You have just been chosen to appear on Hoosier Millionaire! The rules are as follows: There are four hidden cards. One says STOP and the other three have dollar amounts of $150,000, $200,000, and $1,000,000. You get to choose a card. If the card says STOP, you win no money. At any time you may quit and keep the largest amount of money that has appeared on any card you have chosen, or continue. If you continue and choose the stop card, however, you win no money. As an example, you may first choose the $150,000 card, then the $200,000 card, and then you may choose to quit and receive $200,000!

a If you goal is to maximize your expected payoff, what strategy should you follow?

b My utility function for an increase in cash satisfies u(0) = 0, u($40,000) = .25, u($120,000) = .50, u($400,000) = .75, and u($1,000,000) = 1. After drawing a curve through these points, determine a strategy that maximizes my expected utility. You might want to use your own utility function.