Chapter 13 Purpose In this chapter we explore one of the problems associated with urban areas crime We introduc e three tools that allow us to answer each of the following questions What are the factors that determine whether a rational individual commits a crime or not ID: 334406
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Slide1
Crime
Chapter 13Slide2
Purpose
In
this chapter we explore one of the problems associated with urban areas, crime.
We introduc
e three tools that allow us to answer each of the following questions:
What are the factors that determine whether a rational individual commits a crime or not?
What is the equilibrium number of crimes?
How much resources should society allocate to fight crime? Slide3
FBI Index Crimes, 1960 – 2003
victim in physical danger
crimes of stealth rather than forceSlide4
Criminal Victimization
Rates by income, region and residence in 2003Slide5
Criminal Victimization Rates, 2003
By income: Victimization for violent crime decreases with income
Place: highest rates in central cities; lowest in rural areas
Race: victim rate for violent crime is 29.1 (black), 21.5 (white) Slide6
The Costs of Crime
Victim cost ($91 billion): lost property, medical expenses, opportunity cost of lost work time, value of lives cut short
Private prevention ($39 billion): locks, guards
Criminal justice system ($74 billion): police, courts, correction facilities
Opportunity cost of 1.35 million in prison = $46 billion
Total = $250 billion (3.8% of GDP)Slide7
The Rational Criminal
We think of criminals as rational utility maximizing agents who commit the crime if benefits exceed costs
The decision to commit a crime involves risk taking since the outcome is uncertain
Due to uncertainty, the criminal makes a decision based on expected outcomes
People differ in willingness to accept risk
People differ in aversion to anti-social actions--anguish costSlide8
Expected Utility and the Decision to Commit Crime
U
tility maximization under uncertainty
Utility depends on income.
Diminishing marginal utility
: utility increases with income at a decreasing rate. The utility derived from the first dollar of income is higher than that derived from the second and so on.
This generates a concave utility curve (Remember:
marginal utility is the slope of the utility curve
)Example: Utility = (Income)1/2Slide9
Diminishing marginal utility
The utility curve represents the utility of earning a
certain
amount of $
The
utility curve is
concave: the
first dollar of income is worth more than the secondSlide10
The
certain outcome
Values of key parameters:
lawful income ($100)
loot ($44)
probability of prison (0.50)
prison time (0.36)
Lawful utility: point c utility (100) = 10
utils
cSlide11
Expected utility of the crime
Successful
crime:
Income=100+44
utility (144) =
12
utils
Point s
Failed
crime:
Lost income =100*0.36=$36
Income =100-36=64
utility (64) =
8
utils
Point
f
s
f
Expected utility from crime:
0.50*12 + 0.50*8 =10
utils
Slide12
Expected utility
graphically
The expected utility will lie on the line joining points s and f
The probabilities are identical to the weights used in averaging
Because the probabilities are 50-50, the expected utility is the midpoint of the line
If the probability of success was higher will move closer to s.
s
fSlide13
Is it rational to Commit the crime?
Not commit the crime
Commit the crime
Success
p
Failure
1-p
Earn the lawful income
U=10
Earn the lawful income + loot
Us=12
Earn the lawful income – time lost in prison
Uf
=8
EU=
p.Us
+(1-p)
Uf
=10Slide14
Is it rational to Commit the crime?
The expected utility from committing the crime =10
The utility of the lawful income=10
The criminal is indifferent
s
f
cSlide15
Risk aversion
The crime is like a lottery since its outcome is uncertain
What can we say about the criminal’s risk preferences?
s
fSlide16
Risk aversion
The
blue dot
represents the utility of earning a certain income of $104
The
red dot
represents the utility of playing a game with an expected payment of $104
He prefers not to play the game.
In fact earning a certain income of $100 is as good as earning $104 with uncertainty
He is risk averse
s
fSlide17
Preventing Crime
Higher probability of prison: 0.75
EU (crime)
= 0.25•12 + 0.75•8 =9 utils
point n is 3/4 of the way from point s to f
Increase in certainty of punishment reduces crimeSlide18
Preventing Crime
Longer prison term: 0.51 Affects payoff to failed criminal: income drops to $49; utility drops to 7 utils
EU (crime) = 0.50 • 12 + 0.50 • 7 = 9.5 utils
Increase in severity of punishment reduces crime
Less loot: $21
Affects only the payoff to successful criminal.
income drops to $121; utility drops to 11 utils
Morality and anguish cost
Utility is lower when committing the crimeSlide19
The Equilibrium Quantity of Crime
Marginal benefit curve
negatively sloped: Targets vary in loot, with most lucrative at the top of the marginal-benefit curve
Point i: initial equilibrium; for first 60 crimes, benefit ≥ marginal cost
For crime #61, marginal benefit (loot) < marginal costSlide20
The Equilibrium Quantity of Crime
Supply
curve as marginal-cost curve
Criminals with low cost on lower part of the supply curve
Cost:
probability of being caught
opportunity cost of time
length of prison time
anguish cost
As loot increases, people with higher opportunity and anguish costs commit crimeSlide21
Public Policy and Crime
Increase in crime cost shifts the
supply
curve upward:
Increase in lawful income (e.g., education)
Increase
probability of punishment
Longer prison
termSlide22
Empirical Evidence on Crime F
ighting
Longer
prison term causes offsetting changes: Hardening
the
criminal and Prison
schooling
Gould, Weinberg and Mustard (2002): el
asticity of crime wrt wages ranges from -1 to -2
Education as Crime-Fighting PolicySignificance
of high-school educationEach additional year decreases crime participation rate by 0.10 (white) to 0.40 percentage points (black)Graduation decreases crime participation rates of males by 9% (violent), 5% (drug), 10% (property)
Benefits and costs of increase in high-school graduation rateMarginal Cost of a year of schooling = $6,000,
Marginal
private benefit= $8,400/year for life, marginal external benefit=$1,600/year for lifeSlide23
Why are Crime Rates Higher in Big Cities?
Elasticity of crime rate with respect to city size = 0.15
Reasons for higher crime
More loot (25% of difference)
Lower probability of arrest (15% of difference): Table 13-4
More female-headed households (50% of difference)
Higher crime from higher benefits and lower costs: point s (small city) versus point b (big city) Slide24
Discussion: Should Society Fight Crimes?
If crime is simply a transfer from one individual to another there will be little justification to fighting crime.However, this transfer is not without waste
Laws that protect property rights are needed to create incentives to invest and ensure growth.Slide25
Discussion: Should Societies be crime free?
Should society create a zero crime environment?Crime prevention uses scarce resources.
Society should fight crimes up to the point where marginal benefit equals marginal cost.Slide26
The Optimal Amount of Crime
Marginal cost of prevention: Curve is negatively sloped
Reducing crime from 100 to 99 has cost of $300 (point p)
Reducing crime from 90 to 89
has
cost of $700 (point n)
With fewer crimes being committed, it becomes more difficult to preventSlide27
The Optimal Amount of Crime
Why prevent crimes?
To avoid the victim cost of crimes, which in this case is constant at $1500.
How many crimes should be prevented?
Those for which the prevention cost is lower than the victim cost
The socially optimal number of crimes is 72.Slide28
Crime Substitution and the Principle of Marginal Deterrence
Criminals have options, and alternative crimes are substitutes
Increase in the penalty for a given crime will encourage criminals to substitute to other types of crimes.
Assume:
60 People choose between burglary, robbery and a lawful jobSlide29
Crime Substitution and the Principle of Marginal Deterrence
In equilibrium
the net return across the three choices should be equal.
The number of people across the three choices should be 60Slide30
Crime Substitution and the Principle of Marginal Deterrence
How does the increase in the penalty for burglary affect the number of burglaries and armed robberies?
Net return for burglars decline
Substitution to armed robberySlide31
Assignment
Questions: 2, 3, 5, 7, 8Due a week from today