Question

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?

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 payoff^2/3

= 265000.25^2/3

= 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.