2. Moral Hazard and Crime (from Eric Rasmusen's textbook) (40 points) Individuals who are risk-neutral must decide whether to commit zero, one, or two robberies. The cost to society of robbery is 10, and the benet to the robber is 5. No robber is ever convicted and jailed, but the police beat up any suspected robber they find. They beat up innocent people mistakenly sometimes, as shown by the table below, which shows the probabilities of zero or more beatings for someone who commits zero, one, or two robberies. 1 Beatings 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 a. How big should p*, the disutility of a beating, be made to deter crime com- pletely while inicting a minimum of punishment on the innocent? (10 points) b. In equilibrium, what percentage of beatings are of innocent people? What is the payoff of an innocent man? (10 points) c. Now consider a more exible policy, which inicts heavier beatings on repeat offenders. If such exibility is possible, what are the optimal severities for rst- and second-time offenders? (call these p1 and p2). What is the expected utility of an innocent person under this policy? (10 points) d. Suppose that the probabilities are as given in the table below. What is an opti- mal policy for first and second offenders? (10 points) Beatings Robberies 0 1 2 0 0.9 0.1 0 1 0.6 0.3 0.1 2 0.5 0.3 0.2