1. Part F-I The Economic Theory of Crime and Punishment
A model of rational crime
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2. Objectives Develop a predictive model of criminal behaviour
“predictive” What do we mean?
Can we predict who in this room will commit a crime? No.
We want a model that sets out the factors which would affect the decision of a rational individual when contemplating the commission of a crime.
Our model should be able to predict but only within the context of the ‘law of large numbers’
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3. Rational Crime
In order to predict behaviour we must start with rational behaviour
Rational Amoral Person
An individual who carefully considers the means to achieve an illegal goal without restraint by quilt or morality
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4. Do you ever act as a ‘rational amoral person’?
Are we all potentially ‘rational amoral persons’?
Think about some particular crime or criminal act (a particular theft, embezzlement, price fixing scheme, fraud, etc.) and some particular individual contemplating the criminal act.
Illegal satellite receiver, drunk driving, drugs, drinking underage, speeding, income tax evasion, smuggling, assault, robbery, rape, murder, cheating?
Have you, or someone you know, ever done any of these things?
We are the rational amoral people!
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5. We are the rational amoral people! AT TIMES
Society imposes criminal sanctions for many types of behaviour.
Some of these sanctions are in accord with our personal moral beliefs and we would never consider going against the sanction (whether or not they were illegal) – in some cases our actions are constrained by guilt or morality.
Some of these sanctions are not in accord with our personal moral beliefs and we would consider doing them – in some cases our actions are not constrained by guilt or morality.
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6. If our actions are not constrained by guilt or morality, what does constrain them?
Fear of punishment!
Criminal punishment should be designed to deter criminal behaviour (This is the answer to our second basic question concerning a positive theory of crime)
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7. It is important to keep in mind that we are using the terms CRIME and CRIMINAL but our model and discussions apply to ANY BEHAVIOUR SANCTIONED BY SOCIETY’ (jay walking, smoking in non-smoking areas, smuggling a bottle of liquor, parking illegally, not wearing a seatbelt …misdemeanours)
Society punishes CRIMES (acts described in the Criminal Code) but it also SANCTIONS many other behaviours (by-laws, regulations, codes, etc.)
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8. Lets look at deterrence
Consider a rational amoral person contemplating a crime (sanctioned act)
Can we develop a model of deterrence?
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9. Perfect disgorgement - severity of punishment equals
seriousness of offense
Punishment = value of crime
Severity of
punishment
What is the value of a crime?
The net take (net satisfaction
or net utility gained) after
allowance for all costs of
committing the crime x0
‘give back what you took’
punishment = net benefit
450
Seriousness
of offence x0
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10. Perfect disgorgement - severity of punishment equals
seriousness of offense
Punishment = value of crime
Severity of
punishment
‘give back what you took’
punishment = net benefit
If punishment is certain then a rational amoral person will be indifferent to committing or to not committing this type of crime x0
450
Seriousness
Of offence x0
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11. Severity of punishment greater than seriousness of offense
Value of crime
Severity of
punishment
Severity of punishment increases with the seriousness of the crime x1
Punishment exceeds the value of the crime and increases as the seriousness of the offense increases. x0
450
Seriousness
Of offence x0
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12. Punishment > net benefit
Severity of punishment greater than seriousness of offense
Punishment
Value of crime
Severity of
punishment
If punishment is certain, then a rational amoral person would not commit this type of crime
Punishment > net benefit x1 x0
450
Seriousness
Of offence x0
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13. But punishment is seldom (never?) certain
Criminals must be ‘caught convicted and sentenced’
Each of these steps is uncertain.
If actions are to be constrained by fear of punishment, then we need to take the ‘uncertain’ nature of that punishment into account
– since rational criminals will take it into account
EXAMPLE
Expected punishment = probability of being caught 50%
x probability of being convicted 60%
x probability of being punished 75%
x punishment 10 years
Expected punishment = 2.25 years
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14. Expected punishment > net benefit
Uncertainty of punishment
Punishment
if convicted
Value of crime
Severity of
punishment
Expected
punishment
$200
Even if punishment is uncertain, a rational amoral person would still not commit this type of crime
Expected punishment > net benefit
$150
$100
450
Seriousness
Of offence
$100
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15. Decision to commit the crime
Punishment
if convicted
Value of crime
Severity of
punishment
Expected
punishment
$200
A rational amoral person will commit this type of crime
Expected punishment < net benefit
$100
$75
450
Seriousness
Of offence
$100
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16. Decision to commit the crime
Expected
punishment
Expect punishment can increase, or decrease, due to an increase, or decrease, in the punishment if convicted, or the probability of being caught or the probability of being convicted or the probability of being punished.
Expected punishment = p(x)f(x)
Severity of
punishment
$75
$25
Seriousness
Of offence
$100
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17. Rational Crime - a more formal model
x seriousness of the criminal act (say amount embezzled)
y(x) expected net benefit to the criminal of committing the
criminal act (the ‘take’ less any out-of-pocket
expenses such as burglar tools, lawyers fees, payoffs to
officials, the ‘fencing’ discount, ‘laundering’ charges, etc. and any other ‘cost’ such as public shame, reputation effects, etc. )
y(x) = x – c(x),
where c(x) is the cost to the criminal of criminal activity
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18. p(x) probability of being caught, convicted and punished
f(x) punishment if caught (fine, prison sentence, etc.)
Expected gain from the criminal act (net take less the expected cost of punishment) is given by,
y(x) - p(x)f(x) as in text
(x – c(x)) - p(x)f(x) more specifically
Note that the criminal’s gain is generally less than the victim’s loss.
The difference is accounted for by the resources used to commit the crime, c(x).
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19. The terminology tends to be a bit confusing
y(x) = x – c(x) expected net benefit (private benefit to the criminal – revenue net of the criminal’s costs of committing the crime)
p(x)f(x) expected punishment
An optimizing criminal will want to maximize the difference between the expected net benefit and the expected punishment:
y(x) - p(x)f(x)
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20. Δy/Δx = Δp/Δx f(x) + p(x) Δf/Δx, where
An optimizing criminal will want to maximize y(x) - p(x)f(x). How? By equating the marginal net benefit of the crime to the marginal costs of being caught and punished,
Δy/Δx = Δp/Δx f(x) + p(x) Δf/Δx, where
Δy/Δx is the increase in the net benefit of the crime as x increases
Δp/Δx f(x) is the increase in the prob. of being caught, convicted and punished as x increases (multiplied by the punishment if caught)
p(x) Δf/Δx is the probability of being caught multiplied by the increase in the severity of punishment as x increases
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21. Δy/Δx = Δp/Δx f(x) + p(x) Δf/Δx where,
is the marginal net benefit of the crime
Δp/Δx f(x) + p(x) Δf/Δx
is the marginal costs of being caught and
punished,
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22. Again, Δy/Δx = Δp/Δx f(x) + p(x) Δf/Δx, where
Δy/Δx > 0 increases as the seriousness of the crime increases
Δp/Δx > 0 the more serious the crime the more resources
(police, auditors, prosecutors, courts, prisons, parole
officers, etc.) society will devote to catching,
convicting and punishing the criminal
Δf/Δx > 0 the more serious the crime the harsher the
punishment
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23. Rational Crime - in a picture
Severity of
punishment
Value of crime
A rational amoral person will commit this particular crime
Expected punishment < net benefit
$1000
$750
Expected
punishment
450
Seriousness
of the crime
$1000
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24. Rational Crime - seriousness vs. number of crimes
We can transform the above model to explain ‘number of crimes’ instead of seriousness of a given crime.
- express the ‘number of crimes’ along the horizontal axis
- severity of expected punishment is now assumed to increase with number of crimes committed by the individual
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25. Rational Crime - seriousness vs. number of crimes
Severity of
punishment
A rational amoral person will commit this number of crimes
Expected punishment < net benefit
Value of crimes
$1000
$750
Expected
punishment
450
Number of crimes 10
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26. Rational Crime - direct costs and the net benefit of committing crime
Value of crime to victim
= gain of the criminal
Severity of punishment
So far our diagrams have implied that the harm done to the victim is equal to the net benefit gained by the criminal - y(x)
But this is generally not the case
$100
45o
Seriousness
Of offence
$100
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27. Rational Crime - direct costs and the net benefit of committing crime
Value of crime to society (victim) $
Assumed that the direct cost of crime increases with the severity of the crime
$200
Expected net benefit y(x)
$100
Direct cost of doing the crime - $25
$75
45o
Seriousness
Of offence
$100
$200
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28. Direct cost of doing the crime - $25
Rational Crime - the higher are the costs to the criminal of doing the crime, the less crime there will be
Value of crime to society (victim) $
Expected
punishment
Assumed that the direct cost of crime increases with the severity of the crime
$200
Expected net benefit y(x)
$100
Direct cost of doing the crime - $25
$75
45o
Seriousness
Of offence
$100
$200
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29. Rational Crime - from the individual to aggregate crime rates
How do we arrive at the aggregate amount of crime in a society based on the above model of individual crime?
Simply, we add up individual behaviour the same way we would aggregate individual demand curves for a given product
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30. Rational Crime - from the individual to aggregate crime rates
Society sets a level of expected punishment and then individuals choose their optimizing amount of crime – each individual has a different expected net benefit from crime
Severity of
punishment
Aggregate Crime Curve
Expected
punishment
Expected
punishment
Expected
punishment
Expected
punishment ε1 ε2 ε1 ε1 . ε1
Expected
net benefit
Mr. B
Expected
net benefit
Mr. A ε0
Expected
net benefit
Mr. C 30 10 20
Aggregate number
of crimes
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31. Rational Crime - from the individual to aggregate crime rates
If the expected punishment is changed, then individuals decide on new optimum levels of crime – the greater the expected punishment, the lower the optimal number of crimes
Severity of
punishment
Aggregate Crime Curve
Expected
punishment
Expected
punishment
Expected
punishment
Expected
punishment ε2 . ε2 ε2 ε2 . ε1
Expected
net benefit
Mr. B
Expected
net benefit
Mr. A ε0
Expected
net benefit
Mr. C 5 30 5
Aggregate number
of crimes
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32. Rational Crime - from the individual to aggregate crime rates
– the lower the expected punishment, the greater the optimal number of crimes
Severity of
punishment
Aggregate Crime Curve
Expected
punishment
Expected
punishment
Expected
punishment ε0 .
Expected
punishment ε0 ε2 ε0 . ε1
Expected
net benefit
Mr. B
Expected
net benefit
Mr. A .
Expected
net benefit
Mr. C ε0 5 30 38 8 25 5
Aggregate number
of crimes
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33. Rational Crime - from the individual to aggregate crime rates
‘First law of deterrence’
“As the expected punishment increases, the number of crimes decreases” – this describes the slope of the Aggregate Crime Curve
What might cause the Aggregate Crime Curve to shift in or out?
Any factor other than expected punishment that affects the optimal amount of crime for the individuals.
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34. Rational Crime - from the individual to aggregate crime rates
What might cause the Aggregate Crime Curve to shift in or out?
Expected
punishment
Anything that causes the expected net benefit to the criminal to increase (decrease) will cause the ACC to shift out (in). ε1
We will discuss these factors in the next section
Aggregate number
of crimes
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