Crime Chapter 13. Purpose In this chapter we explore one of the problems associated with urban...
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Transcript of Crime Chapter 13. Purpose In this chapter we explore one of the problems associated with urban...
Crime
Chapter 13
Purpose
In this chapter we explore one of the problems associated with urban areas, crime. We introduce 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?
FBI Index Crimes, 1960 – 2003
victim in physical danger
crimes of stealth rather than force
Criminal Victimization Rates by income, region and residence in 2003
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)
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)
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 cost
Expected Utility and the Decision to Commit Crime
Utility 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)1/2
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 second
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
c
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
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
f
Is it rational to Commit the crime?
Not commit
the crime
Commit the
crime
Successp
Failure1-p
Earn the lawful incomeU=10
Earn the lawful income + lootUs=12
Earn the lawful
income – time lost in prison
Uf=8EU=
p.Us+(1-p)Uf=10
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
c
Risk aversion
The crime is like a lottery since its outcome is uncertain
What can we say about the criminal’s risk preferences?
s
f
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
f
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 crime
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 crime
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 cost
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 crime
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 term
Empirical Evidence on Crime Fighting
Longer prison term causes offsetting changes: Hardening the criminal and Prison schooling
Gould, Weinberg and Mustard (2002): elasticity of crime wrt wages ranges from -1 to -2
Education as Crime-Fighting Policy Significance of high-school education
Each 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 rate Marginal Cost of a year of schooling = $6,000, Marginal private benefit= $8,400/year for life, marginal
external benefit=$1,600/year for life
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)
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.
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.
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 prevent
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.
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 job
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 60
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 robbery
Assignment
Questions: 2, 3, 5, 7, 8Due a week from today