1. (25p) The most popular game show in Lintukoto consists of a series of true-or-false ques- tions. The prize for getting the first answer right is 10. After getting an answer right the contestant can either quit and leave with the current prize money, or enter another round where the total prize money for the night is doubled. However, if at any point a contestant gives an incorrect answer then they will go home with zero prize money. The maximum number of questions for a contestant is 12, after which the show would end. (a) (6p) Give a mathematical description of the lottery implied by the game show, for a contestant whose probability of getting the right answer is the same p (0,1) for any question. (b) (10p) Ukko has starting wealth 100,000 and a utility function over wealth u(w) = Vw. He is clueless about the questions and believes that his probability of getting any single answer correct is 50%. If he were planning to quit after two questions then what would be Ukko's certainty equivalent for the game? What if he were planning to never quit? (c) (6p) Continued from 1b. After how many correctly answered questions should Ukko choose to quit the game? (d) (3p) Akka has same the wealth and preferences as Ukko in part 1b, but a 75% chance of answering any single answer correctly. What should be her reservation value to get to play the game? 1. (25p) The most popular game show in Lintukoto consists of a series of true-or-false ques- tions. The prize for getting the first answer right is 10. After getting an answer right the contestant can either quit and leave with the current prize money, or enter another round where the total prize money for the night is doubled. However, if at any point a contestant gives an incorrect answer then they will go home with zero prize money. The maximum number of questions for a contestant is 12, after which the show would end. (a) (6p) Give a mathematical description of the lottery implied by the game show, for a contestant whose probability of getting the right answer is the same p (0,1) for any question. (b) (10p) Ukko has starting wealth 100,000 and a utility function over wealth u(w) = Vw. He is clueless about the questions and believes that his probability of getting any single answer correct is 50%. If he were planning to quit after two questions then what would be Ukko's certainty equivalent for the game? What if he were planning to never quit? (c) (6p) Continued from 1b. After how many correctly answered questions should Ukko choose to quit the game? (d) (3p) Akka has same the wealth and preferences as Ukko in part 1b, but a 75% chance of answering any single answer correctly. What should be her reservation value to get to play the game