This paper shows a world where the individual practices concomitantly legal and illegal activities in two period of their lifetime. The results of the two-period model unveil that effectiveness of anti-money laundering policies and increase of probability of the agent to be apprehended and punished at the second period negatively affects the amount of resources obtained from criminal activities.crime

Tito Belchior Siva Moreira

English

Research Papers in Economics

A Two-Period Model of Money Laundering and Organized
Crime 
Tito Belchior Siva Moreira
Catholic University of Brasilia
Abstract
This paper shows a world where the individual practices concomitantly legal and illegal
activities in two period of their lifetime. The results of the two-period model unveil that
effectiveness of anti-money laundering policies and increase of probability of the agent to be
apprehended and punished at the second period negatively affects the amount of resources
obtained from criminal activities.
Catholic University of Brasília, DF, Brazil: tito@pos.ucb.br. This author thanks the helpful comments of the referee.
Citation: Siva Moreira, Tito Belchior, (2007) "A Two-Period Model of Money Laundering and Organized Crime." Economics
Bulletin, Vol. 11, No. 3 pp. 1-5
Submitted: April 14, 2007.  Accepted: September 30, 2007.
URL: http://economicsbulletin.vanderbilt.edu/2007/volume11/EB-07K00001A.pdf1. Introduction 
  It is widely acknowledged that the linkage between organized crime and money 
laundering affects society in several ways. Crime erodes basic individual liberties in that it 
threatens the right to life and the entitlement to property. The consequences of crime and 
money laundering are noxious for business, development and law. In this sense, activities 
of organized crime and money laundering have a corrosive effect on a country’s economy, 
government, and social welfare (Lawanda, 2005). 
  The combat of criminality must be done in two fronts. Firstly, legal authorities must 
repress organized crime. Secondly, they must also act preventively and repressively against 
money laundering process. Money laundering is the other facet of organized crime.   
  The process of money laundering is usually defined as any process that is carried 
out to disguise or cancel the nature or source of entitlement to money or property from 
criminal activities. This process is critical to the effective operation of virtually every form 
of transnational and organized crime. Anti-money laundering efforts, which are designed to 
prevent or limit the ability of criminals to use their ill-gotten gains, are both a critical and 
effective component of anti-crime programs (MacDowell and Novis, 2001).   
Generally, money launderers tend to seek out areas where there is a low risk of 
detection due to weak or ineffective anti-money laundering programs. As the objective of 
money laundering is to get the illegal funds back to the individual who generated them, 
launderers usually prefer to move funds through areas with stable financial systems. 
Therefore, money laundering is a threat to the good functioning of financial systems; 
however, it can also be the Achilles’ heel of criminal activities. In this context, the 
effectiveness of anti-money laundering policies can be evaluated by actions that prevent 
and repress the organized crime via connections made through financial transaction (FATF, 
2007).   
This paper presents a model that discusses the impact of legal authorities’ effort to 
combat the criminality via punishment and anti-money laundering policy
1. The model has a 
representative agent who is eligible for being involved in both illegal and legal activities, 
based on an adapted concept of “legal-criminal economy” (Araujo and Moreira, 2005). In 
the “legal-criminal economy” there are agents belonging to some kind of criminal 
organization that are mainly devoted to illegal economic activities, but who may also 
engage in the production of legal goods and services. Agents of the legal sector, by their 
turn, can be occasionally involved in illegal production (Masciandaro, 2000). 
  This paper therefore shows a two-period model where the individual practices 
concomitantly legal and illegal activities in the first period and in the second period there is 
no profit of illegal behavior anymore. In this sense, we assume that, in the first period, 
economic agents use income, provided by their legal and illegal activities, for their 
consumption. However, only in the second period they can be punished, i.e., the process of 
punishment and of effectiveness of anti-money laundering policy
2 occurs in the last period 
alone. Furthermore, they may have their legal income in the second period reduced by an 
amount that reflects effectiveness of both anti-money laundering policies and repression of 
criminality. Hence, consumption in the last period might be reduced and thus the 
individual’s welfare might be lower. 
 
 
 
   
  1The Model 
Consider that an agent maximizes lifetime utility, ,  which depends on period 
consumption levels, denoted  : 
i U1
i c
) ( ) ( 2 1 1
i i i c u c u U δ + =       (1) 
where   is the consume of agent i in the period 1,   is the expected consume of agent i 
in the period  , and  
i c1
i c2
2 1 0 < < δ  is a fixed preference parameter, called the subjective 
discount or time-preference factor, that measures the individual’s impatience to consume. 
As usual, the period utility function is strictly increasing in consumption and strictly 
concave:   and .  0 ) ( ' >
i c u 0 ) ( ' ' <
i c u
 The  individual  i can acquire goods and services in the first period with its legal 
income,  , and with illegal income,  .  Hence, we have that 
i r1
i x1
i i i x r c 1 1 1 + =        (2)   
  In the second period, the individual i can consume the equivalent to its legal 
income,  , deduced by value of the illegal income generated in the previous period that 
can be apprehended by legal authorities in this last period, such as those caused by police 
force or anti-money laundering policy. In this context, we have that  
i r2
i i i i x P r c 1 2 2 ε − =       (3) 
where 0 < < 1 denotes the (subjective) probability of the agent be caught and punished at 
the second period and the parameter 0 <
i P
ε  < 1 denotes the rate that measures the 
effectiveness of the anti-money laundering policy
3.  
In law enforcement investigations into organized criminal activity, it is often the 
connections made through financial transaction records that allow hidden assets to be 
located and the identity of the criminals and the criminal organization responsible to be 
established (FATF, 2007). Here, the effectiveness of the anti-money laundering policy is 
measured by the proportion that the illegal income is apprehended, , and the effort of 
the police force and legal system to caught and punish criminals is measured by the 
probability .  
i x1 ε
i P
  On one hand, if the effectiveness of the anti-money laundering policies is very 
high, 1 → ε , and the probability of the agent be apprehended and punished is also high, 
, then the consumption of the individual i in the second period will be equivalent to 
its legal income deduced by the term “ ” that approaches . In this circumstance, 
the incentive for practicing criminal activities will be reduced. On the other hand, if the 
effectiveness of the anti-money laundering policies, as well as the probability of the agent 
be apprehended and punished are very low, i. e., 
1 →
i P
i i x P 1 ε
i x1
0 → ε  and  , then the consumption 
of individual   in the second period will be equivalent to its legal income,  , and the 
incentive for practicing criminals activities will be increased.  
0 →
i P
i
i r2
The term “ ”  reveals aspects of repression and prevention for combating 
illegal markets. It shows law enforcement aspects present in each society in its different 
degrees of effectiveness against illegal activities.  It seems acceptable to assume that, if a 
given society adopts strong disposition for combating criminals’ activities, then the values 
i i x P 1 ε
  2of the parameters 
i P and ε  will be high. Otherwise, they will be low. In this context, we 
assume that both parameters are strongly correlated where   Without loss of 
generality, we admit that  
. ε ≈
i P
            (4)  . ε =
i P
  We can rewrite the equation (3) as 
        (5) 
i i i x r c 1
2
2 2 ε − =
  The sum of equations (2) and (5) results in the budget constraint 
               (7) 
i i i i x r r c c 1
2
2
1
1 2 1 ) 1 ( ε − + + = +
or, alternatively, replacing equation (2) into equation (5) results 
 ) .      (8)  ( 1 1
2
2 2
i i i i r c r c − − = ε
 Given  and , we have a equation for illegal income  
i c1
i c2
           (9)  )
0 / 1 < ∂ ∂
i i P x
, , , ( 2 1 1 ε
i i i i P r r f x =
The illegal income generated in the first period is a function of the legal income 
generated in both periods, the probability of the agent be apprehended and the parameter 
that measures the effectiveness of the anti-money laundering policy. It is expected 
that , , and  . These inequalities are 
consistent with the following propositions, respectively: 
0 / 1 1 < ∂ ∂
i i r x 0 / 2 1 > ∂ ∂
i i r x 0 / 1 1 < ∂ ∂
i i x ε
i)  The amount of illegal resources reduces (increases) when the level of current legal 
income increases (reduces). The higher the legal income, the higher is the 
opportunity cost to practice illegal activities and, consequently, the lower is the 
incentive to practice it. 
ii)  The amount of illegal resources increases (reduces) when the level of expected legal 
income increases (reduces). Given that the agent knows that the punishment is 
applied in the second period, i.e., given ,  the incentive to practice illegal 
activities improves if the expected consumption in the second period improves as 
well. At first, this result seems to be counterintuitive, but it is, in fact, correct. 
Notice that, in the first period, the criminal expects to consume . Given that he 
practices illicit activities in the first period,  if the expected legal income,  , is only 
marginally higher that the value of  , then the incentive for practicing crime is 
very small, since the difference between these values, the expected consume  ,  is 
small as well.  
i i x P 1 ε
i c2
i r2
i i x P 1 ε
i c2
iii)  The amount of illegal resources increases (reduces) when the probability of 
punishment and the effectiveness of anti-money laundering policies reduces 
(increases). The higher the effectiveness of law enforcement, the lower is the 
incentive to practice illegal activities.               
In this context, to solve the problem of maximizing equation (1) subject to equation 
(8), the agent’s optimization problem reduces to    )]. ( [ ) ( 1 1
2
2 1 max
1
i i i i
c
r c r u c u
i
− − + ε δ
  The first-order condition for this problem is 
) ( ' ) ( ' 2
2
1
i i c u c u δ ε =       (10) 
or 
  3  
2
1
2 1
) ( '
) ( '
ε
δ
=
i
i
c u
c u
     (11) 
which is known as an intertemporal Euler equation. This equation is familiar. The left-hand 
side is the consumer’s marginal rate of substitution of present (date 1) for future (date 2) 
consumption, while the right-hand side can be understood as the price of future 
consumption in terms of present consumption.    
  To know how   reacts to change of   and 
i x1
i i r r 2 1 , ε  is necessary to make an exercise 
of comparative static with the differentiation of equation (10) considering equations (2) and 
(5).  Hence, we have that 
) (
1
2 2 1 1 1 ε θ θ θ
θ
εd dr dr dx
i
r
i
r
x
i + + =      (12) 
where 
0 ) ( " ) ( 2
4
1
" < + =
i i
x c u c u ε δ θ       (13) 
0 ) ( 1
"
1 > − =
i
r c u θ        (14) 
0 ) ( " 2
2
2 < =
i
r c u ε δ θ        (15) 
0 )] ( " ) ( ' [ 2 2 1
2
2 > − =
i i i c u x c u ε ε δ θε      (16) 
  The comparative static analysis shows that 
0 1
1
1 < =
∂
∂
r i
i
r
x
θ         (17) 
0 2
2
1 > =
∂
∂
r i
i
r
x
θ         (18) 
0
1 < =
∂
∂
ε θ
ε
i x
        (19)  
  As expected, an increment in the legal income at the second period increases the 
criminal activities, which does not happen with an increment of the current legal income. 
Finally, the effectiveness of anti-money laundering policies and a higher probability of 
punishment for the criminal acts reduce the incentive to illegal activities.   
 
Conclusions 
  The results of the two-period model unveil that effectiveness of anti-money 
laundering policies and increase of probability of the agent to be apprehended and punished 
at the second period negatively affects the amount of resources obtained from criminal 
activities. The corollary of such results is that law enforcement organizations must improve 
their services of repression, prevention, investigation and dissuasion of organized crime and 
money laundering activities.    
  Moreover, in the initial period, the higher the legal income, the higher is the 
opportunity cost to practice illegal activities and, consequently, the lower is the incentive to 
practice it. However, as the consume in the second period is determined by the difference 
between the expected legal income in this period and the value of the illegal income 
generated in the previous period that can be apprehended by legal authorities in this same 
period, than the higher is the expected legal income, given the expected illegal income 
apprehended by legal authorities, the higher is the consume in the final period. In this sense, 
  4the higher the expected legal income in the final period, the higher is the incentive to 
practice criminals’ activities in the initial period.     
  In other words, the higher is the income of the organized crime, the higher is the 
necessity to present legal activities for justifying the status and the successful life of their 
business man, i.e., the criminals that command the organization. Of course, these criminals 
need to look as winners in the legal business world to disguise the nature or source of 
entitlement to money or property from criminal activities and to pass as respectable 
businessmen. In this context, the greater legal income in the second period works as an 
incentive to practice the illegal activities in the first one.   
 
References 
Alweendo, Tom K. (2005) “Crime and Money Laundering – The Challenges”, Governor of 
the Bank of Namibia – African Banking Congress, 8-10, March – Republic of South 
Africa. 
Araujo, Ricardo Azevedo and Moreira, Tito Belchior S.(2005) “An Inter-Temporal Model  
of Dirty Money”, Journal of Money Laundering Control – Vol.8, No.3, March, pp.260-
262.  
FATF, (2007). Home-Page of “The Financial Action Task Force (FATF)”. Available in    
http://www.fatf-gafi.org/pages/0,3417,en_32250379_32235720_1_1_1_1_1,00.html 
MacDowell, John and Novis, Gary (2001) “The Consequences of Money Laundering and 
Financial Crime”, Economic Perspectives – The Fight Against Money Laundering, 
Vol.6, No.2, May, pp.6-8.   
Masciandaro, D. (2000) “The Illegal Sector, Money Laundering and Legal Economy: A 
Macroeconomic Analysis”, Journal of Financial Crime, Vol.4, No.2, pp.103-112.  
 
                                                           
0 1 2 2 ≥ − =
i i i i x P r ε
1 There exists an institution known as “The Financial Action Task Force (FATF)”. It is an 
inter-governmental body whose purpose is the development and promotion of national and 
international policies to combat money laundering and terrorist financing. Hence, the FATF 
is "policy-making body" that works to generate the necessary political will to bring about 
legislative and regulatory reforms in these areas (FATF, 2007). 
 
2 If the agent practices illegal activities in the second period as well, the probability of the 
agent be punished will increase as the anti-money laundering activities and the probability 
of the agent be punished will occur in the last period alone. In this sense, the agent can be 
punished for the criminal acts in the first period or in the second period. Hence, we assume 
that the individual stop this type of activities in the second period. 
 
3  Of course, we need to impose a condition whichc . Hence, the 
representative agent only practices illegal activities if this condition is satisfied.  
 
 
  5

Crime and Money Laundering – The Challenges”,

Home-Page of “The Financial Action Task Force (FATF)”. Available in http://www.fatf-gafi.org/pages/0,3417,en_32250379_32235720_1_1_1_1_1,00.html MacDowell, John and Novis,

The Illegal Sector, Money Laundering and Legal Economy: A Macroeconomic Analysis”,

Tito Belchior S.(2005) “An Inter-Temporal Model of Dirty Money”,

A Two-Period Model of Money Laundering and Organized Crime

http://www.accessecon.com/pubs/EB/2007/Volume11/EB-07K00001A.pdf

A Two-Period Model of Money Laundering and Organized Crime

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