Suppose again (as in exercise 17.12) that the payoff from engaging in a life of crime is x1 if you don't get caught and x0 (significantly below x1) if you end up in jail, with δ representing the probability of getting caught. Suppose everyone has identical tastes but we differ in terms of the amount of income we can earn in the (legal) labor market with (legal) incomes distributed uniformly (i.e. evenly) between x0 and x1.
A. Suppose there are two ways to lower crime rates: Spend more money on police officers so that we can make it more likely that those who commit crimes get caught, or spend more money on teachers so that we increase the honest income that potential criminals could make. The first policy raises δ; the second raises individual incomes through better education.
(a) Begin by drawing a risk averse individual's consumption/utility relationship and assume a high δ. Indicate the corresponding x that represents the (honest) income level at which a person is indifferent between an honest life and a life of crime.
(b) Consider a policy that invests in education and results in a uniform increase in all incomes by an amount x̅

On the horizontal axis of your graph, indicate which types of individuals (identified by their pre-policy income levels) will now switch from a life of crime to an honest life.
(c) Next, consider the alternative policy of investing in more enforcement€” thus increasing the probability of getting caught δ. Indicate in your graph how much the expected consumption level of a life of crime must be shifted in order for the policy to achieve the same reduction n crime as the policy in part (b).
(d) If it costs the same to achieve a $1 increase in everyone€™s income through education investments as it costs to achieve a $1 reduction in the expected consumption level of a life of crime, which policy is more cost effective at reducing crime given we started with an already high δ.
(e) How does your answer change if δ is very low to begin with?
(f) True or False: Assuming people are risk averse, the following is an accurate policy conclusion from our model of expected utility: The higher current levels of law enforcement, the more likely it is that investments in education will cause greater reductions in crime than equivalent investments in additional law enforcement.
B. Now suppose that, as in exercise 17.12, x0 = 20 and x1 = 80 (where we can think of these values as being expressed in terms of thousands of dollars).
(a) Suppose, again as in exercise 17.12, that expressing utility over consumption by u(x) = lnx allows us to express tastes over gambles using the expected utility function. If δ = 0.75, what is the income level at which an individual is indifferent between a life of crime and an honest life?
(b) If an investment in education results in a uniform increase of income of 5, what are the pre-policy incomes of people who will now switch from a life of crime to an honest life?
(c) How much would δ have to increase in order to achieve an equivalent reduction in crime? How much would this change the expected consumption level under a life of crime?
(d) If it is equally costly to raise incomes by $1 through education investments as it is to reduce the expected value of consumption in a life of crime through an increase in δ, which policy is the more cost effective way to reduce crime?
(e) How do your answers change if δ = 0.25 to begin with?