Question

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

	g	p
Neighborhood 1	$1,000	.1
Neighborhood 2	$2,000	.25

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?

Answer 1

1. Net Expected returns in Neighbourhood1 is

E1 = 0.1*(-5000)+0.9*1000 = $400

Net expected return in neighbourhood2 is

E2 = 0.25*(-5000) + 0.75*2000 = $250

2. Since the expected return from crime in both the neighbourhood is less than the amount he will get by by working legally. Therefore, her optimal strategy is to work legally.
3. The lowest fine that would deter the criminal from any crime will be obtained by

0.9*1000+0.1*(-A) <=0. Solve for A we get A>=9000. Therefore, lowest fine tat can deter from committing crime is $9000.