A government seeks to minimise the maximum expected utility of migrants and smugglers, but has to do this under constraints. It is argued that a vote maximising government should choose policies based on the relative weight of the introduced lobby utility function, which acts as a constraint. The model allows for calculation of simplified but optimal punishments, however this would require information about country-specific parameters. The model setting assumes that there is almost perfect competition between the facilitators (people smugglers).illegal migration; illegal immigration; irregular migration; undocumented migration; optimal punishments; punishments; Moldova; Ukraine; people smuggling; human smuggling; international migration; people smugglers; border control; punishment schemes; WNIS

Lundgren, Ted

English

Research Papers in Economics

I L L E G A L   T O   P U N I S H   O R   P U N I S H   T H E   I L L E G A L S   -   WH I C H   WA Y
S H O U L D   U K R A I N E   A N D   MO L D O V A   C H O O S E ?[51 rl.  Young  Moldovan  migrants  make  use  of  these  smugglers.  il1cg~lIy 
crossing the Slolak border from the Ukrainian town of Stryi [3  16]. 
In tile  West. there is an ongoing debate on v... hether legislation against illegal 
immigr<ltion is working or not.  There is also a discussion on whether policies of 
punishment  can  be  seen  as  etllically jnst  The current ,iew adopted  by  most 
recwing countries is  that the illegill  nligrant should be considered as  innocent, 
or  e\'en  ilS  i!  victim.  The  nligrant onlY  wilnts  to  come  and  \york  in order to 
sUrYlve, and  to  support  himself and  his  fanlily  back  home  [6:4)  The  people 
smuggler, or facilitator, on the other hand is someone \\ho should be brought to 
justice since he is taking ildvantage of a person in desperate need, and is making 
money from  breaking  the  law  [ibid).  In  most of today 's  deyeloped  nations,  a 
common  policy  is  to  deport  the  illegal  nligrant  but  to  ptmish  thc  facilitator, 
sometimes giving tJle  latter a jail sentence. In other ccuntrics. s~ch as Malaysia, 
an illegal imnligmnt can face a fine of $2,600. iI mandatory jail term of five years 
and si.\  lashes with a rattan cane [4168-1691. In l\larch 2(1()2.  Malaysia issued an 
amnesty  which lilsted  until  August 2002.  in order to  ghc illegal ilTunigrants  iI 
chance  to  leave  the  country  without  fear  of  pLUllshment.  318.272  illegal 
imnligrants left tile country [ibid] . Thus, there might be some e\ idence thilt harsh 
punishments.  directed  not  only  against  facilitators  but  also  against  illegal 
inunigrants,  are  working. So  what policy  of punishment  should countries  like 
Ukr3ine  alld  Moldova  choose?  Who should  be  punished and who  should  not? 
Generally:  How  should  European  gOH:rrunents  allocate  resources  for 
inunigration bet\\een competing ends? An economist such ilS  Gary  Becker has 
recently mglled that Western goverrunents currently have only two options. They 
must either open up their borders and start allQ\ying  illegal  immigrants or they 
must begin to  punish the latter as well, preferably witlljail[2]. 
Objectives 
In t!lis imicle J take on ~ neoclassical, Beckerian approach [I) of indil'idll~ls 
who can choose  b c ~\ ccn earning an honest income and beconwlg iJlcgalh  in tlie 
migration 111<lrket.  In il  general model, I study the conditions of a rational scheilic 
under which  potclltiill  migrJnts, faciliUltors  and  a  government are  maximising 
their utililies.  The market form resembles perfect competition as there are  manl 
billers  (llligmlHs)  and  sellers  (facilitators).  The  sellers  (facilitators)  ca.n  for 
88 
example  be freelancers  who  live  i.n  some  border area  in  the  \Vcstem  Newly 
Independent States - WNlS - such as the CmpallliallS in Ukraine, who know the 
terrain and  who  are willing to  take  migrants  across  tlle  Schemer border for  a 
predefined sum of money  The aim of the article is  to deriYe tlle conditions under 
\vhich migrants.  irllermediaries and governments ma\imise their utilities, find  a 
solution, and give a hint at what a choice of punisluncnt policies could look like 
for  host  countries.  The  act  of  illegnUy  crossing  a  state  border  and  the 
consequences tJlereof is described as a von NeLUnann-Morgenstern lottery. 
The Model 
We  consider  the  case  where  there  is  a  large  number of facilitators  (F) 
working on a freelance basis in some given border area. Migrants (:\1) ",-'anting to 
cross the border illeg!JJly do not face any particular difficulty finding a filcilitator. 
TIle  market structure somewhat resembles perfect competition. We assume that 
the  facilitator has linlited  influence over the  price  and  tJlill  he  cares  about llis 
reputation (R) 
From the potential migrant's  point of view.  tllere are il  limited  nLUnber  of 
choices, given in the decision tree ill fig  L  The migr:1nt  can choose io  lUre  the 
services  of a  facilitator.  If he  does,  then  there  is  a  probabiJity  PI  that  the 
facilitator is honest and will, to the best of his ability and after having received a 
fixed sum of money from the migrant. fulfill his obligillions and take him across 
the border. There is  a probability  I-P)  that the  facilitator is  e\ploitative  In that 
case,  he  will  simply  take  the  migrant's  money  and  "dump him in  the forest" 
before  having  crossed  the  border.  If lhe  facilitator  is  honest,  then  there  is  a 
probability P2  that the  border crossing will be successful and il  probability  I-P 
2 
that the party IS caught. Likewise, all other options that the pOlCntiill  nligrant has. 
and their associated probabilities. are given in the tree 
89 2, - the maximum possible Slim  for the migT<lnt. 

Let us indicate the cost of each branch of the tree fo r the migrant and for the 

facilitator, going from up to  dOI\"n 
Probability 
1'(1 ) 
11  I' 
pel) =p  . Pi  .p, .p, 
P(2) =pH  . p':' .(I _ p,)  p,c .Q, 
P(3) =p H. p;,.I. p,  .(1 - p,)p~ 'Q, 
P(4) =pH. p,U 'p, ' (1- p,) p ~ 'Q, 
peS) = p" .p;"'  . p, '(i  - P,JP;  Q. 
P(6) =,," .pt'· p, .(\-p,)p;Q, 
P(7) =pH. Pi'  p,  (1- p,)p ~ .Q. 
P(8) = p' .P:'  . p,  (1-p,)p;  2,0, 
j.(,)) =,,' .pt' · p,(I- p,)pi(!·;), 
P(IO) = ,,' . p,"  . p, ·(1- P:)P; ' (J,(J, 
P(l l) = p" . P:' . p, ·(1- p, )p; .Q,Q, 
P(l2) =  p'  . p;" ,p,  (I-p,)p; 'Q,Q, 
P(l3)=p· .p;" ' p, ' (1 - p,)p;  Q,Qo 
P(l4) = p H. p, M. p,  (, 1- p,)p;: .9,9, 
P(15) = p" .p; " .p,  (I - p, )p;  Q,Q, 
P(1 6) =  p H.  p;" .p, ·(1- p, )p~Q,Q . 
P( 17) =  pH p;" (1- p,)r 
P(IS) =  pH pj" (I- p,)(1-r) 
P(19) =pH .p;" . P, 
P(20) = pH . p;" ·(1-P,  )p~Q, 
P(21) =  pH  .p;"  .(1- p)p~Q, 
P (22) = pH . p;" .(1- p.,) p~Q) 
P(23) =p  . p;". p, 'p, 
92 
Migrant  Facilitator 
cel)  F(J) 
Z' 
- z;- ·c  Z{ 
k·i ,-X;  - £ 
Z' 
-Z; - C - TZH  Z' L 
7.{  - C 
-Z~ - C- p"  £ 
k· 7." -Z; 
kZc-7!  X; - C-R-P. 
k  i f/ -I{  Z; - C -R-TZF 
- ,  Z,' - C -R 
-- / '  -('  :t;  -C~ R -P, 
-/! -c  i ; -C -R-TZ, 
- Z;'  -(" - PI(  ' - C-R 
.- !. t -C -1~\J  Z: - C - R - PF 
7:- .. C - Pe  z;  - C-II -T  Zr 
-Z,' -c-r·  Ze  Z ~ - C-R 
-z; -C-TZH  Z{-C -R- PF 
- Z; - C-TZN  7.{  -C -R-TZ, 
-Z;  I; - R 
- Z;  ZF 
£ 
o kill  -Ct ·Z. 
-aZH  - C  o 
o -aZk  -C- p  U 
o -Ct.Z4 -C  - TZ~ 
k?H - fJl.{  (3 ..,::" 
f',2-l) = p"  . p~. p,  .(1 - p, )p;c .Q, 
P(25) = ,:.,,;'p,O  - I', )p,' .Q, 
P(2G) =,,' .  p;". p, ·(1-p, )p;Q, 
P(27) =,:  .p;'f . p,  (1 - p,)Pi.Q, 
P(28) =  /  .p;"  p,  (1- p,)Pi. .Q, 
P(29) =p·.";4 . P, .(\ - p,)p~ 'Q. 
P(30) = p . . p;"  .p, .(1- p,  )p~  .Q,Q, 
P(3 1) = p H p:'  P,  (1 - p, )p~  .Q,Q, 
P(32) =p" .p';' . PI . (1-p,)pfQ,Q. 
P(33) =,,". Pi" · p,(\- p,)p'j .Q.:Q" 
1'(34) =p" . p~  . p,(I - p,)p;Q.Q, 
1'(.1';) =p H. p;"  . p, .(1 - p,)p~ 'Q,Q. 
1'(36) = p o'  .pt' ·p, .(1-p,)p; 'Q,QJ 
P07) =P -.  . Pi"  p, ' (I - p,)p~  .Q,Q, 
l'!  . ~8) = p"  . P:'  p,' (1- p,)p; 'Q,Q. 
1'(77) =pH P:" 
PUR) = pi p;" 
The  probabilities  P(39) - P(76) 
substituting  p L  for  p H  and  ZL  for 
ciln be wrinen as 
-jJZ{-C  Ii  7.: 
- (ll.:~ - C - P"  jJ  ZL 
-fjZ{  - C - T  ZH  jJ zt 
k·ZH-jJ·L:  (l  zt -c 
k,ZH -/3·Z:  fi i:  - C-R- P y 
k,ZH -jJ Z{  /3 l {  - C - R-T Z, 
- /3Z{-C  jJ  7.; -C-R 
- fj  Z[  - C  /3  Z: - c - R - PI 
- fi'Z{ - C  jJzt - C-R- T  ZF 
-jJ·Z[ - C-P M  P  Z; - C - R 
- jJZ: - c - P",  $1.; - C - R - p.. 
-fJZ;-C-P.,  fJZ:  - C- R- rZ, 
- j3Z[  - C-TZ
H  PZ; -C - R 
-fiZt -C -T  'I.{f  f/7. t -('  R  P, 
- /3Z r-C- T  Z  H  N:  -C - H  Tl. , 
ZH  0 
ZL  0 
are  obtained  from  1'(1) - P(38)  by 
ZH  . The expected utilit), of the  migrant 
' 8 
E[C.": (Z;)]  = L,P(i)UM (Z41(i ) +C(i)) , 
i=1 
where ZM  (i) = ZH  for i = 1, ...,38, and  ZM  (I) = ZL  for i =39,,76 
The expected utility of  the facilitator is 
78 
E [Ur(Z{)  ] =LP(i)Ur(Zr +F(/) 
1=1 
All \'aJues in the slims could be taken from  the table. We come  lip Ilith the 
problem 
93 2 
m E [ UM(Z ; ) ]+f ' E[U«  Z r) J -4 ~~X  (I) 
under constraints  Os2; sZ,  (2) 
The optimisation problem 0-2) could be solved by  taking the derivative of 
(1) and put it equal to  zero. The solution would appear either in the critical point 
or in  the end points. Taking the derivative of the left side of (I) wc get the ftrSt 
order condition 
IS  38  X, 
-mLP(i)U;,(ZH +C(i» - m· jJ. LP(i)U".t CZII +C(ll) - 11/ L  P(I )C  \{ (7.,  ... C(i))­
1"'1  '... 23  , -)9 
-rrl  ' fJ  "  LP(i)u;" cz L +C(i» + 
(3 ) 
i .•  61 
18  3S  ~  :l 
+fLP(t'YJ~(I,  +F(i»+ f  · jJLP(i'jj ~ (ZF +F(I»"'.lI:  P(I)/. ',(7. " F(i» 
bd  /=:23  ! '  ,.I 
76 
+jJ  f  LP(i)U~ ( Zf + F (i» ; 0 
1 = 6 1 
Comparing the values ofthc utilit\  function  III ( I) in  thc cnd points with the 
value in the critical point we obtain the solulion "f ( l-~) 7 :"  . This is an optimal 
solution for illegal migrants and facilitators. 
We now introduce the govenunelll of tilc  ilost  COUIllj'\  into  the  model. The 
government faces the problem of allocating scarce resources bcm'cen competing 
ends. We assume that the aim of the  government  is  to  minimize the maximum 
expected utility of the migrant and the facilitator. The gO"cffiment has to  do this 
with respect to  a fixed budget and a  set of specified constrdints  For example, 
though it  might be desirable for the goverrunent to punish both the facilitator and 
the illegal migrant with jail, thereby causing the highcst possible negati"e utility, 
building prisons and detention centres, and keeping people  in them  is  costly. 
The government must also act with respect to  human rights and immigraJlt lobby 
groups in order not to lose votes. 
To keep it simple, let the government tend  to  minimi:ce the function 
E[U M(Z{")] +E[uI (Zr  )] ~  , vL'L(- f'w -PF' -(), 
,,,here  y  is  the weight of the lobby utility [unction C
L t- PM ' - P
F 
, -T) . 
The constraints are the foUowing: 
pln."S  PM  S  P'nla."  Pl nu"s  l ~  s  l' l ",~"  rcrrins Tsrm~ " 
94 
Let the utility fllllctiolls of the migrant and facilitator be as follows 
2 x X'
[ i 
M (x) = x-- 2o,  ..  x 5 b ,  UF(x)=x --,xs  b, ' 
2b_ 
where  x s: hi  for the  migrant and  x  :S: b2  for the  faci! itator. We assume  that 
,alues b, and b2are sufficiently large and that (ZH+ C(i))  :s:  b" (ZL+F(i))  ~ b
IIthe utility functions are quadratic then equation (3 ) takes the [orm 
lR  ]8 
-mLP(i)(-I- CZ H  -C  (i)-I{) / 6, )-mjJ. LP(I)(-l-(ZH - C  U) -' fJZ; )/q )­
I~I  ~D 
-mfp(I)(-I - CZL  - C  (I)- Z{)l b,» ­
h  J9 
"  -m  fJ  L  l'(i)( - 1-(I L -C(i) - /J/.{)I b, »+ 
1= 6 1 

18  38 

+fLP(i)( I-.(7., 1 -F  (i) +l{) ' b,»+ ffJLP(I)(l - C Z, +F-(l)+ fJI { )/6, )+ 
H'1  ;=13 
50 ,.,  76 
+f LP(l)U~ C Z ; + FUl) + f· jJ .LP(i)(l-(Z" +r  e i) + fJI{  )I b, ) ;  0 
i  -N  1- 61 
where C  (I) =C(I) + Z; , r  (I) =F(i) - Z; . 
Collecting the tcnns with Z{  and without Z{  we have 
11  )I  .16 
[(-"'L,"(/) q )-'/1J Ii' L  I1"I) ' !.J )-mLP(/)'4»)­
••  ;_t l  I 
-m{r"  ±i1:')  ~  - /r.P( I).b ,-f/f r.P( /) I b, -ft,P( /) '  b, 
·41  ,·1  "':0  I..;f) 
-If· tf· ,,\1)  l  ) ~ m±A: /X"'I- (Z" -C'(1)) .'4 )+m.  {3. i:P(IX-J-(z" - C'(i) /4)+mI:P(IX-t-(Z, -C'(I») '11))+ 
,,",,I  01  -­
+m./I. t  ,R:X-i- (Z  -C' (I »  ; ~ »)-!± P(iXI - (Z, +F(I»  /h,»-F pr,P(/Xl-(Z, + P-(/»)flj)­
,·°1  ,"I  ,  ..  D 
..t,P(/Xl - iL, t!·"(I)  h, l-P /  i:P(IXl-(Z,+F(i) fG  )=0 
:,."R  .<41 
Let 
95 

Illegal to punish or punish the illegals: Which way should Ukraine and Moldova choose?

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