Theoretical Economics Letters, 2013, 3, 267-278
http://dx.doi.org/10.4236/tel.2013.35045 Published Online October 2013 (http://www.scirp.org/journal/tel)
A Political Economy Model of Capital Expropriation
and Skilled Migration
Kirk A. Collins
Schwartz School of Business, St. Francis Xavier University, Antigonish, Canada
Email: kcollins@stfx.ca
Received July 4, 2013; revised August 4, 2013; accepted August 13, 2013
Copyright © 2013 Kirk A. Collins. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
This paper studies the interplay of capital reso urces in a small open economy by way of a general equilibrium political
economy model. Normative implications for hu man capital migration resultin g from physical capital lobbying are ana-
lyzed. Findings reveal that lobbying designed to mitigate the capital levy problem leads to increased human capital mi-
gration and that optimal tax policy for a social welfare maximizing government necessarily implies “brain drain”. The
implication being that skilled migr ation may be an inevitable by-product of a self-interested government. As such, while
governments may vow to do something to stem the flow of their “best and brightest”, the financial pull of increased
revenues appears simply too great to imply anything other than lip service, when general equilibrium effects are con-
sidered. As a corollary, we find that restrictions on political contributions are welfare enhancing in the two-sided ex-
propriations model we present.
Keywords: Lobbying; Migration; Human Capital; Taxation; General Equilibrium
1. Introduction
Much has been made about highly skilled or human
capital migration, the so-called brain drain, in political
circles.1 Governments remain concerned that there will
be (or will continue to be) shortages in key areas of the
economy, such as health care, education and science (see,
e.g., Gibson and McKenzie [2]). Researchers have shown
that skilled migration is a persistent and somewhat
dominant pattern in our globalized economy, but need
not present negative externalities in all situations (Doc-
quier and Rapoport [3]). The analysis here contributes, in
part, to the externality arguments presented in previous
research by adding an overlooked and under-analyzed
synergistic behavior between capital resources in an open
economy; namely, the interplay between physical and
human capital that results from political economy deci-
sions. We illustrate this relationship between the capital
resources by way of a general equilibrium political eco-
nomy model that permits lobbying by owners of physical
capital and migration by workers, the owners of human
capital, if you will.2 It is in this latter sense that we also
add to the literature on capital expropriation and it is
where the main value -ad ded of the paper originates.
The traditional capital levy problem relates to the un-
derinvestment in physical capital that arises because of
government incentives to expropriate surplus from sunk
capital, since it imposes little deadweight loss (Eichen-
green [6]). Researchers have explored various iterations
of the problem, such as reversibility of physical capital
investments in the presence of lobbying (Marceau and
Smart [7]), persistence of inefficient policies in equilib-
rium as a result of sunk costs (Coate and Morris [8]), and
lobbying by owners of sunk capital (Garfinkel and Lee
[9]). Building on this and using the work of Bernheim
and Whinston [10] as a starting point, our model takes
into account the influence of human capital in the ex-
propriations argument; thereby, it affects the two-sided
argument we advocate and the one that has yet to be fully
explored in the literature.3
By modeling this interdependence amongst capital re-
2Heckman and Klenow [4] and Heckman, Lochner and Taber [5] have
examined human capital policy and general equilibrium cost-
b
enefit
effects of policy initiatives,but do not model the critical political
economy ideas we are expressing here. That is, rather than simply
examine the effects per se, we are examining the government’s percep-
tion of and/or role in these effects.
3While not expressed here, given the focus of the paper, the model also
adds to the growing literature of computational models in political
economy; those with no closed-form solution. For a discussion of such
models and their value,see e.g.,Kollman, Miller and Page [11].
1For a discussion on the importance of human capital, in general, see,
e.g., Davies and Whalley [1].
C
opyright © 2013 SciRes. TEL
K. A. COLLINS
268
sources, we find that if th e link is strong enou gh between
human and physical capital and/or individuals are suffi-
ciently mobile, then taxing one type of capital in favor of
another may lead to (more) harmful disincentive effects
and may even reduce the overall tax revenue of the gov-
ernment; the possibility that a change in the tax rate on
physical or human capital may lead to spillover effects,
which can have positive or negative repercu ssions on the
residual capital, can also not be ruled out.4 We show that
in its effort to maximize the welfare of its constituents, a
government will face inevitable human capital loss as a
result. Optimal policy dictates that the government
maximize welfare of non-migrants at the expense of this
select cohort of highly skilled workers; as such, the loss
of individuals at the upper end of the human capital lad-
der is simply an unfortunate byproduct of a self-inter-
ested government.5 Therefore, while governments may
vow to do something to stem the flow of their “best and
brightest”, the financial pull of increased revenues ap-
pears simply too great to imply anything other than lip
service, when general equilibrium effects are considered.
The reason for the outcome is that a marginal increase in
labor taxation, culminating in some skilled migration, is
less detrimental than a marginal drop in public goods,
which would manifest if no tax increase were enacted.
Given this, we find that it is indeed advantageous to have
a restriction on capital lobbying for countries that bleed
top talent (i.e. experience negative political economy
externalities) and it can go a long way in mitigating the
implications that this two-sided capital levy problem has
on skilled migration.
The rest of the paper is organized as follows: Section 2
introduces the model, while Section 3 presents the im-
plications of lobbying and human capital migration; Sec-
tion 4 provides some concluding remarks.
2. Model
2.1. Preferences and Payoffs
Consider a small open economy in which one public
good—labeled good 0—and N private consumption
goods—labeled —are produced. We shall as-
sume that the pub lic good is non-traded, while th e N pri-
vate goods are freely traded. The world price of good i,
1, 2,,N
1, ,iN
is denoted by i
p. The industry that pro-
duces good i is called industry i. Each private good is
produced by a single industry, using labor and capital. As
for the public good, it is produced by the government,
also with inputs of labor and capital.
There exists a continuum of consumers in this econ-
omy and, to simplify, we shall normalize the population
size to 1. The population is divided into two major
groups: capitalists and workers. Workers earn their living
by supplying part of their time endowment – normalized
to 1 – on the labor market. Capitalists do not work. They
are the owners of capital stocks in the private sector,
which constitute the sources of their income. Let 0
i
,
1, ,iN
denote the fraction of the population who are
the owners of the capital stock in industry i. We suppose
that the group that consists of the owners of the capital
stock in industry i and the group that consists of the
owners of the capital stock in industry j, , are dis-
joint. As a group, the capitalists thus make up a fraction
of the population equal to 12N
ji


while the
proportion of the population who are workers is given by
12
1
N

 . We shall assume that for each i
the owners of the capital stock in industry i are equal
residual claimants of the profits made by the industry.
Workers, however, are assumed to differ in their earning
capacity – specifically, by their human capital level. The
human capital level of a worker is denoted by
. To
avoid corner solutions the distribution of types among
workers is represented by a continuous density function
:,hh
with
0h for all 0
where
1
0d1 i
i
hN


.
To model the difference in earnings due to variation in
human capital levels, we shall assume that labor inputs
are measured in effective labor units and that for each
hour that a worker of type
spends in the production
of a good, she provid es
units of effective labor input.
If we let
denote the wage rate paid to one unit of
effective labor input, then the labor income earned by a
worker of type
, when she works one hour, is
. A
worker’s preferences is represented by the utility func-
tion,
,x

1
,, ,
NN
xxu

00
ux 12 where 0
u
x
is
consumption of the public good; ,1
i,,
x
i
N is con-
sumption of the ith private good; and is labor supply
in hours. We impose the following conditions on prefer-
ences: (i)
0
00, 0uu
0 0
x
and

00 0ux

for all
4Pecorino [12] examines the interesting question of the effect of tax
structure on long run growth of income and consumption. To do so,he
relies on changing the tax mix between human and physical capital,
which must satisfy an exogenously determined government budget
constraint. Similar in its treatment to Marceau and Smart [7], the ques-
tion being addressed is not a political economy one, and as such differs
from the work undertaken here.
5This finding goes against that of Razin, Sadka and Swagel [13] that
suggests migration does not necessarily tilt the political balance in
favor of those with the power to create this hold-up problem. In other
words, the fiscal leakage they talk about does not seem to be present,
when general equilibrium considerations are taken into account; at least
not to the same extent they talk about.
0
x0; and
010 0x
lim ux
. (ii)
00
1N
u
,
100
N
u
,
10
N
u
and for all

10
N
u

0. Also,
11
lim N
u


. (iii) The subutility
function u is linear homogeneous and increasin g in all its
arguments.
As for a capitalist, who does not work and thus does
not suffer from the disutility of working, her utility de-
Copyright © 2013 SciRes. TEL
K. A. COLLINS 269
pends only on her consumption bundle. The preferences
of a capitalist are therefore represented by
 
00 12
,,, .
N
ux uxxx
To finance the production of the pub lic good, the gov-
ernment levies a capital income tax and a labor income
tax. Let i
be the tax rate on profits made by firms in
industry i and t the tax rate on w ages. There is no double
taxation of physical olicy is therefore
represented by a list .
capital. A tax p


,
N
it
1i
We want to explore the impact that taxation has on
workers’ incentives to migrate, therefore we allow them
to be perfectly mobile within the boundaries of the small
open economy—at no cost. They could also choose to
leave the home country and work in the outside world if
they are willing to pay some cost of adjustment. Th e cost
of adjustment of a worker of type
denoted by
,a
is continuously differentiable, strictly positive, and
strictly decreasing in
.
Let
denote the wage rate earned by one unit of ef-
fective labor abroad. Fo r a wo rk er of typ e
, leaving the
home country to work in a foreign country will yield a
net labor income—net of adjustment costs—equal to

a
in industry i wil
, if she chooses to work hours.
To influence the tax policy implemented by the gov-
ernment, the owners of the sunk capital stock in each
industry get together and form a special-interest group to
lobby for favorable tax treatments. This allows them to
mitigate the physical capital levy problem. In what fol-
lows, the owners of the capital stockl be
referred to as industry lobby i. Let 1i be the tax
policy implemented by the government. Under this tax
policy, the representative firm in industry i, solves the
following profit maximization problem:

,
N
it
 

max 1,1.
i
Liiiii iii
pF K LL


(1)
In Equation (1),
,
iii
F
KL is the technology used in
the production of good i; Ki is the capital stock in this
industry; and Li is the labor inputs – measured in effect-
tive labor units. It is assumed that
,
iii
F
KL is con-
tinuously differentiable and strictly increasing in each of
its arguments. Furthermore, there are diminishing returns
in each factor and the following Inada conditions are
satisfied

0
lim ,
i
iii
Li
FKL
L

and

lim, 0
i
iii
Li
FKL
L

.
As defined,

i
represents the before-tax profits
made by industry i, given that it faces the effective labor
wage rate .
Note that the capital income tax does not
influence the production plan of the industry. We shall
denote by

i
L
the demand for effective labor by
industry i.
As a group, the owners of the capital stock in industry
i receive an income equal to


1ii
 , which gives
each capitalist in this group a capital income of
1ii i
 . Thus, a member of the group that
owns capital stock in industry i solves the following util-
ity maximization problem:

 
 

100 1
,,
00
max, ,
1,
NN
xx
ii
i
ux uxx
ux





(2)
subject to,



110
N
iii ii
i
px

 
.
Note that in solving, the capitalist takes as given 0
x
,
the level of the public good provided by th e government.
Also, in Equation (2), we have let denote the in-
direct utility function associated with the consu mption of
the N private goods, as a function of the after-tax capital
income. Since the subutility function associated with the
consumption of the private goods is linear homogenous,
without any loss of generality we can set

11
,
which allows us to assert that the utility of a capitalist is
the same as her net income.
Consider a worker of type
, who chooses not to
emigrate. Her disposable income is then
1t
,
which will be spent on private goods. The utility ob-
tained from the consumption of the pri vat e g oods is

11tt
 

and the disutility from working is . Thus she
solves the following utility maximization problem:

1N
u


00 1
01
00
max 1
,, ,
N
uxt u
ux t

 
  


(3)
where we have let
,,t

denote the indirect utility
function associated with the consumption of the N pri-
vate goods and the disutility of working for a worker of
type
, who chooses not to emigrate. Using (ii) of the
preference assertions made earlier, we can assert that
Equation (3) has a unique interior solution, which is
characterized by the first-order condition

1
10
N
tu

.
The optimal labor supply of a worker of type
who
chooses not to leave the country is then given by




1
1
11
N
tu t

 
,
where w e have let

1
1N
u
denote the inverse of 1N
u
.
Because the marginal disutility of working is strictly in-
creasing in , it is clear that the optimal labor supply of
a worker of type
who does not emigrate is strictly
increasing in
1t
.
Copyright © 2013 SciRes. TEL
K. A. COLLINS
270
A worker who chooses to leave the country will solve
the following utility maximization problem:
 


01 1
max .
N
au

 
 
 (4)
Note that in the objective function (Equation 4) there
is no public good. In essence, we are restricting the indi-
vidual to a migration decision based on income and ad-
justment costs.6 By doing this we are essentially saying
that public goods are not an overriding factor for migra-
tion, particularly when the latter has an uncertain, but
positive, cost attached.
Now consider a worker with human capital level
. If
she emigrates and decides to work hours, then after
paying for the adjustment cost, she is left with a net in-
come of

a

. On the other hand, if she decides
to stay, then her disposable income is

1t
. It is
clear that if

1,at
 

then

1at
 

1
for all , which in turn implies that it is not op-
timal for her to leave the country. Hence only a worker
with a human capital level
0
that satisfies the strict
inequality
 
1at
 

or equivalently,
 
1at
 

, could entertain the idea of leav-
ing the country. Thus if
t1
 , then no worker,
regardless of her human capital level, will choose to
leave the country. The phenomenon of brain drain could
only occur if

1t
 , i.e., if the net wage rate in
the home country is below that abroad. If migration costs
are positive then the wage abroad must reflect this, oth-
erwise no emigration will occur. Furthermore, when the
utility of the public good is taken into consideration, only
a worker with a sufficiently high level of human capital
would think of leaving the country.
To see why, note that

a
is strictly decreasing
in 0
and tends to infinity when
tends to 0.
Hence when

1t
 , there exists a unique value of
, say

1t
, such that

1at
 

.
It follows directly from the definition of
1t
that




 

11
11
tat
tt

 
 
 
1
for all , which in turn implies
0






1,,1ttt
  
 
When the impact of the public good is taken into con-
sideration, the loss in utility suffered by a worker of type
1t
, if she decides to leave the country will be




00
1,,1tttu
  
 x,
which is even more pronounced.
To continue, let


00 ,,quxt
 
 
for all
1t

. Then



10qt

.
Through the use of the envelope theorem and the optimal
labor supplies (and some manipulation), we get,







11
11
1
11.
NN
N
uu
ut
a







Observe that when
, we have


1
111
N
ut

.
This last result together with the inequality
1t

0
 implies that
q
is positive and
bounded below by
1t
 when
. There-
fore,
q
is strictly increasing to infinity as
tends
to infinity. Furthermore, q

is strictly negative at
t1
. Hence there exists a unique value of
,
say
0.
1t

, such that

qt
10

.
Therefore, this unique value,
, is the value of
that
solves
00 ,, 0ux t
 
. We refer to this
value as the critical human capital level and denote it as
0
1,tx

. The level is strictly increasing in
and 0
x
, but strictly decreasing in t.
2.2. The Level of the Public Good and the
Payoffs Induced by the Tax System
The aggregate supply of effective labor in the small open
economy is




0
1,
01d
tx th


,
while the aggregate demand for effective labor by the
private sector is

1
N
j
j
L
. Furthermore, the total tax
revenues collected by the state are given by





0
1,
0
1
1d
tx
N
jj
j
tt

h



.
These tax revenues are used to pay for the effective
labor inputs used in the production of the public good.
The wage rate for effective labor that clears the labor
market in the small open economy satisfies the following
6See Arntz [14] for an empirical study supporting this theoretical as-
sessment for human capital migration.
Copyright © 2013 SciRes. TEL
K. A. COLLINS 271
market-clearing condition:





 





0
0
1,
0
1,
0
1
1
1d
1d
1.
tx
Ntx
j
j
N
jj
j
th
Lt th





 

(5)
In order for the labor input to be sufficient for produc-
ing the amount of public good 0
x
, the following condi-
tion must also be satisfied:






0
1,
00
01
0
1
,1d
.
N
tx
jj
j
FKtt h
x

 


(6)
In Equation (6),
000
,
F
KL is the production func-
tion used in the production of the public good, where
0
K
is the stock of public capital and is the input of
effective labor. It is assumed that 0
L
000
,
F
KL is con-
tinuously differentiable and strictly increasing in each of
its variables. Furthermore, the marginal product of labor
is strictly decreasing when increases and the Inada
conditions are satisfied. 0
L
Together, Equations (5) and (6) constitute a system of
two equations in two unknowns –
and 0
x
. For any
given tax system , we shall let

1,
N
iit


1,
N
iit

and

01,
N
ii
x
t
be the values of
and 0
x
that
solve the system. As defined, is the equi-

1
ii

,
Nt
librium wage paid to one unit of effective labor and

01,
N
ii
x
t
the equilibrium amount of public good
produced when the tax system is imposed.

1,
N
iit
N
Under the tax policy 1
ii, the critical level of
human capital that separates the workers who stay from
those who leave the country is

,t





0
11
1,,
NN
ii
ii
ttx


,t
.
To keep the notation from becoming too burdensome,
we shall write , instead of

1,
N
iit







0
11
1,,,
NN
ii
ii
ttxt

,
to denote the critical human capital level. A worker will
stay if and only if her type is less than or equal to
. For a worker who stays, her utility under

1,
N
iit

the tax policy is given by

1,
N
iit


00 11
,,
NN
ii
ii
ux ttt,,
 

.
As a group, the welfare of the workers who stay is
given by











1,
00 1
0
1
00 11
,
,, d
,,
N
iitN
ii
N
ii
NN
iii
ii
ux t
tt h
ux tHtt

 
 



1
,.
N
i
(7)
In Equation (7), we have let

H
denote the cumu-
lative distribution of
. Also note that on the right-h and
side of Equation (7) the first part gives the utility from
the consumption of the public good, while

,
N
it
1i
represents the utility from the consumption of the private
goods and the disutility of working, for all workers who
stay.
As for the owners of the capital stock in industry j,
1,, ,jN
each of them has a capital income equal to


1
1,
N
j
ji
itj
 
 ,
which according to our earlier calculations is also the
capitalist’s utility from the consumgoods.
Her utility under the tax policy is thus given
by,
ption of private

1,
N
iit




00 11
1
,1 ,
NN
ijj
ii
j
ux tt


i
.
Therefore, as a group, the owners of the capital stock
in industry j obtain the following utility under the tax
policy

1,
N
iit
,








00 11
00 11
,1 ,
,,.
NN
ji jji
ii
NN
ji ji
ii
ux tt
ux tt
 
 


 
 (8)
In Equation (8), we have l
1,t denote
the utility that this group obtains from the consumption
et

N
ji
i
of the private goods under the tax policy .


1,
N
iit
Without political contributions, the social welfare ob-
tained under the tax policy , is given by

1,
N
iit









1
00 1
11
11
1
,
,,
,,.
N
ii
NN
ii
ii
N
NN
iji
ii
j
Wt
uxt Ht
tt
N





 
 (9)
Let

,t
1
ii
N
be a solution of Equation (9). The
equilibrium wage rate and the level of public goods pro-
vided under the tax policy are given, re-

1,
N
iit

spectively, by

1,
N
iit

and

01,
N
ii
x
t

. Now
define,
Copyright © 2013 SciRes. TEL
K. A. COLLINS
272


1
11
,,
NN
NN
jj ij i
i
jj
tt
 
 









1
,
i
then denote by the ordered pair the tax policy
under which capital is taxed uniformly at rate
,t

across
industries and wages are taxed at rate . We claim that
is also a tax policy that maximizes social wel-
t

N

,t

fare. Indeed, when the wage rate prevails,
1,
iit
the representative firm in industry j will use the same
level of effective labor input whether its profits are taxed
at rate
j
or at rate
. As for a worker, if the level of
public goods provided remains at

01,
N
ii
x
t
and if
the wage rate 1i still prevails, then her labor
supply is still the same when the home government

,
N
it

switches from the tax policy to

1,
N
iit

,t
.
Given the behavior of the firms and the workers just de-
scribed, the home government collects the same amount
of taxes under the tax policy as under the tax
,t

policy , i.e., the same level of public goods

1,
N
iit
is provided when the home government switches from

1,
N
iit
to . We state formally this result in
,t

the following lemma:
Lemma 1. In finding the tax policy to generate the
revenues needed for the provision of the public goods,
the home government can restrict itself to a uniform tax
on capital.
In what follows, the ordered pair
,t
represents the
tax policy under which capital is uniformly taxed at rate
across industries and wages are taxed at rate t. When
the tax policy

,t
is implemented, the social welfare
obtained will be written under the following form:
 



 
01
1
,,,
,,.
N
o
j
N
j
j
WtuxtHt
tt
j


 
(10)
Under this scenario, the home government solves the
following social welfare maximization problem:


,
max ,.
tWt
(11)
While a tax on profits is neutral, a tax on wages dis-
torts the labor-leisure choice of workers and might in-
duce emigration. Therefore, we expect that the home
government will favor taxing capital, the immobile, sunk
factor, over taxing labor in it efforts to raise the revenues
needed in the provision of the public goods. This is sim-
ply the traditional capital levy problem, but in general
equilibrium context. Proposition 1 confirms this intuit-
tion.
Proposition 1. Let denote the
optimal tax rate on capital, given that only this factor of
production is taxed to raise the revenues needed for the
provision of the public goods. Then, if , we have t
= 0. On the other hand, if , then optimal tax policy
dictates that all profits be taxed away while wages be
taxed at the rate which solves the following maximization
problem:
argmax ,0W
1
1

max 1,.
tWt (12)
Furthermore, the optimal tax rate on wages in this
case is strictly positive if and only if






0
0 00000
0
, 1,0, 1,0
1, 00.
F
uFKL KL
L

(13)
Proof. See Appendix A.
3. Lobbying and Human Capital Migration
When the industry lobbies are active, the global payoff of
the home government and the N industry lobbies is given
by






1
00 11
1
1
,
,,
,.
1
N
ii
NN
ji ji
i
j
N
ii
t
ux tt
Wt
 

N
i
(14)
The tax policy implemented by the home government
is a solution of the following m a ximization problem:


1
1
,
max, .
N
ii
N
ii
tt
(15)
Let

1ˆ
ˆ,
N
iit
be a solution of Equation (15). Under
this tax policy, the equilibrium wage rate is

1ˆ
ˆ,
N
iit

and the total capital income tax revenues collected are
given by


1
1
ˆ
ˆ,
NN
jj i
i
j
t

.
Let 1

ˆ
N
i
i
be a capital income tax policy that satis-
fies the following condition



11
11
ˆˆ
ˆˆ
,,
NN
NN
jj ijj i
ii
jj
tt
 




.
It is clear that the tax policy induces the

1ˆ
,
N
iit
N
same equilibrium as the tax policy . That is,

1ˆ
ˆ,
iit
Copyright © 2013 SciRes. TEL
K. A. COLLINS 273
the equilibrium wage rate and the equilibrium level of
public goods provided are the same under both tax poli-
cies. Hence the critical human capital levels are also the
same under both tax policies, and the utility of a worker
who stays under these tax policies remains
whernment switches from
to .
the same
n the home gove
ang
men

1ˆ
ˆ,
N
iit
e when the


ˆ
,
Nt
i


ˆ
,
N
it
e govern


ˆ
,
N
it
1i
Furthermore, because the equilibrium wage rates are
the same under both tax policies, the (before-tax) profits
earned by each industry are also the same, as are the total
capital tax revenues collected. Hence, the welfare of the
owners of capital, as a group, does not ch
homt switches from 1
ii to
1i, although the welfare of the owners of capital
in a particular industry, say i, will rise (fall) if
ˆ
is less
than (greater than) ˆi
.
At the global level, the joint payoff of the home gov-
ernment and the N industry lobbies thus does not
whernment switches from 1i
to 1i. In particular, if the home government
taxes capital uniformly across industries at the following
rate,
change


ˆ
ˆ,
N
it


n the hom

ˆ
,
N
it
e gove


11
ˆ
,,
NN
i
ii
tt

olicy is
11
ˆ
ˆˆ
NN
i j
jj
 





this tax p
ˆjj
 
 ,
and labor at rate , then the joint payoff of the govern-
ment and the N industries under the
same as that under the tax policy 1i. Therefore,
the home government can restrict itself to the case
12 iN
ˆ
t

ˆ
ˆ,
N
it


 
 , i.e., the case where capi-
tal is taxed at the same rate across industries. A tax pol-
icy can now be represented by an ordered pair, say
,t
,
where
is the uniform tax rate on capital and t is the
tax rate on wages. The gross equilibrium wage rate and
the equilibrium level of public goods provided will be
denoted, respectively, by
,t
and 0

,
x
t
. Given
this, we offer up the following proposition.
Proposition 2. Let
1argmax ,0
 denote the
tax rate on capital imposed by the home government
when the N industry lobbies are active, given that it
chooses to tax only this factor of production in its efforts
to raise the revenues needed for the provision of public
goods. Then we have 1
, with strict inequality hold-
ing if .
1
Proof. See Appendix B.
In other words, if the home government chooses not to
tax wages, then the tax rate it imposes on capital is lower
when the N industry lobbies are active than when they are
inactive: lobbying activities, under this scenario, reduce
the capital income tax rate and a fortiori the le vel of public
goods provided.
Here we have simply shown what others have done be-
fore us, but in a general equilibrium sense; namely, that
the introduction of lobbying can help mitigate the capital
levy problem. We have provided additional insight into the
argument by explicitly modeling public good provision.
Since the government does not use lobbying money to-
wards the production of the public goods, workers see a
reduction in their welfare.
Now consider a tax policy

,t
, with 0,0t

and t is sufficiently small. Because t is sufficiently small
and 0
, there will be no brain drain when the tax pol-
icy
,t
is implemented. For the workers, as a group,
their total welfare is given by,




00 10
,1,,, d
N
j
j
uxttt h
.

 





.
(16)
As for the owners of capital in the home country, as a
group, their total welfare is given by


 

00
1,1 ,
N
jj
j
ux tt
 

(17)
Differentiating Equation (16) with respect to t, then
evaluating the result at 0t
, we obtain



 

 

0
00 1
0
0
,0,0 1
,0,0 d
,0,0d .
N
j
j
x
ux t
h
t
h
 
 






(18)
Now we have shown that

,0 0.t

  Also,
0,0 0xt
. Using these results, we can interpret
Equation (18) as follows. The first expression represents
the rate of change in the welfare of the workers due to a
higher level of public goods, which is financed by raising
the wage rate slightly above 0. The second expression rep-
resents the rate of change in the wage bill received by the
workers due to the rise in the gross equilibrium wage rate
,0 0t

 when the tax rate on wages rises
slightly above zero. Both the first and second expressions
are positive. The last expression represents the rate of in-
come loss suffered by the workers as t rises in a right
neighborhood of 0. The Inada condition
000
0
lim
x
ux

ensures that the first expression dominates the last ex-
pression where 0
. Therefore, Equation (18) will be
positive when
is not too high. However, it might be
negative if
is substantial.
Differentiating Equation (17) with respect to t, then
evaluating the result at 0t
, we obtain,


 


00
1
0
,0
,01,0,0.
N
j
j
j
ux
xL
tt




(19)
Copyright © 2013 SciRes. TEL
K. A. COLLINS
274
Observe that for each , the expression
1, ,jN



0
00,0 ,0
j
x
ux t
 
represents the rate of change in the welfare of the own ers
of capital in industry j due to a higher level of public
goods provided, while the expression
 


1,0
j
Lt,0
 
represents the loss of capital incomes suffered by this
group due to a higher wage bill that the industry pays to
its workers. As in the case of workers, the first expres-
sion dominates the second expression when
is small.
However, when
is substantial, the summation in
Equation (19) might be negative. Under such a scenario,
raising the tax rate on wages above zero might make the
owners of capital in the home economy worse off as a
group. Because the impact on the owners of capital of a
rise in the wage rate operates indirectly through the rise
in the gross equilibrium wage rate and the rise in the
level of public goods provided, while the impact on
workers operates both directly – through the reductions
in labor income – and ind irectly – through the rise in the
level of public goods provided and the rise in the gross
equilibrium wage rate – the impacts, when they are nega-
tive, are more adverse to the workers. In particular, it is
difficult to imagine th at a slight increase in the wage rate
above zero will improve the situ ation of the workers, but
make the situation of the owners of capital worse off.
Therefore, for any 01
, if the home government has
already taxed capital at rate
and can raise the welfare
of the workers by also taxing wages slightly, then this
action also raises the welfare of the owners of capital,
which leads to the following,
Proposition 3. The tax rate on wages will be positive,
, if industry lobbies are active. 0t
Proof. See Appendix C.
Thus, once again in the presence of lobbying firms can
alleviate some of their tax burden by providing financial
support for a political party’s platform. The resulting lo ss
in tax revenues used to fund the provision of the public
goods must either be recouped by increasing the taxation
on labor income or by redu cing the lev el of public good s.
But, any reduction in public goods will lower the welfare
of the government’s constituents by a larger amount, than
a small increa se in inco me taxes. Therefore, taxes on labor
income rise in the presence of lobbying and the govern-
ment concedes the resulting migration by some highly
skilled labor in an effort to make the remaining constitu-
ents better off, thereby ensuring its persistence in office.
While no dependence of unskilled on skilled labor is
built into the model, it is not hard to imagine that if
skilled labor leads to job creation for unskilled workers,
the reduction at the upper end of the human capital scale
will intensify the negative spillover effects. This type of
argument would exacerbate the implications of our find-
ings for countries that bleed talent, in particular, or, at
least, have an inequitable impact on skill differential be-
tween those that leave versus enter from abroad. As such,
a restriction on capital lobbying would likely imply a
more efficient solution.
4. Concluding Remarks
By modeling the two-sided expropriations problem, we
have shown how changes in tax policy can influence mi-
gration patterns of skilled workers. By doing so, we have
explored some indirect implications of the traditional
problem which has yet to be examined. For example,
whether or not a country is human capital intensive will
depend directly on the taxation of skilled labor and its
mobility and indirectly on policies guiding political con-
tributions and capital income taxes. The more lax the
policies are on the indirect effects, the greater the direct
incentives for mig ration of highly sk illed ind ividuals will
be.
Modeling the expropriation decision in a general equi-
librium framework also affords a commentary on the
externality caused b y physical cap ital lobb ying on h uman
capital migration. For example, all else being equal, if
adjustment costs rise in the home country, then a greater
number of highly skilled workers remain and the econ-
omy is now more human capital intensive; this, accord-
ing to endogenous growth theory, leads to an improved
economic outlook. Of cou rse, this goes for countries that
bleed talent. For countries that rely on attracting skilled
labor from abroad, the results are the opposite. If migra-
tion costs rise, then fewer workers are choosing to emi-
grate. Therefore, countries that relied on skilled labor to
supplement their workforce may fall short of their nec-
essary requirements.
Finally, we show that while equilibrium under social
welfare maximization calls for a high capital income tax.
This result falls apart with the allowance of lobbying.
Fortunately, the mobility of skilled labor provides a de-
terrent to the government when determining the stru cture
of taxation. Hence, labor income taxation remains low
even in the face of lobbying. This result casts doubt on
previous findings that believe restrictions on lobbying
have ambiguous results (e.g. Marceau and Smart [7]).
Certainly, in our framework such restrictions appear to
be positive in terms of providing increased welfare for
government constituents. To be fair, unlike Marceau and
Smart [7], we include a labor-migration choice for a
worker, which acts as a constraint.
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K. A. COLLINS
276
Appendix A
In proving Prop osition 1, we let be a tax pol-
icy that maximizes social welfare. We have

,t











00 00
000
1
,
1
0
,,,
,,
1,
N
j
j
t
N
WtuFKL t
pFKL t
ut th


d.






(1a)
where we ha ve denoted by
  




01
,
0
,,
,
1,
N
j
j
t
Lt t
t
ttth




d
 




(2a)
the equilibrium level of effective labor input in the pub lic
sector under the tax policy
,t
. Next, let
be the
value of
that solves the following equation






0
,
0
d
(1, d
t
h
tth

 






As defined,
is the wage rate that must prevail to
elicit the same aggregate supply of effective labor as the
tax policy , given that wages are not taxed and

,t
that emigration is forbidden. We claim that









1
0
,
1
0
d
1,
N
t
N
uh
ut th

 
d





(3a)
To establish the claim, let

,
,t

, be
the wage rate that satisfies the following condition:








0
,
0
d
1,
t
h
tth

 
d
 





(4a)
and for all , let
,t


 



1
0
d
N
uh



(5a)
Differentiating the expression on the left-hand side of
Equation (4a), with respect to
, we obtain




2
0
d0
h
h



 
(6a)
Differentiating Equation (5a) with respect to
, we
find that
0

, where the right-hand side is ob-
tained from Equation (6a). Hence,
,
t

,
,
is non-increasing. Furthermore, when
,t

, we
have

,1 ,tt
 
 
 ,t
which implies





,
1
0
,
1,
t
N
t
utth


d.






Hence the claim is proved. Note that when 1
, we
have




0
0 00000
0
,,0 ,,0
,0 0.
F
uFKL KL
L




(7a)
Furthermore, according to profit maximization,




,,0 ,0
j
jjj
j
F
pKL
L


0,
N
(8a)
for 1,,j
. Also,
 




01
0
,0 ,0
,0 d
N
j
j
LL
h

 


(9a)
is the form assumed by the market-clearing condition for
labor under the tax policy
,0 .
Hence

01
,0 ,,0 ,,,0
N
LL L
 
 ,
and
,0

constitute the solution of the maxi-
mization problem for the case where
,0

. If
we let 1
be the wage rate at which

crosses the
forty-five degree line, then because

,0,0 ,


we must have
1
,0

. We have just shown that
when 1
, the socially optimal tax to policy dictates
that wages should not be taxed, but capital should be
taxed at rate
.
Copyright © 2013 SciRes. TEL
K. A. COLLINS 277
Next, consider the scenario . This scenario oc-
curs when 1






0
0 00000
0
, 1,0, 1,0
1, 00.
F
uFKL KL
L

(10a)
If inequality holds in Equation (10a), then the argu-
ment just presented for the case can be repeated
verbatim obtain the same conclusion: capital should be
taxed at rate , but wa ges sh o ul d n ot be taxed.
1
1
We now claim that if Equation (10a) is a strict ine-
quality, then the optimal tax rate on wages is positive.
Indeed, if it is not optimal to tax wag es, then capital will
be taxed at rate
W
and the optimal social welfare will
be given by . However, when (10a)
is a strict inequality, we must have

,0 1,0W

1, 00Wt,
i.e., social welfare can be raised by also taxing wages
after having taxed away all profits.
Appendix B
If , then obviously 1
1
, as claimed by the
proposition. We now show that if , then
1
1
.
To this end, suppose that the home government chooses
to tax only capital and at rate 0
. We have

,0

,0


,0
and that both the equilibrium wage rate
and the equilibrium level of the public good
0 provided rise with x
. That is, as
rises the
tax policy induces no brain drain and raises the welfare
of the workers as a group. The social welfare obtained
under this tax policy is given by
 








00
1
00 001
,0,0 ,0
,0,01,0.
N
j
j
N
j
j
Wux
ux ux









(11a)
Differentiating Equation (11a) with respect to
, we
obtain
 








00
1
00 001
,0 ,0 ,0
,0,0 1
,0 .
N
j
j
N
j
j
Wux
t
ux ux
 










(12a)
Note that if , then
1

,0 0W

 for all
. Using this result and the fact that
1








00 001
,0,0 1,00
N
j
j
ux ux









we can assert that if
, then



00
1,0,0 0
N
j
j
ux
 


 



.
Now the joint payoff for the home government and the
N industry lobbies under the tax policy is given
by
,0
 



00
1
,0,0 ,0
,0 .
1
N
j
j
ux
W

 
(13a)
For any
, we have




00
1
,0 ,0 ,0
,0 0,
1
N
j
j
ux
W
 


 






(14a)
which has been ob tained with the help of Equation (12 a)
and the fact that
,0 0W

 when 1

.
We have just shown that the joint payoff for the home
government, given that only capital is taxed, is strictly
decreasing in the interval . Hence, when
1


1
, the value of
, namely 1
, that solves the
maximization problem in Proposition 2 must be strictly
less than
. Proposition 2 is now proved.
Appendix C
There are two cases to consider in the proof of Proposi-
tion 3: 1
and 1
. When , we have 1
1
according to Proposition 2. Because ,
we must have
1




11
0
00 0000
0
1
,,0,,0
,0 0.
F
uFKL KL
L



(15a)
Note that Equation (15a) also implies that
1,0 0Wt
.
Therefore, we claim that



 


11
0
00
1
111
,0 ,0
1,0,0
N
j
j
j
x
ux t
Lt
 
 
0.

(16a)
Indeed, if this is not the case, then we must have
Copyright © 2013 SciRes. TEL
K. A. COLLINS
Copyright © 2013 SciRes. TEL
278
It follows directly from Equation (18a) that
11
,t




 





1
00 1
11
0
11
0
,0 1
,0,0 d
,0,0d 0.
N
j
j
ux
h
t
h

 
 







(17a)
,0, i.e., taxing capital at rate 1
and
wages at a low rate will yield a higher joint pay-
off for the home government and the N industry lobbies
than taxing only capital. Thus when the industry lobbies
are active, their lobbying activities will induce the home
government to tax wages at a positive rate.
0t
Because the sum of the expression on the left-hand
side of Equation (16a) and the expression in Equation
(17a) is equal to

1,0Wt

, we will be led to the
conclusion that


1,0 0Wt
  if Equation (16a)
does not hold, a conclusion that is opposite to the result


1,0 0Wt
 
, already established. Using Equation
(16a) and the result

1,0 0Wt
 
, we obtain
 


 


11
0
00
1
111
1
,0,0 ,0
1,0
,0 0.
1
N
j
j
j
x
ux
tt
Lt
W
t







1
,0
(18a)
Having considered the case , we next consider
the case 1
1
. The case arises when Equation
(14a), of Appendix B, holds. If Equation (14a) holds
with equality, then
1
1
and the preceding argument
can be repeated verbatim to show that the tax rate on
wages is positive. If Equation (14a) holds with strict
inequality, then
01, 0Wt
. The preceding ar-
gument can be repeated verbatim with 1
replaced by 1
to show that
1, 0t0,
 i.e.

1,1, 0tt t
for small values of t. The tax rate on wages is thus also
positive in this case. The proof of Proposition 3 is now
complete.