Individual deterrence
Basic model (see Becker 1968)
Y = return from a specific criminal action,
X = return from legal activity = opportunity cost of crime
F = fine
r = prob(conviction | suspect is guilty)
w= prob(conviction | suspect is innocent)
r-w serves as a measure for the detection skill of the enforcement system:
• r=w
=> zero detection skill
• 0<w<r<1
=> imperfect, positive detection skill
• r=1, w=0
=> perfect detection skill
Possible amendments to the basic model
(not in the following figure, but in the overnext slide)
• cost of committing the crime C,
• probability of success p<1
20050901.doc - 1
Dr. Roland Kirstein, Visiting Professor UCSB
Law and Economics 117A, Summer Session B
20050901.doc - 2
Dr. Roland Kirstein, Visiting Professor UCSB
Law and Economics 117A, Summer Session B
Deterrence
a potential offender prefers the legal over the criminal action if
X-wF > qY-rF-C
<=>
r-w > (qY-X-C)/F
Hence: higher detection skills (r-w), higher opportunity costs X, higher cost of
committing crime C, higher fines F, lower success probability q, lower gross return from crime Y increases the likelihood of deterrence.
Positive detection skill (i.e., r>w) is a necessary (not sufficient) condition for
selective incentives.
Maximum fine result (Becker 1968):
• Deterrence depends on the expected punishment pF (neglects detection skill).
• p depends on the authority’s resource input.
• To reduce costs: keep pF constant by reducing p and increasing F.
• F has a maximum (the offender’s wealth) => F*.
=>Set F=F* and reduce p so that pF* is sufficient for deterrence!
20050901.doc - 3
Dr. Roland Kirstein, Visiting Professor UCSB
Law and Economics 117A, Summer Session B
Criticisms of the Becker-result:
• Severe punishment for minor crime is not credible (juries might hesitate to
convict).
• People tend to neglect small probabilities.
• w>0 implies that error costs are higher the higher F.
• Alternatives to increased punishment are
o increase X (education => productivity => wage)
o decrease q (private precaution against crime)
q depends on the private person’s investment in crime prevention,
r-w depends on government’s expenses => the two factors may be substitutes.
=> The optimal production of internal security may require setting incentives for
both the government and the citizens to engage in crime deterrence/prevention.
20050901.doc - 4
Dr. Roland Kirstein, Visiting Professor UCSB
Law and Economics 117A, Summer Session B
Optimal deterrence
What are the costs of offenses?
=> not the value of stolen goods (this is only re-distribution),
but the inefficiencies caused by imperfect protection of property rights.
=> primary costs
(the foregone opportunities)
=> secondary costs (the risk borne by risk averse citizens)
=> tertiary costs
(costly defense against crime)
What are the costs of enforcement?
• opportunity costs of resources spent for police, attorneys, prisons
• incarceration costs (fines are returns)
• wasted human capital
• judicial errors
Optimum: marginal deterrence cost = marginal deterrence benefit
(where the total curves have the same slope or the marginal curves intersect)
20050901.doc - 5
Dr. Roland Kirstein, Visiting Professor UCSB
Law and Economics 117A, Summer Session B
The figure presented in class showed the number of offenses on the horizontal axis
(from left to right), here it is just the other way round.
20050901.doc - 6
Dr. Roland Kirstein, Visiting Professor UCSB
Law and Economics 117A, Summer Session B
Deterrence of another “unit of crime” brings a marginal benefit (=avoided costs
of crime), but also incurs marginal opportunity costs (=foregone benefit if the
resources invested into crime prevention would have been spent for something
else, like kindergartens).
Assumption:
marginal deterrence costs are increasing, marginal benefit is decreasing
=> in most cases, an internal solution exists.
=> it is not rational for society to fight crime down to zero, since the (marginal)
opportunity costs would then greater than the (marginal) benefit.
Becker has called the “allowed” crime rate society’s “demand for crime,”
since saving the marginal deterrence cost is nothing else but the
marginal benefit of allowing crime (= demand).
20050901.doc - 7
Dr. Roland Kirstein, Visiting Professor UCSB
Law and Economics 117A, Summer Session B
Inspection Game
Becker: Increasing p or F increases deterrence => reduces the crime rate.
Inspection game: punishment plays no role in the decision to commit crime
Two players, a potential offender O and an enforcer E
Assumptions:
• Monitoring requires costs C and perfectly reveals crime.
• Enforcer prefers to detect crime (benefit B from catching a criminal, B>C).
• Enforcer (society) suffers damage D if the crime is committed.
• Offender prefers to commit crime if, and only if, undetected: Y-F<X<Y.
q
1-q
O, E
commit crime
not commit
p
monitor
Y-F, B-C-D
X, -C
1-p
not monitor
Y, -D
X, 0
=> no Nash equilibrium in pure strategies.
=> one in mixed strategies
20050901.doc - 8
Dr. Roland Kirstein, Visiting Professor UCSB
Law and Economics 117A, Summer Session B
Mixed strategy equilibrium: apply formula/indifference procedure
i) O chooses his q such that E is indifferent between his pure strategies
q(B-C-D)-(1-q)C=-qD <=> qB=C <=> q*=C/B
ii) E chooses his p such that O is indifferent between his pure strategies
p(Y-F)+(1-p)Y=X <=> Y-X = pF <=> p* = (Y-X)/F
Both players’ behavior only depends on the opponents’ payoff parameters.
Thus, the probability with which O commits the crime is independent of F.
F only enters the probability of (monitoring and) punishment, p.
Becker’s theory and the inspection game come to different conclusions
as to the deterrence effect of F, even though they both assume rationality.
Becker assumes that the enforcer can commit to a monitoring behavior
(while the enforcer in the Inspection Game chooses his as a strategic player).
Typical case where the inspection game is more appropriate: auditing.
20050901.doc - 9
Dr. Roland Kirstein, Visiting Professor UCSB
Law and Economics 117A, Summer Session B