Question: problem 4 prospect theory explanation for the common ratio effect...
Problem 4: (Prospect theory explanation for the Common Ratio Effect): A famous experimental violation of EU is the finding by Kahneman and Tversky that most people preferred $3000 with certainty over an 80% chance of $4000, but preferred a 20% chance of $4000 over a 25% chance of $3000. Using the probability weight w(𝑝) = (1 − 𝜃)𝛼 + 𝜃𝑝 for the probability of the best outcome of a lottery and the weight w(𝑝) = (1 − 𝜃)(1 − 𝛼) + 𝜃𝑝 for the probability of the worst outcome of a lottery, and setting
𝜃 = 0.80, 𝛼 = 0.10, show that prospect theory explains this classical demonstration of the common ratio effect. Use the weight 𝑤(𝑝) = 1 for a lottery that offers a single outcome with probability 𝑝 = 1. Assume a simple linear value function of the form 𝑣(𝑥) = 𝑥.