Question

You are on the game show “Deal or No Deal!” and have made it almost until...

You are on the game show “Deal or No Deal!” and have made it almost until the end. You are left with four suitcases. One of them holds $1,000,000, one of them holds $50,000, one of them holds $10,000, and the other holds $1. Assume your payoff is one of these four amounts in equal probability. What is the expected payoff? The banker is offering you a fixed sum in exchange for the four suitcases. If your utility of the random prize W is equal to U(W)=W^(2/3) what is the minimum amount you would accept from the banker? Why is this less than the expected payoff?

Homework Answers

Answer #1

Statement showing expected payoff

Winning Probability Expected winnings
A B A x B
1000000 25% 250000
50000 25% 12500
10000 25% 2500
1 25% 0.25
Expected payoff 265000.25

Thus Expected payoff = $ 265000.25

If utility function = U(W)=W^(2/3)

Thus minimum amount to be demanded = Expected payoff2/3

= 265000.252/3

= 4125.70$

Minimum amount is less than expected payoff because the risk of not winning is being transfered to bank . Thus bank will now bear risk of getting $ 1.

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