A potential offender contemplates committing burglary in one of two neighborhoods.
If caught, he faces a fine of $5,000 regardless of where he commits the crime. (Assume he can afford to pay it.) However, the gain from committing the crime, g, and the probability of apprehension, p, differ by neighborhood as follows:
(a) What is the net expected return from crime in each of the two neighborhoods?
(b) Suppose the criminal can work legally for $700, or commit a crime in one of the neighborhoods. What is his optimal strategy?
(c) What is the lowest fine that would just deter the criminal from committing any crimes?