You have just been chosen to appear on Hoosier Millionaire! The rules are as follows: There are three hidden cards. One says "STOP" and the other two have dollar amounts of $2, and $10. 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. a. Suppose your utility is U(x) = x^1/3 = 3âx what is the strategy that you can maximize your expected utility?
b. Consider the generalized utility function of the form x^θ where θ is your risk averseness parameter. Show that if your preference of risk averseness is θ >= 0.43, then you would play the game until you draw $10 or stop card; whereas if θ < 0.43 you would be more conservative and play only one round.
c. Find your expected utility for both of the cases θ >= 0.43 and θ =< 0.43. Notice that your expected utility (EMV with utility function) will now be a function of θ.