You are a contestant on the game show Deal or No Deal. In this game show, you are given the choice of opening boxes in succession. The last box you open is the prize you take home. Alternatively, the producers of the game show give you a certain amount after you open each box that allows you to quit the game.

You have opened most of the boxes and there are 3 left. By process of elimination you know that the remaining boxes have $1,000,000; $1,000 and $10. If you choose the boxes containing $1,000 and $10 the last box will have $1,000,000 and you will win the grand prize.

Before you choose which box to open next, you are offered $250,000 to quit the game.

Answer the following questions:

A) Assuming that you use expected value as a guide in your life, would you choose the sure amount or would you play to the end of the game? Explain showing calculations.

B) Assuming that you use expected utility as a guide in your life, would you choose the sure amount or would you play to the end of the game if your utility function is defined as the square root of x? ie u(x) = (x). Explain showing calculations.

C) Given the utility function in part b, what is the lowest amount in exchange for which you would give up your right to open boxes? Explain showing calculations.