Modern Economy, 2012, 3, 608-616 Published Online September 2012 (
Tax Incentives, Competition and Welfare
Claudio Andre Gondim Nogueira
University of Fortaleza (UNIFOR), Fortaleza, Brazil
Received June 3, 2012; revised July 2, 2012; accepted July 10, 2012
The main objective of this paper is to analyze the impacts of the concession of tax incentives as a tool for entry promo-
tion in a developing region. The simple model and the numerical example presented indicate that the adoption of tax
incentives can cause very important effects. The productive structure could be heavily changed and production could
increase improving conditions to consumers that benefit from the larger output and lower prices. Furthermore, the need
for strategic action by the government in order to increase the chance of success of their development strategies is also
emphasized, especially if one considers that firms often behave strategically.
Keywords: Tax Incentives; Industrial Structure; Competition; Welfare
1. Introduction
Tax incentives are important policy instruments that can
be used in different contexts in order to facilitate the ach-
ievement of pre-established governmental goals. Accord-
ing to the modern economic literature, tax incentives have
been used to stimulate investments in physical and human
capital and in new products and technologies (through
research and development—R & D—activities), environ-
mental protection, export promotion, and the development
of key sectors of an economy, even though their adoption
in this case could end up generating unexpected and/or
undesirable results in some specific situations (see [1-4]).
Among many other possible cases, it is relevant to dis-
cuss one specific use of this type of policy instrument
that is becoming increasingly important. Tax incentives
have also been used in order to facilitate the attraction of
new firms to a country or region. This case is particularly
important if less-developed countries or regions are con-
sidered basically because, in general, tax incentives are
used in this context to compensate for considerable defi-
ciencies in the existing infrastructure. More specifically,
given the existing conditions, if tax incentives are not
conceded fewer would be the incentives that new firms
will have to enter that specific market.
In fact, many countries throughout the world use this
type of mechanism in order to attract foreign companies
to their markets, especially in specific areas of the coun-
try that are less developed. Among these countries one
can mention Brazil, Canada, US, Vietnam, Malta, Greece,
India, etc.
When tax incentives are used as instruments for entry
promotion, the diversity of approaches used is significant,
since several different tax-incentive schemes and contexts
can be analyzed. Hence, in this context, the point that
must be emphasized is that the free international move-
ment of goods and capital could mean free international
movement of tax bases. In other words, the desire to at-
tract new investments (plants) to a country or region
through the concession of tax incentives may lead to a
process of tax competition among these countries or re-
gions (see e.g. [5]).
It is also important to emphasize that such policy of
attraction of new firms through the concession of tax in-
centives often alters the structure of the existing industry
by affecting the profitability and the competitiveness of
the already established firms. Furthermore, the concession
of such incentives has considerable implications to wel-
fare that cannot be forgotten. This remark becomes even
more important as one considers that tax competition ex-
ists and affects the decisions of the agents involved.
Then, the most important lesson that can be obtained
from this discussion is that the impacts of this type of
policy in question, especially in a context where there is
tax competition among countries or regions, are a priori
indeterminate, i.e., different models could give different
explanations and predictions according to the assumptions
made and the methodology chosen.
Thus, the main objective of this paper is exactly to ana-
lyze the impacts of the concession of tax incentives as a
tool for entry promotion in a developing region, consid-
ering the effects over the existing productive structure as
well as over social welfare.
For that intent, it will be considered an entry-deterrence
framework where the incumbent firm can actually com-
pete with the entrant in another way rather than predatory
opyright © 2012 SciRes. ME
price competition, which could often lead to bad outcomes
both to the firms and to the region in consideration (see
The model presented here is in fact based on a simpli-
fied version of the Dixit-Spence framework discussed by
Fudenberg and Tirole [8], and Romp [9]. The use of this
framework is indeed appropriate in this context because
it enables the analysis of the decision process of the
companies involved and, at the same time, the analysis of
the behavior of the government as it attempts to maxi-
mize total welfare when it decides how much incentives
to concede.
The model considers the case where there are two com-
panies in the analysis, one that is already established in
the market in consideration (the incumbent firm) and the
other that is deciding whether or not it should enter in
that market (the entrant firm). More specifically, it is con-
templated the case where the incumbent firm can invest
in new organizational techniques and/or in new produc-
tive processes as it tries to reduce its costs of production
and to become more competitive.
Dixit [7] and Gabszewicz [11], for example, discuss
the importance of the investment in the entry-deterrence
framework. The main concern of these authors is cen-
tered on how the incumbent firm will define its optimal
productive capacity in a two-period game in order to de-
ter the entry of a new firm in the market. The approach
used in this paper is, however, closer to the examples pre-
sented by Fudenberg and Tirole [8] and Tirole [12] where
the investment made in fact reduces the marginal cost of
the firm (of the incumbent in this case) and allows it to
become more competitive.
Thus, this paper is divided as follows. In Section 2, the
basic model and fundamental assumptions will be pre-
sented. The basic model contemplates only the behavior
of the entrant and incumbent firms. The purpose of this
model is to analyze how the firms will react given the
amount of incentives conceded by the government. In Sec-
tion 3, the role of the government will be analyzed as the
decision of how much incentives to concede will become
endogenous as it tries to maximize a specific welfare func-
tion whose properties and characteristics will be presented
opportunely. Additionally, the importance of the existing
infrastructure will be emphasized and the model will be
adapted. Since the problem that the government faces is
somewhat difficult to solve then, in Section 4, a numeri-
cal example will be used in order to verify how the gov-
ernment should behave. Finally, concluding remarks and
references will be presented.
2. Basic Model and Assumptions
Consider that the government of a developing region is
trying to attract firms to the region. The government’s basic
intention is to stimulate the expansion of key sectors of
the local economy and to promote an overall increase in
the total output produced. The people of the region are
expected to benefit from this process as they are able to
increase their consumption levels and pay lower prices as
competition increases in the market.
Assume for simplicity that in a strategic sector of this
economy only one firm supplies a specific product and
there are no close substitutes. This firm will be referred
to as the incumbent firm (and denoted by I). The demand
for this product in question is given by
PQb Q, if
Q < b, or by
PQ , otherwise. The total cost incurred
by the incumbent to produce qI units of output is given by
Cq cq
where cI represents the cost to produce an additional unit
of the good and τ is a tax that the firm pays to the gov-
ernment for every unit produced (it is exogenously de-
termined). It is important to mention that cI depends both
on the technology and on the effectiveness of the organ-
izational techniques that the firm adopts. It is expected
that more advanced technologies and more efficient or-
ganizational techniques would yield lower values of cI.
Given the demand of the market, the incumbent firm
will earn profits given by
mmm m
bq qcq
where m indicates that firm I is a monopolist in this
market. Then, this firm will try to maximize its profits by
choosing the optimal amount that it should produce. If an
interior solution is assumed (i.e., if I), then
the first-order condition for profit maximization implies
that the optimal quantity that the incumbent will produce
is given by
 
qbc (3)
and the incumbent will earn profits of
 
The problem with this market structure is that in de-
veloping regions it is often the case that firms operate
with high marginal costs because there are practically no
incentives to change the ongoing situation. As a result,
according to expressions (3) and (4), the output produced
will be relatively small while the market price and the
monopolist profits would be somewhat high. This is in-
deed not a very good scenario because consumers cannot
consume as much as they would like to (prices are high)
and the government will have low tax revenues (because
output is small).
Then, the government will try to attract new firms to
this market hoping that by doing so competition will drive
output up and prices down. One mechanism that is often
Copyright © 2012 SciRes. ME
used to promote entry is the concession of tax incentives
to the entrant firm (denoted by E). This concession is usu-
ally temporary and after the period stipulated this firm will
decide if it is going to remain in the market or search for
new opportunities elsewhere.
Assuming that installation costs are sunk, with the con-
cession of incentives, the total cost of the entrant to pro-
duce qE units of output is given by
 
Cq E
c q
where δ represents the tax incentives (see [13,14]). As-
sume that
and that
. This condition im-
plies that there is a limit to the concession of such incen-
tives, often determined by law, and that it cannot exceed
the value of the tax charged.
If the entrant firm effectively enters the market, then it
should be the case that Q = qI + qE, and then it will have
profits equal to
π 
bq qqE E
c q
The problem is that the incumbent firm will not always
simply accept the entrance of another firm without a
proper reaction, i.e., the incumbent firm will try to deter
the entry. One possible way to compete with the entrant
would be to start a price war, which often leads to ineffi-
cient results (see [8,9]).
Hence, a credible entry deterrence strategy that the in-
cumbent could choose would be to invest in new tech-
nologies, new production processes, and new organizational
techniques, i.e., the incumbent could make an investment
) that would lower its marginal costs (see [8,12]). More
specifically, it should be the case tha
I where the
firm invests a determinate amount, say
(refer to this
process as the cost-reducing effect). Then, if this is the
case, then the incumbent will have profits equal to
bq qqc
  (7)
represents the investment made (with ).
Otherwise, i.e., when , it should be the case that
 
π 
bq qq
c q
Finally, if entry is effectively deterred, first assume
that the entrant could earn profits of in some other
region without the concession of incentives, or that
would be the guaranteed return that the firm would have
if it invested in financial markets the same amount of
money needed to build a new plant. And, in this case,
consider also that the incumbent firm could decide whether
to invest or not. It could perceive the investment as a way
to becoming more efficient and, consequently, more prof-
itable. Hence, in case the investment is not made, the
incumbent will have profits as shown by expression (4).
Otherwise, profits will be equal to
π14 .
 
 
Thus, given all these fundamental assumptions and
expressions, then the best way to analyze this problem in
detail would be to put it in an extensive game form where
all possible outcomes could be investigated.
The basic game in question could then be explained as
follows. At t = 0 (t denotes the time period in question),
the government will offer tax incentives equal to δ to a
firm (the entrant) with marginal cost given by cE (since it
is considered the full information case, it is implicitly
assumed that knowing the true cost of the entrant is cost-
less, and that this information is freely spread throughout
the economy, because the government cannot keep secrets).
Since the market demand is constant over time and pro-
duction in previous periods could be considered public
information, one could easily infer the cost of the in-
cumbent, by rearranging expression (3). Then, at t = 1,
the entrant will either enter the market or not. Represent
these strategies by e and , respectively. Finally, at t =
2, if the entry is confirmed, then both firms will compete
as in the Cournot model of duopoly (see [8,9,15]) as the
incumbent firm will either accommodate (a) or fight (f)
as described before. And, if the entry is not confirmed,
the incumbent firm will remain the monopolist in that
market and will decide whether or not to make the in-
vestment described before.
In the case that
ea is the outcome of the game,
even if the incumbent accommodates the entrant will not
have enough incentives to enter the market. This case
could be possible basically if δ is not large enough and/or
cE is larger than cI. And, in the case that the outcome is
, the incumbent’s strategy to deter the entry will be
effective (the factors just mentioned could also be impor-
tant in this case). In both cases the entrant will not be
able to earn profits greater than and, therefore, will
have no incentives to enter the market.
But, when the entrant effectively enters the market, then
if the incumbent firm accommodates, i.e., when the out-
come of the game is
, they will, respectively, receive
profits (derived from profit maximizing conditions and
assuming interior solutions) equal to
 
π19 22
qbcc (10)
 
π19 2
qbcc (11)
But, if the incumbent fights, the outcome of the game
will be
and the payoffs will be
π19 22
qbcc (12)
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 
It is important to notice that, in both cases, the profits
of the incumbent are decreased because of the incentives
received by the entrant that is clearly beneficiated. Fur-
thermore, profits will decrease the higher are their own
costs and increase the higher are the other’s costs.
The fundamental point of the analysis is that the gov-
ernment would like to induce the outcomes where the
entrant enters the market while the incumbent will fight
or not (it wants to avoid the case that entry is effectively
deterred). Specifically, since there is full information, the
government could solve the game by backward induction
and then offer at t = 0 the amount of incentives necessary
to induce one of the desired outcomes, provided that
At this point it is difficult to clearly specify which of
the desired outcomes (
) will be chosen
by the government because this choice depends on wel-
fare considerations that will only be discussed in detail in
Section 3. If this decision depended solely on efficiency
criteria, however, it would be reasonable to consider that
the government would be more inclined to induce the out-
come because entry would not be deterred whereas
the incumbent firm would improve its levels of produc-
tive efficiency as it reduces its marginal costs.
Hence, which are the conditions that will guarantee
that one of the desired outcomes will be a sub-game per-
fect Nash equilibrium (SPNE) of this game? Before an-
swering this fundamental question, the decision-making
process of both the incumbent and the entrant should be
analyzed according to parameters’ values. Note that since
the equilibrium of this game will be determined by back-
ward induction, then it is important to fully analyze the
behavior of the incumbent firm first and, afterwards, ana-
lyze the behavior of the entrant given the expected in-
cumbent’s strategy.
Proposition 1. Suppose there is entry. Then, given the
value of δ, the incumbent will (a) choose to fight if and
only if , and (b) choose to accommodate if
and only if , where
bcc c
 
Proof. If there is entry, then the incumbent firm will
decide to fight if an only if
I. Hence, according
to expressions (11) and (13), and since by assumption
when the incumbent fights, this condition would
imply that
 
bcc c
 
And, thus, the incumbent will choose to accommodate
if and only if
, which would imply that .
This proposition, as in Fudenberg and Tirole [8], states
that fight should be a dominant strategy for the incum-
bent firm if and only if the level of investment necessary
to make it more competitive is not sufficiently high. More
specifically, in this case, given the value of the incentives
conceded by the government, even though the incumbent
will not be capable of deterring the entry it could pay off
to fight anyway because the investment made could gen-
erate higher profits to the incumbent than if it had just
accommodated the entry. However, if the necessary level
of investment is too high, then it could drive profits down.
At this point a very important question would be the
following: if the government offered very high tax incen-
tives then how would this affect the reaction by the in-
cumbent firm? One could think a priori that higher levels
of incentives would automatically lead to the reaction by
the incumbent firm basically because high incentives
would negatively affect its reaction function forcing it to
produce less. But, should this be necessarily true for all
levels of δ? As expression (14) indicates as δ increases A
will decrease. Thus, in accordance with Proposition 1, by
offering high levels of incentives the government could
actually discourage the reaction by the incumbent firm.
Thus, in general, one could establish a range of values
of δ in which the incumbent firm will be stimulated to
react (as long as the condition is satisfied).
In this range, the incumbent firm will choose to fight the
entry until δ reaches a threshold, say . More specifi-
cally, one should have that
ˆ94 
bcc ccc
And, if
, then it is possible to define another
range of values for δ where the incumbent firm will de-
cide to accommodate the entry (i.e., Proposition 1a can
no longer be satisfied). More specifically, this would hap-
pen when ˆ
Notice that this discussion above is about possible sce-
narios (consider the case where these situations described
are simultaneously possible as the benchmark case). Cer-
tainly, more situations may emerge according to parame-
ter values, but the benchmark case actually gives a good
interpretation on how the incumbent firm should behave
in general given the level of incentives conceded by the
government. But, what if entry is not confirmed?
Proposition 2. Suppose entry is not confirmed. Then,
the incumbent will a) choose to invest (fight) if and only
, and b) choose not to invest (accommodate)
if and only if , where
14 22
  
bc ccc
Proof. If entry is not confirmed, then the incumbent
firm will decide to fight if and only if I. Hence,
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© 2012
according to expressions (9) and (4), this condition would
imply that
0142 2
bc c
 
And, the incumbent will choose not to invest if and only
The interpretation of this proposition is very similar to
the one given for Proposition 1. More specifically, as a
monopolist, the incumbent will invest if and only if the
level of investment necessary to make it more competi-
tive is not sufficiently high so that it could become more
profitable. But, differently from Proposition 1, this deci-
sion is completely independent from the level of incen-
tives granted by the government. Hence, for simplicity,
consider that in the benchmark case the investment by
the monopoly is always feasible if entry is not confirmed.
, which would imply that . (Q.E.D.)
Thus, after analyzing how the incumbent firm would
react, then it is possible to establish the conditions that will
guarantee that the entry will be effectively effectuated.
More specifically, as the government offers the amount
of tax incentives, the entrant will be able to anticipate which
one will be the strategy chosen by the incumbent firm and
then it would be able to decide if entry is the best option.
Proposition 3. Given
, if ππ
I then the
entrant will effectively enter the market if and only if
. And, if ππ
I then the entrant will
effectively enter the market if and only if
max 0,
123 π
bc c
123 π
Proof. By assumption
. Then, if ππ
in accordance with Proposition 1, the entrant will know
that fight would be a dominant strategy for the incumbent
firm and then the entrant will effectively enter the market
if and only if , which implies that
max0,1 23π
And, if
I, to accommodate would be a weakly
dominant strategy for the incumbent firm and then it will
effectively enter the market if and only if , which
would imply that
max0,1 23π
only enter if the incentives are high enough to guarantee
profits greater than even when the incumbent firm
chooses to fight.
At this point, since
I, one should notice that cc
. Furthermore, in accordance with Proposition 3,
one should consider that the condition given by expres-
sion (17) will be binding only when
. Similarly,
the condition given by expression (18) will be binding
when ˆ
From this proposition one is able to conclude that only
for high enough levels of incentives the entrant will ef-
fectively enter the market. In other words, the firm will
Thus, given parameter values and considering the benc-
hmark case discussed before, the infimum of the possible
values of δ that would stimulate the entry of the firm (
could also be inferred. More precisely, one should have that
(see the Equation (19) below).
It is also important to notice that in this benchmark
case three equilibria for this game are possible. More
specifically, if 0
, the incumbent firm will choose
to fight, but the entrant will have no interest in entering
the market because the level of incentives conceded is
not high enough to grant it profits higher than (the entry
will be deterred). Therefore, the sub-game perfect Nash
equilibrium of this game will be given by in this
case. If
, then the entrant will have incentives
to enter the market in despite the fact that the incumbent
would still try to deter the entry. Hence, the SPNE of the
game will be given by
,ef in this case. And, finally,
if ˆ
, the entry will not be deterred nor will the
incumbent firm have incentives to invest in new tech-
nologies, new productive processes, and more efficient
organizational techniques, as explained before. Thus, in this
case, the SPNE of this game would be given by
,ea .
Certainly, according to parameter values, other possi-
ble scenarios could be analyzed. But, the benchmark case
discussed above already provides a good intuition of how
the model works when the decisions of both the incum-
bent and the entrant are considered given the amount of
tax incentives conceded by the government.
The next logical step is, therefore, to consider how the
government should choose the optimal level of incentives
that it would concede to the entrant. According to this
analysis above, the government is able to induce the out-
come of the game as it sets the value of δ. But, at this
point, it is not possible to specify exactly what the value
of δ should be. As mentioned before, the choice of δ and,
therefore, the outcome of the game will depend on wel-
fare implications and/or on other factors. And, this is ex-
actly the analysis that will be made in the following section.
3. Welfare Analysis
In general, the basic intent of the government when it
offers tax incentives is to attract firms to the region in
0,. . ππππ ππππ
Infs tiforif
consideration and increase total output produced. Overall
conditions to society are then supposed to improve as
lower prices would be charged for the good in question
as competition increases (due to the entry of a new firm
in the market).
As already mentioned, when the government pursues
this type of policy, in accordance to the model presented
before, two types of outcomes would be desired a priori,
,ea and
,ef . Additionally, it was shown that the
government is able to induce one of these outcomes by
choosing the amount of tax incentives that should be con-
ceded. Then, which one should the government choose?
Certainly this choice should depend on efficiency criteria,
i.e., it should depend on how efficiently firms produce
the good in consideration. In this sense, probably
WCS T
would be the best outcome since the incumbent firm would
be induced to improve its production processes and or-
ganizational techniques even though it is not able to deter
the entry. But, is this outcome really the best one to soci-
ety? That is why welfare implications of such policy should
also be reckoned.
One interesting and more comprehensive way to think
about the effects on welfare is to consider the impacts of
the concession of tax incentives on three important vari-
ables: consumer surplus (CS), total profit () and tax
revenues (T). The consumer surplus and total profits would
provide measures of how consumers and producers are
respectively affected by this type of policy, while tax
revenues will be important to ascertain whether or not
this policy represents a burden to society as the govern-
ment may have its ability to provide public goods com-
promised by the effort to attract new firms to the region
or country in consideration. The results obtained should
then be compared to the situation where only one firm is
in the market (as it was initially). Then the government
will be able to assess if the policy adopted was really
effective in improving overall conditions to society.
The proposed format for the welfare function in all
possible cases is given by
where , m represents the case where the
incumbent firm is the sole producer of the good in that
market but does not invest, while m' is the case where the
investment is made. a represents the case where there is
entry but the incumbent decides to accommodate, and,
finally, f represents the case where there is entry and the
incumbent decides to fight.
There could be, however, differences on the definition
of each term of the welfare function according to the case
considered. The detailed discussion about each of these
terms follows.
First, since the demand of this market is given by
, if , and , otherwise, then,
in accordance with Gibbons [15], the consumer surplus
for each case considered could then be defined as
PQ b Qb
CSpdQ pQ
As expression (21) shows, the consumer surplus in-
creases monotonically with the total output produced.
Therefore, the outcome that would generate the highest
level of output would also yield the highest consumer
surplus. In this sense, the government has incentives to
induce the outcome that is more efficient in terms of pro-
duction. And, these incentives tend to be even greater if
one considers that profits are also intrinsically related to
the amount of output produced (at least when the Cour-
not model of duopoly is considered).
Then, the total profit function could be defined for the
monopoly cases as
  (22)
when M = m, and
. And, for the other cases, one should have
 
jj jj
  (23)
= 0 when j = a, and where
when j
= f.
Finally, the tax revenue function for the monopoly
case is given by
where as for the other cases on should have that
 
 
One could notice that the tax revenues, in both cases,
is multiplied by an additional term,
0, with
This parameter, λ, is somewhat related to what is usually
called in public finance theory the shadow cost of public
funds. According to Laffont and Tirole [16] and Atkinson
and Stiglitz [17], this concept shows that for each dollar
that the government raises society actually pays
dollars, i.e. , it shows that society could perceive that the
real opportunity cost of public funds could be in fact
greater than its monetary cost. The use of this concept is
appropriate in situations as the one described by Laffont
and Tirole [16] where the government uses public funds
to finance a firm’s deficit. In this case, it is straightfor-
ward to verify that the government is taxing consumers
and giving up valuable resources that could have been
used to finance the provision of public goods and, there-
fore, the cost to society may be in fact greater than the
monetary cost, especially in less developed countries or
regions where the basic infrastructure available (basic
Copyright © 2012 SciRes. ME
education, health care, etc.) is in many cases extremely
In the present study, however, this is not necessarily
the case. In fact, in developing countries or regions, when
the government concedes tax incentives it gives up part
of the potential tax revenues had the new firm entered the
market on its own in exchange for increments on consumer
and producer surplus, but tax revenues could still be greater
than in the monopoly case. The important point is that λ
should represent that every dollar the government receives
may value much more to society than the monetary value
that the firms pay according to the infrastructure avail-
able in the country or region considered, because the poorer
the country or region is, the more important should be con-
sidered the resources obtained by the government through
Hence, from now on λ should be referred to as the
shadow value of public funds. And, more specifically, the
case where λ = 0 represents a country or region whose
basic infrastructure is already satisfactory. But, in cases
where λ > 0, the greater this term is the more deficient is
the infrastructure and, therefore, the more valuable are
the public funds obtained.
Thus, after these important comments, it is possible to
re-write expression (20) according to the cases contem-
plated by the model. More specifically, for the monopoly
case one should have that
32 1
  (26)
and, for the other two cases, one should have that
 
 
 
 
At this point it is possible to properly address the ques-
tion posed on the beginning of this section: which out-
come of the game should the government induce? Before
that, however, it would be of the utmost importance to
further investigate the relationship between social wel-
fare and the existing infrastructure. Without any doubts,
infrastructure can become an even more decisive variable
in the model, especially when one considers that a firm´s
decision to open a new factory in a determinate region
depends not only on the tax incentives received, but also
on other factors. And, these other factors can be impor-
tant because they probably affect the costs of production
of both firms (see [18,19]).
In Section 2 it was mentioned that c should reflect how
efficiently the firm is able to produce the good according
to the technology and the organizational techniques that
the firm adopts. But, in reality, one should also consider
how well the firm uses these factors according to the char-
acteristics of the region that it is located. Hence, other
factors that may affect the cost of the firms are, for ex-
ample, the availability of basic infrastructure (electricity,
water, highways, etc.), the educational level of the work-
force available, the proximity to other firms (e.g. suppli-
ers), the proximity to consumers, transportation costs, the
firm experience in that specific market, etc. For simplic-
ity, call this set of factors infrastructure.
Then, it is reasonable to assume that hhh
, with
,hIE, where h
is the cost associated with the
technology and organizational techniques in use by firm
h and ωh is a parameter
h that captures how effi-
ciently the firm is able to use its technology according to
the specific regional characteristics or according to the
infrastructure available. Therefore, from now on, ch will
be referred as the effective marginal cost of firm h.
As discussed previously, the impacts of the infrastruc-
ture on tax revenues and welfare is measured by the shadow
value of public funds, λ. Hence, in order to unify these
two approaches in a simple way, one must make the fol-
lowing relevant assumptions:
Fundamental Assumption 1. There is a positive and sig-
nificant correlation between λ and ωh, with
Fundamental Assumption 2. The correlation between λ
and ωh, could be represented by a linear equation like
 ,0, with
hh .
Given these assumptions, then the model presented so
far can be considered as a particular case of this more gen-
eral model (where costs are related to the existing infra-
structure), when h and
Thus, considering these modifications, the answer to
the fundamental question of this section will depend ba-
sically on which case would yield a higher level of total
welfare. More specifically, the government will try to
choose the outcome that locally maximizes welfare ac-
cording to parameter values. It is also important to notice
that the government cannot affect the level of welfare in
the monopoly case, since none of the parameters involved
can be directly changed by the government. But, it could
certainly affect the level of total welfare on the other two
cases as it determines the amount of tax incentives that
will be granted to the entrant. Therefore, in each of these
cases, the government will try to maximize Wj by choos-
ing the optimal level of δ.
The optimization problem that the government faces may
assume different forms according to the different possible
outcomes. More specifically, when incumbent firm fights
the entry, this maximization problem should be written as
. .0,0,.
ff ff
ff E
Max Wqqqq
qq q
stqq and
 
 
And, when it accommodates the entry, the maximization
Copyright © 2012 SciRes. ME
problem is given by
aa aa
aa a
. .0,0,
ax Wq
st qqand
 qq q
qq q
 
 
The results should then be compared to each other and
to WM, in order to verify which one would yield the high-
est level of welfare. With this information, then the gov-
ernment will be able to ascertain if this type of policy is
justifiable (i.e., if
M) and which outcome should
then be induced according to the value of δ.
The drawback of this type of optimization problem that
involves a series of nonlinear constraints is that it is vir-
tually impossible to find an algebraic solution for δ in
terms of the other parameters of the model. Therefore, a
numerical example will be used to illustrate how the pro-
posed model works. In this example all the parameters of
the model will be fixed, and variations will be attributed
to λ, i.e., it will be considered different levels of infra-
structure (more specifically, the values chosen for λ were
0.5, 1.0, e 2.0). Then, the optimal value of δ will be in-
ferred in each case analyzed.
4. A Numerical Example
Assume that the demand of this market is given by
, if , and , otherwise,
and that τ = 1,
12 Q 12Q
, , κE = κI = 1.50,
, and .
Assume also that ωI = 0.94 + 0.06 λ and that ωE = 0.98
+ 0.08 λ. These expressions show how the firms’ costs are
affected by the existing infrastructure. One can notice that
the entrant is more affected by the conditions available
, and since
(The parameter νh
measures the change in ωh due to variations in the avail-
able infrastructure). In other words, for the same value of
λ, the effective marginal cost of the entrant will be greater
than the incumbent’s. The justification for such distinc-
tion is based on the differences of experience that these
firms have. That is, since the incumbent firm is already
established in that market, then it is reasonable to assume
that it can make better use of the regional characteristics
of the country or region in question since it is already
adapted to the existing conditions.
Then, it is possible to perform calculations considering
the impacts of the infrastructure on costs. Table 1, below,
shows the results obtained.
As Table 1 shows, the case study presents a series of
relevant insights. First, given parameter values, it is strai-
ghtforward that the welfare levels attained with the con-
cession of incentives are always greater than the levels
when entry is deterred (i.e.,
Table 1. Numerical example—Results of the calculations.
= 0.50
= 1.00
= 2.00
1.46 1.50 1.59
0.97 1.00 1.06
1.53 1.59 1.71
δE 0.28 0.33 0.42
0.37 0.64 1.14
δ* 0.29 0.34 0.43
51.46 53.67 57.64
43.15 45.40 49.86
Some other aspects, however, provide more interesting
discussions. First of all, since different values of λ yield
changes on ωh and ch, then for each case one should ex-
pect not only different values of δ*, but also of δE and ˆ
i.e., each firm’s decision would change according to the
value of λ.
More specifically, one can notice for instance that δE
increases monotonically with λ, which is indeed a very
intuitive result. In fact, this pattern of δE implies that
when the infrastructure available is not satisfactory (i.e.,
when λ is large), the government would only be able to
attract another firm to the market if it offers a sufficiently
high level of incentives. This explanation is pretty rea-
sonable if one considers that, in practice, the entrant firm
actually bases its decision to enter or not on its potential
profits given a bundle of factors (tax incentives and in-
frastructure in this case) offered by a country or region.
Thus, in this sense, it is reasonable to consider that the
government will try to compensate a poor infrastructure
with a higher level of incentives.
The incumbent’s decision to fight or to accommodate
the entry also depends on the existing infrastructure, as
mentioned before. In particular, it seems that the worse
the existing infrastructure becomes, the more incentives
the incumbent firm will have to fight the entry in each
case (i.e., ˆ
increases fast as λ changes). When λ = 2,
for example, the incumbent firm will decide to fight the
entry whenever 0 < δ < ˆ
= 1.14. Notice that the value
of ˆ
is reasonably greater than
, which implies that
this strategy in question will be chosen for any level of
incentives that the government decides to concede in this
Finally, in each case the government should evaluate
the optimal level of incentives to grant according to the
expected reactions of the firms. More specifically, as λ
increases, since the incumbent will have more incentives
to fight the entry, then the government should actually
offer the minimum amount of incentives possible in or-
der to maximize welfare. And, in these cases, the out-
come of the game will be given by
,ef .
5. Concluding Remarks
WW in all cases). Hence,
this policy is justifiable. The simple model and numerical example presented in
Copyright © 2012 SciRes. ME
Copyright © 2012 SciRes. ME
this paper indicated that the adoption of tax incentives as
development policy tools can cause very important ef-
fects in a developing region. The productive structure could
be heavily changed and production could increase im-
proving conditions to consumers that benefit from the
larger output and lower prices. Furthermore, the need for
strategic action by the government in order to increase
the chance of success of their development strategies is
also emphasized, especially if one considers that firms
often behave that way.
Probably, the key for the success of this type of policy
in the long run lies on the association of tax incentives
schemes with the expansion and improvement of the ex-
isting infrastructure, especially when it is considered the
case where the new firms attracted to the market are small.
Certainly, if long-run objectives are considered, it in-
creases even further the need for strategic action by the
government. And, the model presented gives good in-
sights on how the government should behave.
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