14. You are offered the opportunity to play in the following game, which involves a coin toss. The coin will be tossed a maximum of 10 times. If the coin ever turns up Tails, the game ends immediately; otherwise the game proceeds until the coin has been tossed 10 times or turns up Tails in another round. [Note: We'll count the 10th toss as a "Tail" no matter how it actually lands so the game will at most last 10 rounds] Your payout is a function of the number of Heads that occur before the game ends. If there are two tosses before the game ends (i.e., the coin lands Heads then Tails), you receive $21. If there are four tosses (i.e., H, H, H, T), you receive $23. Thus, your payout from the game is given by the function $2", Where n is the number of Heads to occur before the game ends. Your utility is given by the function U = ln(W), where Wis the payout you receive from the game. 1) Assume it costs $2 to play the game. What is your expected payout 'om the game? 2) Assume it costs $2 to play the game. What is your expected utility from the game? 3) What is the most you would be willing to pay to play this game? [Hint Think about the certainty equivalent]