Question \#4: Cheating in Sports [20 Points] Scottie Scheffler, is a top American professional golfer. Rumors have been circulating throughout the PGA that Scheffler is a cheater. Scheffler is suspected of moving the golf ball closer to the hole after the ball lands. This is a violation of PGA rules. If Scheffler chooses to cheat by moving the ball closer to the hole and is not caught he would get a better score in tournaments and earn more prize money. Assume that Scottie Scheffler's wealth if he cheats and is not caught would equal $850,000. However, if Scheffler were to cheat and was caught moving the ball closer to the hole, he would receive a two stroke penalty, fall down the leaderboard and earn less prize money. Assume that if Scottie Scheffler cheats and was caught his wealth would equal $390,000. Assume that there is a 24% chance (p=0.24) that if Scheffler cheats he would be caught and assume that Scheffler has the following utility function: U(W)=8W. Also assume that if Scheffler decides not to cheat, he would have a wealth of $560,000. (a) What is Scottie Scheffler's expected wealth, E(W), if he decided to cheat? [2 Points] (b) What is Scottie Scheffler's utility if he cheats and is not caught? Round vour answer to two decimal places. [3 Points] (c) What is Scottie Scheffler's utility if he cheats and is caught? Round vour answer to two decimal places. [3 Points] (d) Using your answers from Parts (b) and (c) what is Scottie Scheffler's expected utility, E(U) if he decided to cheat? Round your answer to two decimal places. [4 Points] (e) Should Scottie Scheffler cheat and move his ball? Show vour work. [4 Points] (f) Suppose that the PGA hires more course officials to catch golfers cheating. If Scheffler tries to cheat there is a greater likelihood that he will be caught. Assume the probability of getting caught increases to p=0.60. Would Scheffler's decision about cheating change? Assume that all other variables remain the same. Show vour work. [4 Points] Question \#4: Cheating in Sports [20 Points] Scottie Scheffler, is a top American professional golfer. Rumors have been circulating throughout the PGA that Scheffler is a cheater. Scheffler is suspected of moving the golf ball closer to the hole after the ball lands. This is a violation of PGA rules. If Scheffler chooses to cheat by moving the ball closer to the hole and is not caught he would get a better score in tournaments and earn more prize money. Assume that Scottie Scheffler's wealth if he cheats and is not caught would equal $850,000. However, if Scheffler were to cheat and was caught moving the ball closer to the hole, he would receive a two stroke penalty, fall down the leaderboard and earn less prize money. Assume that if Scottie Scheffler cheats and was caught his wealth would equal $390,000. Assume that there is a 24% chance (p=0.24) that if Scheffler cheats he would be caught and assume that Scheffler has the following utility function: U(W)=8W. Also assume that if Scheffler decides not to cheat, he would have a wealth of $560,000. (a) What is Scottie Scheffler's expected wealth, E(W), if he decided to cheat? [2 Points] (b) What is Scottie Scheffler's utility if he cheats and is not caught? Round vour answer to two decimal places. [3 Points] (c) What is Scottie Scheffler's utility if he cheats and is caught? Round vour answer to two decimal places. [3 Points] (d) Using your answers from Parts (b) and (c) what is Scottie Scheffler's expected utility, E(U) if he decided to cheat? Round your answer to two decimal places. [4 Points] (e) Should Scottie Scheffler cheat and move his ball? Show vour work. [4 Points] (f) Suppose that the PGA hires more course officials to catch golfers cheating. If Scheffler tries to cheat there is a greater likelihood that he will be caught. Assume the probability of getting caught increases to p=0.60. Would Scheffler's decision about cheating change? Assume that all other variables remain the same. Show vour work. [4 Points]
