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