Question

Problem 3: (Application of the prospect theory probability weighting function): A famous implication of prospect theory is a preference for positively skewed prospects and an aversion to negatively skewed prospects. For example, Tversky and Kahneman (1992) found that people frequently preferred:

1. 1) Gaining $95 with certainty over a 95% chance of gaining $100 and a 5% chance of gaining $0.

2. 2) Losing $5 with certainty over a 5% chance of losing $100 and a 95% chance of losing $0.

3. 3) A 5% chance of gaining $100 and a 95% chance of gaining $0 over gaining $5 with certainty

4. 4) A 95% chance of losing $100 and a 5% chance of losing $0 over losing $95 with certainty.

Let (?, ?; ?, 1 − ?) denote a lottery that has outcome ? with probability ? and outcome ? with probability 1−?.

Using the value function below, with a linear utility function (?(?) = ?), find the lowest value of ? and the highest value of ? such that prospect theory simultaneously predicts all four choices above.

?(?, ?; ?, 1 − ?) = ?[??(?) + (1 − ?)?(?)] + (1 − ?)[?max{?(?), ?(?)} + (1 − ?)min⁡{?(?), ?(?)}]

Answer 1

Solution: