Consider the utility maximization problem of a burglar. If he commits a crime, he gets caught with proba- bility14("bad" state), and is not caught with probability34("good" state). If he is caught, then he has to pay a fine of $100. If he successfully burgles a house, then he gets a reward of $1,000. Thus, his incomes in the bad and good states are:

Ib=$100Ig=$1,000

The outside option for the burglar (if he does not commit crime) is to be an honest citizen and earn an income ofIw= $500. The burglar will choose to commit a crime if the expected utility from the crime is higher than the utility from his outside option:

41u($100) +34u($1,000)> u($500)Let the burglar's utility functionu(I)be concave:u>0andu<0.

1. What is the burglar's expected income from committing a crime,E[I]? [2 points]
2. Draw the burglar's utility function over income,u(I), on a graph, with income on the horizontal axis, and utility level on the vertical axis. Label the incomesIb,Ig, andE[I]. Is the burglar risk averse, risk loving, or risk neutral? [3 points]
3. On the same graph, draw a chord connectingu(Ib)andu(Ig)to depict expected utility. Find the point on the chord that represents the expected utility of committing a crime,E[u(I)], and label this utility level on the vertical axis. [3 points]
4. The government is considering three different policies to reduce crime in the neighborhood. For each policy, state what will happen to the burglar's comparison of the expected utility of committing a crime,E[u(I)], and the utility from his outside option,u(Iw). (Note: Full credit will be given to answers that show clearly how each policy changes the graph in parts (2) and (3), but if you are not sure, you can get partial credit for explaining the intuition in words.)
5. (a) Policy A: The government increases the fine from $100 to $200. [4 points] (b) Policy B: The government installs street cameras on every block. [4 points]
6. (c) Policy C: The government starts a training program for at-risk youth to provide them with better job opportunities. [4 points]