A potential offender contemplates committing burglary in one of two neighborhood

Question

A potential offender contemplates committing burglary in one of two neighborhoods. If caught, he faces a fine (f) of $5,000 regardless of where he commits the crime. The potential offender can afford to pay this fine. However, the gain from committing the crime (g) and the probability of apprehension (p) differ by neighborhood as follows:

Location

g

p

Neighborhood 1

$1,000

0.1

Neighborhood 2

$2,000

0.25

What is the net expected return (gain minus expected sanction) from crime in Neighborhood 1?

· What is the net expected return from crime in Neighborhood 2?

· Suppose the criminal can work legally for $700, or commit a crime in one of the neighborhoods. Will the criminal work legally? (Enter "Yes" or "No")

· What is the lowest fine that would just deter the criminal from committing any crimes?

Location

g

p

Neighborhood 1

$1,000

0.1

Neighborhood 2

$2,000

0.25

Explanation / Answer

Net expected return from crime in neighbourhood 1=-0.1(5000)+0.9(1000)=900-500=400

Net expected return from crime in neighbourhood 2=-0.25(5000)+0.75(2000)=1500-1250=250

Hence total net gain =$650

Ans b)

if $700 is provided then they will work legally becuase $700>$650

Net expected retun must be zero

0.9(1000)-0.1(x)+0.75(2000)-0.25(x)=0

900+1500-0.35x=0

0.35x=2400

x=2400/0.35=6857.6

Lowest fine $6857.6

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.