? Show how Peter ranks the following gambles:
(a) 0 for sure;
(b) Win $25 with 50 percent probability; lose $10 with 50 percent probability;
(c) Win $300 with 2 percent probability; lose $10 with 98 percent probability;
(d) Win $45 with 98 percent probability; lose $300 with 2 percent probability;
(e) Win $300 with 70 percent probability; lose $315 with 30 percent probability;
(f) Win $6,000 with 30 percent probability; lose $900 with 70 percent probability.