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Crime. Chapter 12. Purpose. In this chapter we explore one of the problems associated with urban areas, crime. We examine the behavior of a utility maximizing criminal why crime rates are higher in big cities, and the policy response. FBI Index Crimes, 1960 – 2003.

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Chapter 12


In this chapter we explore one of the problems associated with urban areas, crime. We examine

  • the behavior of a utility maximizing criminal

  • why crime rates are higher in big cities, and

  • the policy response.

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


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



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.



Is it rational to Commit the crime?

Not commit the crime

Commit the crime





Earn the lawful income – time lost in prison


Earn the lawful income


Earn the lawful income + loot





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




Risk aversion

  • The crime is like a lottery since its outcome is uncertain

  • What can we say about the criminal’s risk preferences?



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



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

Supply curve as marginal-cost curve

  • Criminals with low opportunity cost and anguish cost on lower part of the supply curve (low marginal cost of crime)

  • Cost: probability of being caught, opportunity cost of time, anguish cost

  • As loot increases, people with higher opportunity and anguish costs commit 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

Public Policy and Crime

  • Increase in crime cost shifts the supply curve upward:

    • Increase probability of punishment

    • Longer prison term

  • But Longer prison term causes offsetting changes

    • Hardening the criminal

    • Prison schooling

Legal Opportunities and Education

  • Increase in lawful wage increases opportunity cost, shifting the marginal-cost (supply) curve upward, reducing crime. Improving job prospects for low-skilled workers reduces crime

  • Education as Crime-Fighting Policy.

    • Education increases wages, decreasing crime

    • Evidence of link for 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

    • Cost per year of schooling = $6,000, extra earning/year= $8,400, marginal external benefit/ year=$1,600

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 12.4

    • 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 as 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


  • Questions: 2, 3, 5, 7, 8

    Due a week from today

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