3. Adverse Selection and Crime (from Eric Rasmusen's textbook) (20 points) Some people are strictly principled and will commit no robberies, even if there is no penalty. Others are incorrigible criminals and will commit two robberies, regardless of the penalty. Society wishes to inict a certain penalty on criminals as retribution. Retribution requires an expected penalty of 15 per crime (15 if detection is sure, 150 if it has probability 0.1, etc.). Innocent people are sometimes falsely convicted, as shown in the table below. Convictions Robberies 0 1 2 0 0.81 0.18 0.01 1 0.60 0.34 0.06 2 0.49 0.42 0.09 Two systems are proposed: (i) a penalty of X for each conviction, and (ii) a penalty of 0 for the first conviction, and some amount P for the second conviction. a. What must X and P be to achieve the desired amount of retribution? (5 points) b. Which system inicts the smaller cost on innocent people? How much is the cost in each case? (5 points) c. Compare this with Problem 8.2. How are they different? (10 points)