Problem 3. Recall the Allais paradox from lecture. Question 1: (S1,1) or (S1,0.8

Question

Problem 3. Recall the Allais paradox from lecture. Question 1: (S1,1) or (S1,0.89; $5,0.10; S0,0.01) Question 2: (S1,0.11; $0,0.89) or (S5,0.10; S0, 0.90) Most people prefer the first lottery in Question 1 but the second lottery in Question 2 Suppose someone chooses according to prospect theory with value function r01 if > 0 u (z) where all units are in millions of dollars. The probability weighing function they use is VP (p)-- Show that even without any editing, this can explain the Allais paradox (set reference point to $0 in both questions).

Explanation / Answer

Let's calculate the expected value of each gamble in Question 1 and Question 2 without any editing in cost and probabi;ity:

Expected value = Winning amount * Probability

As we can see below expected values.

If expected utility axiomatic was applied, the preference 1A > 1B should imply that 2A > 2B. However, the experiment shows that most rational individuals would choose so that 1A > 1B but 2A< 2B, even though it can be easily seen above that the expected value of each gamble is 1A=1, 1B=1,39, 2A=0.11, 2B=0.5

In the first gamble the less risky choice is preferred over a higher expected utility, while in the second gamble a higher expected utility is preferred over a less risky choice.

This shows the Allais paradox.

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