Discussion Paper No. 717

MULTINATIONALS, TAX HOLIDAYS,
AND TECHNOLOGY TRANSFER

Kaz Miyagiwa
andYuka Ohno

July 2008

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Multinationals, tax holidays, and technology transfer

Kaz Miyagiwa and Yuka Ohno

Abstract
Host country governments often grant investment incentives to foreign firms locating intheir territories. We show that such preferential treatment of foreign firms can facilitatetransfer of foreign technology, induce entry by the local firm, and increase host country
welfare. However, this pro-competitive result occurs when preferential treatment isgranted for a limited time; i.e., it takes the form of tax holidays, and is absent underpermanent tax concessions.
JEL code: F1, O3
Keywords: Tax holidays, Free trade zones, Foreign direct investment, Technology transfer,
Multinational firms
Author Affiliations: Miyagiwa: Institute of Social and Economic Research, Osaka University,and Department of Economics, Emory University; Ohno: Deloitte Tax LLP
Acknowledgment: This paper was presented at the 2008 Japanese Economic Association
Conference, and at Ritsumei-kan and Waseda Universities. We thank participants for theirhelpful comments. We alone are responsible for errors.
Corresponding Author: Kaz Miyagiwa, The Institute of Social and Economic Research,
Osaka University, 6-1 Mihogaoka, Ibaraki, Osaka 567-4700, Japan. E-mail:kmiyagiwa@gmail.com

1. Introduction
Governments often grant investment incentives to foreign firms locating in theirterritories. A typical incentive package includes preferential tax treatment, lower duties onimported raw materials and components, subsidized labor training costs and financial loans.
Such investment incentives may be needed to attract limited supplies of foreign capital.
However, there is the concern that preferential treatment of foreign multinationals puts local
firms at an unfair disadvantage and is therefore anticompetitive. The objective of this paper is
to show that preferential treatment of multinationals can be pro-competitive and welfareimproving for the host country. However, to induce this pro-competitive and welfare-improving
effect, investment incentives must be granted only for limited periods; i.e., they must take theform of “tax holidays.”
We demonstrate such a pro-competitive and welfare effect by extending the classicalmodel of entry deterrence (Dixit 1979, 1980) to an infinite-horizon setting. The game begins
when the foreign firm opens a subsidiary in the home country and takes measures aimed atpreventing unintended transfer of the technology it brings. Such preventive measures may
include keeping key production steps privy only to the firms’ top management. Firms are also
known to resort to what is called “masquing,” that is, altering products and production methods
so as to make reverse engineering more difficult or even imbedding physical security systems
hidden in the product so as to facilitate conviction of technology thieves, should thievery occur(Taylor 1993). Firms may eve invest in legal procedures, working with the host country
governments, to prosecute imitators and infringers of firms’ intellectual property rights. The

2
immediate consequence of such anti-theft investment is to make it harder for the entrant to gain
access to the foreign technology needed for entry.
Once the foreign firm commences production, the home firm tries to imitate the foreign
firm’s technology (or product) and enter. This sequence of moves is natural in the real world,
where foreign technology is often indispensable for entry by local entrepreneurs; see, e.g.,
Maskus (2000). Once the home firm enters, the two firms compete in prices or quantities overtime. Without entry, the foreign firm remains a monopoly.
The analysis of this paper centers on the foreign firm’s decision whether to deter or
accommodate entry by the home firm. The foreign firm naturally dislikes competition. But,
since entry deterrence is costly, the foreign firm would be willing to accommodate small-scale
or inoffensive entry rather than pursue the costly entry-deterring strategy. The home firm would
also prefer to delay entry rather than have entry denied. This is in the spirit of judo economics
as explicated in Gelman and Salop (1983). The problem is, unlike the entrant featured in theGelman-Salop analysis, the home firm here cannot commit to delayed entry.
It is in such circumstances that tax holiday programs work as a commitment device forthe home firm. The intuition is simple. Preferential tax treatment makes the foreign firm a“tougher” competitor temporarily, making immediate entry less profitable, and prompting thehome firm to postpone entry until the foreign firm loses its tax advantage. Thus, tax holiday
programs serve as a puppy-dog ploy (Fudenberg and Tirole, 1984), and facilitate entry by thehome firm into the new market that would otherwise be monopolized by the foreign firm.
Now, it is immediate that this entry-promoting effect is absent under permanent tax
concessions. Under permanent tax concessions, the foreign firm’s competitiveness remains

3
constant over time, so there is no incentive for the home firm to delay entry. But, if entry is notdelayed, the foreign firm has every incentive to ensure that entry does not occur. Furthermore,because subsidies benefit the foreign firm more when it is a monopolist than when it is aduopolist, the foreign firm has more of an incentive to defend its monopoly status. For these
two reasons, permanent tax concessions prove indeed to be anti-competitive as is generally
believed.
Today, most of foreign investment incentives are dispensed to foreign firms locating infree-trade zones (FTZs), and indeed take the form of tax holidays. For example, Costa Rica
offers 100-percent tax exemption for 8 years and 50% exemption for another 4 years. Israel
provides foreign multinationals with the choice between 10-year tax exemption and upfront
cash subsidy. In Morocco, the incentives packages come with 5 to 10 year tax concessions,depending on which region of the country foreign firms invest. Ghana and Malaysia, too,
provide tax exemption and duty-free status on manufacturing machinery during the first 10
years of firm’s operations. China grants 5-year tax breaks followed by another 5 years with
50% tax liability.
FTZs made their first appearances during the first decade of the 20th century but theirimpressive growth began during the 1970s and 1980s. According to World Bank reports, there
are about 3,000 FTZs in 120 countries, as of 2007. While countries creating FTZs expressedhopes that the presence of foreign firms in their territories would increase employment
opportunities and boost the economy’s productivity through technology transfer, the formal
analysis of FTZs has primarily focused on the welfare impact of tax exemption in the static
general competitive equilibrium framework; see e.g., Hamada (1974), Miyagiwa (1986),

4Young (1987), and Facchini and Willmann (1999).1 This paper, to the best of our knowledge, isthe first to extend the literature to the case of imperfect competition and to examine the effect oftax exemption on technology transfer in a dynamic setting.
There also exists work explaining tax holidays in terms of the host country
governments’ inability to commit to long-term tax policies; Bond and Samuelson (1986) andDoyle and van Wijnbergen (1994). However, most of FTZs are operated by the nongovernment enterprises sanctioned by the host country governments, with the consequence thatFTZ authorities and firms are legally bound to honor the terms of contracts, including tax rates,
they have signed at the time of the opening of subsidiaries. Thus, there seems little concern oftime inconsistency featured in those studies.
The remainder of the paper is organized in 6 sections. The next section sets up themodel. Section 3 solves the model under the assumption that the foreign firm receives subsidies
at a constant rate over time. Section 4 applies the model to show that, if it deters entry at zerosubsidies, the foreign firm has a greater incentive to deter entry under a permanent subsidy
program. Section 5 presents our main result, that is, the pro-competitive effect of temporary
subsidy programs. Section 6 discusses the welfare impact of temporary subsidy programs.
Section 7 extends the model to the case of eventual entry, that is, when entry cannot be deterredforever, and shows that our main result generally carries over to the case of eventual entry.
Section 8 summarizes our findings and makes suggestions for future research.

2. The model setup
1

Young and Miyagiwa (1987), Miyagiwa (1991), Chaudhiri and Adhikari (1993), and Gupta (2000) study the effectof FTZs on unemployment.

5
The model involves two firms, one foreign and one home, which interact over time.
The foreign firm is incumbent while the home firm is a potential entrant, needing the foreign
firm’s technology to enter. Time runs continuously from zero to infinity and is indexed by t. It
is useful to think of the game in three stages. The first stage occurs at t = 0, at which only theforeign firm moves. It builds a factory in the home country, and chooses a level of investment,
K, aimed at preventing unintended transfer of its technology to the home firm, as describedearlier. The one-time cost of this investment is denoted by C(K), which we assume is convex
and differentiable, with C’(K) > 0 and C”(K) > 0 (primes denote differentiation).
The second stage has the home firm deciding whether to imitate the foreign firm’s
technology at a one-time cost of f(K). Assume f’(K) > 0; that is, the more the foreign firm
invested, the higher the cost of imitation. As for the timing of entry, there is no loss ofgenerality in assuming that imitation is immediate so assume that the home firm can enter at
any time t ∈ (0, ∞).
The third stage begins only if the home firm enters. Then, the two firms compete inquantities or prices. If there is no entry, the foreign firm remains a monopoly. The environmentis stationary; the market demands and factor prices do not change over time.

3. Equilibrium
We first solve the above model under the assumption that subsidies are given at aconstant rate s per unit of output over time. Seeking a subgame-perfect equilibrium, we beign
with the subgame that starts when the home firm enters. We then move back to the home firm’s

6
entry decision problem, and finally we determine the foreign firm’s optimal investment
strategy.
In solving the post-entry game, we seek Markov-perfect equilibrium as a solution
concept. Since flow profits do not depend explicitly on time due to the stationary environment,
the Markov-perfect equilibrium profits are just the Nash equilibrium duopoly profits of a oneshot game. Write these flow profits as Π(s) and π(s) for the foreign and the home firm,
respectively. Denote the foreign firm’s flow monopoly profit by M(s). These profit functions
are assumed to be continuously differentiable and satisfy the following properties.

Assumption 1: M’(s) > Π’(s) > 0 > π’(s).

The first inequality states that the benefit of a subsidy is greater when the foreign firm is amonopolist than when it is a duopolist. This assumption is rationalized by the intuition that amonopolist produces a greater quantity of output than a duopolist and hence must benefit morefrom a per-unit-of-output subsidy, and is satisfied in the standard Cournot and (differentiatedgoods) Bertrand models. It is also the standard assumption in the literature investigating similar
issues; e.g., Besley and Suzumura (1992), McAfee and Schwartz (1994) and Miyagiwa andOhno (1995). The last inequality follows because a lower marginal cost for the foreign firm
harms the competitiveness of the home firm.
Having described the post-entry subgame equilibrium, we turn to the second stage: thehome firm’s entry decision problem. If the home firm enters at time t ≥ 0, its discounted total

7
profit is:e- rt[π(s)/r – f(K)],
where r is the (common) instantaneous rate of interest, and f(K) is given in the first stage of thegame. If the term in brackets, π(s) – rf(K), is positive, the home firm enters at t = 0. If it is nonpositive the home firm never enters.2 We assume that there is K(s) at which the home firm is
indifferent between the two options.

Assumption 2: For given s, there is K(s) such that π(s) = rf(K(s)).

By Assumption 1, an increase in s decreases the minimum level of K needed to prevent entry,i.e., dK(s)/ds < 0. Thus, the home firm’s optimal strategies can be restated as follows:(i) Enter at t = 0, if π(s) – rf(K) > 0 or K < K(s);(ii) Never enter, if π(s) – rf(K) ≤ 0 or K ≥ K(s).
Finally, we turn to the foreign firm’s investment strategy. If the foreign firm remains amonopoly, its net total profit is:∞⌠ - rz⎮ e M(s)dz − C(K) = M(s)/r − C(K).
⌡0

Since this profit is decreasing in K, the foreign firm, if unthreatened, would optimally set K = 0.
In this analysis, however, assume f(0) is sufficiently low so that the home firm enters when the2

We adopt the convention that there is no entry unless there is strictly positive profit, no matter small.

8
foreign firm chooses K = 0, i.e., π(s) – rf(0) > 0 for relevant values of s. Thus, entry deterrence
requires investing at least K(s) > 0. Since an increase in K reduces the net profit, however, theforeign firm never invests more than K(s). Thus, the maximum profit from deterring entry
equalsM(s)/r − C[K(s)].
On the other hand, any investment less than K(s) induces entry at t = 0, yielding the net profit:∞⌠ - rz⎮ e Π(s)dz − C(K) = Π(s)/r − C(K).
⌡0

When entry is inevitable, however, the foreign firm optimally sets K = 0, which results in the
total maximum profit Π(s)/r.
Let Ω(s) be the difference in profit to the foreign firm between deterring andaccommodating entry:(1)Ω(s) ≡ M(s)/r − C(K(s)) − Π(s)/r

The foreign firm chooses to deter entry if and only if Ω(s) ≥ 0. This completes the descriptionof the basic model.
Evaluating the above model at s = 0 yields the equilibrium outcome without subsidies.
We assume that without subsidies the foreign firm prefers to deter entry.

Assumption 3: Without subsidies the foreign firm deters entry; i.e.,9Ω(0) = M(0)/r − C(K(0)) − Π(0)/r > 0.

4. Permanent subsidies
We now apply the above model to analyze the effect of a permanent subsidy program.
We want to find out the sign of Ω(s), given that Ω(0) > 0 (Assumption 3). Differentiate (1)yields:(2)

Ω’(s) = [M’(s) − Π’(s)]/r - K’(s)C’(K(s)).

The first term on the right-hand side is positive by Assumption 1. The second term is negative
since K’(s) < 0 and C’(K) > 0. Therefore, Ω’(s) > 0. It follows that Ω(s) > Ω(0) > 0 for s > 0.

Proposition 1: A permanent subsidy program increases the foreign firm’s incentives to deter
entry, thereby preventing technology transfer.

The intuition is straightforward. A permanent subsidy program decreases the post-entry profit
to the home firm, making it easier for the foreign firm to deter entry, as indicated by the second
term in (2). In addition, the foreign firm benefits more from subsidies as a monopoly than aduopolist, as indicated by the first term of (2). Thus, a permanent subsidy gives the foreign firm
more of an incentive to deter entry. Even if the foreign firm is willing to accommodate entry
without subsidies, a permanent program with sufficiently high subsidies may induce the foreign
firm to switch to entry deterrence. It is obvious that such a policy is deleterious to the homecountry.

10

5. Temporary subsidies
We now examine the effect of a temporary subsidy or a tax holiday program. Consider
a program with the constant subsidy rate s > 0 that begins at time zero and ends at T. Note that
under this subsidy program the environment is stationary after t = T so, if the home firm
does not want to enter at t = T, it never wants to do so at t > T. This allows us to focus on
the possibility of entry during the interval [0, T]. Entering at t ≤ T, the home firm receives
the flow profit π(s) between t and T and π(0) afterwards, which totals:(e- rt − e- rT)π(s)/r + e- rTπ(0)/r – e- rtf(K)(t ≤ T).

Since π(0) > π(s), the following describes the optimal strategies for the home firm:(a) if π(s) – rf(K) > 0, enter at t = 0,(b) if π(0) – rf(K) ≥ 0 > π(s) – rf(K), enter at t = T > 0,(c) if 0 ≥ π(0) – rf(K), do not enter.
Given K(0) > K(s), the above entry rule is restated as

Lemma 1: (the best responses for the home firm)(A) If K < K(s), enter at t = 0.
(B) If K(0) > K ≥ K(s), enter at t = T > 0.
(C) If K ≥ K(0), do not enter.

11
We next characterize the foreign firm’s optimal strategy under a temporary subsidy
program. Lemma 1 presents three options. Firstly, investing K < K(s) induces entry at t = 0, in
which case the foreign firm optimally sets K = 0, earning the maximum profit
A1 ≡ (1 − e- rT)Π(s)/r + e- rTΠ(0)/r.
Secondly, investing K ∈ [K(s), K(0)) entails entry at T, yielding the profit(1 − e- rT)M(s)/r + e- rTΠ(0)/r − C(K).
In this case, investing the minimal level of investment, K(s), yields the maximum profit:
A2≡ (1 − e- rT)M(s)/r + e- rTΠ(0)/r − C(K(s)).
Lastly, investing K ≥ K(0) deters entry. Again, investing the minimum, K(0), yields the
maximum profit:
D = (1 − e- rT)M(s)/r + e- rTM(0)/r − C(K(0)).
Now we present our main result.

~
Proposition 2: Let the subsidy rate s be given. Then, there is a unique time, T, such that for any~
temporary subsidy program lasting from t = zero to T > T the foreign firm accommodates entryat T.

To prove this we must show that D < Max{A1, A2}. To that end, we begin by comparing A1
and A2. Taking the difference yields

12A2 − A1 = (1 − e- rT)[M(s) − Π(s)]/r − C(K(s))(3)

At T = 0 the right-hand side of (3) is negative because the first term vanishes. But as T
increases sufficiently, the right-had side of (3) approaches Ω(s), which by Proposition 1 is^positive. Then, due to continuity, there exists T satisfying A2 − A1 = 0, such that A2 ≤ A1 for T^^≤ T and A2 > A1 for T > T .

^Consider T ≤ T . Then, since A1 ≥ A2, we compare A1 and D. The difference is
D – A1 = (1 − e- rT)[M(s) - Π(s)]/r + e- rT[M(0) - Π(0)]/r − C(K(0)).
Differentiating we haved(D – A1)/dT = [M(s) - Π(s)] – [M(0) - Π(0)]e- rT
s

⌠
- rT
=⎮
⌡ [M’(v) - Π’(v)]e dv > 00

by Assumption 1. Thus, as T is increased, D is increased relative to A1. Further, at T = 0
D – A1 = [M(0) - )Π(0)]/r − C(K(0)) = Ω(0) > 0.

^

These two result indicate that D > A1 for T ≤ T . Thus, if a temporary subsidy program lasts^

less than T the foreign firm prefers to deter entry.

^

Turn next to the case in which T > T . Since A2 > A1, we consider the difference

13
D – A2 = e- rT[M(0) - Π(0)]/r + [C(K(s)) − C(K(0)].

(4)^

At T = T , A2 = A1, and hence by the preceding analysis
D – A2 = D – A1 > 0.
However, as T is increased sufficiently, D – A2 turns negative. To see this, note that the firstterm on the right-hand side of (4) becomes arbitrarily small as T approaches infinity, but thesecond term, the cost difference, remains unaffected and negative. Then, by continuity there is~~
T at which D = A2, and for all T ≥ T we have D ≤ A2, i.e., the foreign firm accommodates entry.
This competes the proof.

Now we state the intuition underlying Proposition 2. Since entry deterrence is costly,
the foreign firm may prefer to allow for small-scale (or delayed) entry rather than deter entry
completely. The home firm also prefers delayed entry to no entry at all. However, the homefirm cannot make a credible commitment to delay entry, because if the foreign firm drops its
guards and invests below K(0), believing that entry will be delayed, the home firm would havethe incentive to enter at t = 0. It is in such a case that a temporary subsidy program can change
the home firm’s optimal entry strategy (lemma 1). Even if the foreign firm invests less than K(0), the prospect of making negative profits under the temporary subsidy program forces thehome firm to delay entry, thereby making delayed entry a credible commitment. Not having tospend so much on anti-theft investment further boosts the foreign firm’s profit, making entry
accommodation more attractive than entry deterrence under a temporary subsidy program.

14

6. Optimal temporary subsidy programs
In the previous section we showed that a temporary subsidy changes the home firm’s
best responses from an aggressive top-dog strategy to a less aggressive puppy-dog ploy andprompts the foreign firm to accommodate entry. In this section we consider the optimal natureof a temporary subsidy program. The welfare-maximizing government has two policy
instruments, T and s, to affect its welfare under the temporary subsidy program. We supposethat the goods are sold to home-country consumers. Then, home country welfare consists of the
discounted sum of consumer surpluses and home firm profits less the subsidies. The case inwhich goods are sold exclusively in the export (third-country) market can be analyzed
analogously by ignoring the consumer surpluses without affecting our results qualitativley.
~~ ~Clearly, T depends on the rate of subsidy, so write T = T(s). Differentiating the defining
equation, D – A2 = 0, in (3) totally, we obtain~~T’(s) = dT(s)/ds = G1 /G2 < 0.
where
G1 ≡ ∂(D – A2)/∂s = C’(K(s))K’(s) < 0,andG2 ≡ ∂(D – A2)/∂T = [Π(s) – M(s)]e- rT < 0.
~Thus, T(s) is decreasing in s.

15~
In Figure 1 we illustrate T(s) by the locus DA2. Any pair (T, s) to the right of the locus
implies that D < A2 so that the foreign firm accommodates entry. The opposite is true for any
pair (T, s) to the left of the locus.
Let CSM(s) denote the flow consumer surplus when the foreign firm is a monopoly
under the subsidy s. Similarly, let CSA(s) be the flow consumer surplus when entry isaccommodated. Obviously, we have CSA(s) > CSM(s).
By proposition 2, there is entry under a temporary subsidy program at the rate s and~with duration T > T(s). Then, home country welfare is given by(5)

WA(T, s, K(s)) = (1 − e- rT){CSM(s) – sXM(s)}/r+ e- rT{[CSA(0) + π(0)]/r – f(K(s))}.

The first term on the right is the pre-entry home country welfare, consisting of the consumer
surplus under monopoly less subsidy payments to the foreign firm (with XM(s, K(s)) denoting
the foreign firm’s flow output during the subsidy program.) The second is the post-entry
welfare, comprising the consumer surplus under duopoly and the home firm profit less the onetime imitation cost.
Without subsidies, there is no entry, so the maximum home welfare is
WD = CSM(0)/r.
Focusing on welfare after T, subtracting CSM(0)/r from the corresponding expression under thesubsidy program in (5) yields(6)

e- rT{[CSA(0) + π(0) - CSM(0)]/r – f(K(s))}.

16
Since entry is accommodated we haveπ(0)/r – f(K(s)) > 0(see the discussion leading to Lemma 1). We also have CSA(0) > CSM(0). Thus, (6) is positive.
A temporary subsidy generates profits for the home firm and increases consumer surplus.
Further, differentiation of (5) with respect to T yields:∂WA/∂T = e- rT{CSM(s) - sXM(s) - CSA(0) - $(0)} < 0.
~Thus, the optimal policy calls for the shortest possible T; i.e., T = T(s).
~Substituting T(s) into (5) and differentiating with respect to s, we find
(7)~~
dWA[T’(s), s, K(s)]/ds = (∂WA/∂T)(∂T(s)/∂s) + (∂WA/∂K)K’(s) + ∂WA/∂s.

The third term on the right-hand side of (7) describes the direct effect of a subsidy in thepresence of a foreign monopoly:∂WA/∂s = (1/r)(1 − e- rT)∂[CSM(s) – sXM(s)]/∂s
This is the familiar expression in the literature on FDI, capturing the (static) welfare effect ofsubsidy (or tax) on the foreign firm. Let so denote the optimal subsidy (tax if negative) in thestatic sense. In the literature on FDI so is usually assumed negative (i.e., tax) but it could bepositive, depending on the curvature of the demand function, as discussed in the classicalanalyses of Brander and Spencer (1984a, 1984b).
The first term on the right-hand side of (7) is positive because ∂WA/∂T < 0 as just~shown above and also ∂T(s)/∂s < 0. In the second term on the right of (7), we have
∂WA(T, s, K(s))/∂K= – e- rTf’(K) < 0

17
and K’(s) < 0, so the second term is also positive.
Since the first and the second term in (7) are positive, the expression in (7) is positive
when evaluated at s = so. That implies that the optimal subsidy rate exceeds that in the static
model. We have obtained the following result

Proposition 3: Let (s*, T*) denote the optimal temporary subsidy program. Then,(A)~
T* = T’(s*)(B)

s* > soPart A says that under the optimal policy the subsidy program should be made as short as
possible to induce accommodation. Part B says that the optimal program indeed involves
subsidies or tax concession for the foreign firm relative to the static model.
~
The optimal FTZ program (s*, T(s*)) is illustrated in Figure 1. The curve W*
corresponds to the iso-welfare curve representing the maximum welfare under the optimal FTZ
program. so (< s*) is also indicated.

7. Eventual entry
We have assumed up to this point that the foreign firm can forever deter entry by
investing enough in “masquing.” While some firms successfully keep their trade secrets andtechnologies hidden from the competitors for decades or more (e.g., the Coca-Cola formula), it
is also conceivable that technologies and products are copied eventually. The objective of this18
section therefore is to relax the assumption of the basic model and examine the consequence of
eventual entry.

7.A. Model setup
Assuming that the foreign firm’s technology will eventually spill over to the publicdomain and become available to the entrant, we model that eventuality by supposing that theimitation cost gradually declines to zero over time. More specifically, we suppose that theimitation cost now comprises two multiplicative components in the form of f(K)h(t).3 The firstcomponent is familiar from the basic model. The second component h(t) declines over time at adiminishing pace, that is, h’(t) < 0 and h”(t) > 0. We assume that h(t) goes to zero as t goes toinfinity so that, no matter what K is, the imitation cost eventually becomes zero. The foreign
firm can only delay entry by investing in theft preventive measures.
Otherwise, the analysis here closely resembles that of the previous sections. We begin
by solving the model by assuming that there are subsidies at constant rate s at each instant.
Once entry occurs the game is exactly the same that we described earlier. In the second stage,
the home firm chooses an entry time t to maximize its profit:[$(s)/r – f(K)h(t)]e-rt,
given the component f(K) of the imitation cost as given. The first-order condition can bearranged to yield(9)3- $(s) + f(K)[rh(t) – h’(t)] = 0,

A more general functional form, e.g. f(K, t), with appropriate assumptions about cross-partial effects ,can be used
to get the same results as we do here.

19
which determines the optimal entry date t*(s, K), which depends both on K and s. The secondorder condition holds sincerh’(t) – h”(t) < 0.
It is easy to show thatdt*(s, K)/ds = $’(s)/{f(K)(rh’ – h”)} > 0
anddt*(s, K)/dK = - f’(K)(rh – h’)/{f(K)(rh’ – h”)} > 0.
In the first stage the foreign firm chooses K to maximize(1 – e-rt*)M(s)/r + e-rt*Π (s)/r – C(K),knowing that K influences the home firm’s entry date via t* = t*(s, K). The first-ordercondition is
e-rt*[M(s) - Π (s)]dt*/dK – C’(K) = 0,(10)which determines the optimal level of investment K*(s). The second-order condition is satisfied
if d2t*/dK2 < 0; that is, ff” – f’2 < 0, which we assume. This completes the description of themodel with eventual entry.
Now, we evaluate the equilibrium outcome at s = 0. This is depicted in Figure 2. With
the foreign firm investing K*(0) optimally in the first stage, the locus labeled A traces themarginal imitation cost, f(K*(0))[rh(t) – h’(t)]. According to the first-order condition (9), thehome firm optimally enters at t*(0) = t*(K*(0), 0). The corresponding profit to the foreign firm
is given by(1 – e-rt*(0))M(0)/r + e-rt*(0)Π (0)/r – C(K*(0)).

20
7.B. Permanent subsidies
We next examine the effect of a permanent subsidy program. The effect on theequilibrium date of entry is obtained from total differentiation of the first-order condition (9):- $’(s) + f’(K)[rh(t) – h’(t)]dK/ds + f(K)[rh’(t) – h”(t)]dt/ds = 0.
Thus,
(11)

dt*/ds = [$’(s) - f’(K)[rh(t) – h’(t)]∂K/∂s]/{f(K)[rh’(t) – h”(t)]}.

Thus, the effect of a permanent subsidy is decomposed into two effects: the direct effectthrough a permanent change in flow profits, and the indirect effect that operates through achange in K by the foreign firm. Given that the denominator is negative by the second-ordercondition, and $’(s) < 0, the direct effect is negative. This is intuitive. Since the flow profit for
the home firm is smaller under the permanent subsidy, it is worthwhile delaying entry till theentry cost falls more.
However, the foreign firm will also react to a change in the permanent subsidy rate. If
the foreign firm reacts by investing more (∂K/∂s > 0), then the right-hand side of (11) is
positive, implying that the home firm delays entry. Even if the foreign firm reduces investmentin theft prevention (∂K/∂s < 0), entry will be delayed if the direct dominates the indirect effect.
We therefore take the case in which dt*/ds > 0 as the normal case.4

7.C. Temporary subsidies

4

Differentiating the first-order condition (10) yields the expression for ∂K*(s)/∂s, whose sign, however, is in generalambiguous. As s is increased, there is more of an incentive to defend the monopoly status. But since an increase in scauses entry to delay, less investment is needed to keep the home firm out for as long.

21
Given that a permanent subsidy delays entry, this subsection shows that granting atemporary subsidy program can still speed up entry by the home firm. To show that, begin witha temporary subsidy program that ends exactly t*(0), i.e., set T = t*(0). Then, the home firm’s
profit is decreased from $(0) to $(s) between t = 0 and t = T, but returns to $(0), as indicated infigure 2. Thus, if K remains at K*(0), earlier entry is even less profitable, so the optimal entry
date remains at t*(0). With this, the foreign firm’s profit equals(1 – e-rt*(0))M(s)/r + e-rt*(0)Π (0)/r – C(K*(0)).
However, K*(0) is not an optimal choice for the foreign. Since T = t*(0) satisfies thefirst-order condition for the optimal entry by the home firm:- $(0) + f(K*(0))[rh(T) – h’(T)] = 0,
we have that
- $(s) + f(K*(0))[rh(T) – h’(T)] > 0,
implying that the foreign firm can decreases K a little without speeding up entry. In fact, the~foreign firm can decrease K to K, which satisfies~- $(s) + f(K)[rh(T) – h’(T)] = 0
while keeping entry at T = t*(0). In figure 2, the locus B represents the corresponding marginal~

imitation cost, f(K)[rh(t) – h’(t)], which equals $(s) at T, indicating the optimality of entry at T.
With this reduction in investment, the foreign firm’s profit is increased to~(1 – e-rt*(0))M(s)/r + e-rt*(0)Π (0)/r – C(K),~the saving of C(K*(0)) – C(K) > 0.

22Now, consider offering a shorter subsidy program T1 < T = t*(0). The home firm’s
flow profit now jumps from $(s) to $(0) at T1 instead of T. By the preceding argument, the~~foreign firm can reduce investment even below K (say, K1) so that the corresponding marginal
imitation cost is given by the locus C and entry occurs at T1. This results in profit(12)~(1 – e− rT1 )M(s)/r + e− rT1 Π (0)/r – C(K1).

But this profit is less than the obtainable when the program lasted until T, not only because theforeign firm receives subsidies for a shorter period but because entry occurs earlier.
The foreign firm of course always accommodate entry at t*(0) by investing K*(0) andearning the profit(13)(1 – e− rT1 )M(s)/r + ( e− rT1 - e− rt *(0) )M(0) + e− rt *(0) Π (0)/r – C(K*(0)).

Subtracting (13) from (12) and rearranging, we obtain(14)~

C(K*(0)) - C(K1) - ( e− rT1 - e− rt *(0) )[M(0) - Π (0)]/r

If this expression is positive, the foreign firm prefers to accommodate entry at T1 than at t*(0) =T. The first term in (14) is the cost saving from accommodating at T1 and is strictly positive.
The second term in (14) is also positive but can be made arbitrarily small by making T1
sufficiently close to t*(0). Thus, one can always make (14) positive by taking T1 sufficiently
slow to t*(0). We have established the following result.

23
Proposition 4: With eventual entry, suppose that a permanent subsidy can delay entry. Then,
one can always design a temporary subsidy program that results in earlier entry by the homefirm than without subsidies.

Since we assumed that a permanent subsidy delays entry, proposition 4 implies that we can finda temporary subsidy program that results in earlier entry than under the permanent subsidy at
the same subsidy rate s.
Earlier, however, we showed that we could not rule out the possibility that a permanent
subsidy program can also speed up entry. We close this section with a brief discussion of thiscase. For concreteness, suppose that under a permanent subsidy the foreign firm chooses
investment such that the marginal cost of entry is presented by the locus C. This results in entry
at t*(s) = T1. In this case, granting a temporary subsidy that ends at T1 reduces profit to theforeign firm, prompting it to increase K so as to delay entry. However, for delaying entry, theoptimal strategy is to invest K*(0) and accommodate entry at t*(0), as we argued earlier. Thus,
the foreign firm faces two options: allow entry at T1 or t*(0). Although the foreign firm may
not necessarily prefer T1, here we can always raise the rate of subsidy under a temporary
subsidy program so as to make accommodation at T1 more attractive than under a permanent
subsidy or without subsidy programs.

8. Concluding Remarks
The main conclusion of this paper is that, when a multinational makes investment
aimed to preventing unintended transfer of its technology, granting of tax holiday status, as is24
customary for FDI in FTZs, induces transfer of foreign technology and facilitates entry byindigenous firms. Our welfare analysis indicates that an optimal subsidy program should bemade as short as possible to induce entry and the subsidy rate should be adjusted to achieve theoptimum. We also find that the optimal tax policy calls for tax rate reductions relative to thestandard static welfare analysis.
Our results are based on the fact that a temporary subsidy granted to a foreign firmmakes entry less profitable to a potential entrant and induces the latter to delay entry. The
commitment to delayed entry combined with receipt of subsidies upfront makes deterrence lessimportant for the foreign firm. As a result, the foreign firm allows for delayed entry. A
permanent subsidy does not change any incentive to enter over time, and has no such entryinducing effect.
It is possible to relax some assumptions of the model without qualitative effect on our
main result. First, suppose that there are many potential local entrants. This really does notaffect our main conclusion. For simplicity, assume that there are an infinite number of potential
entrants, which will behave perfectly competitively upon entry. The implication is that the postentry profit to the foreign firm is zero. Nonetheless, a temporary subsidy program can boost the
profit to the foreign monopoly initially and delay entry the same way as described in the text.
Thus it is possible to find a policy structure that increases profit to the monopoly enough so thatthe monopoly prefers to abandon the costly entry-prevention strategy.
Secondly, some FTZs are created with export markets in mind, so that all output
produced in the zones are exported. As consumer surpluses are no longer part of home country
welfare, what matters is the profit to the entrant. Thus, our conclusions remain valid.

25
Finally, the model can be extended to include the government or governments amongplayers. Once the multinational makes investment so that entry occurs at T under a temporary
subsidy program, the home government may have the incentive to renege and terminate thetemporary subsidy program earlier to speed up entry or save subsidy payments. The
multinational is likely to see through this and will invest the level of investment necessary to
deter entry. This time-inconsistency problem could be avoided in a repeated-game setting,however, because such myopic governmental behavior would turn off future investors.

26
Appendix~

If K is less than to K, the home firm will enter at t*(s) < T, which satisfies the first-ordercondition:- $(s) + f(K)[rh(t) – h’(t)] = 0,
and the foreign firm’s profit will be(1 – e-rt*(K))M(s)/r + (e-rt*(K) – e-rT)Π(s)/r + e-rTΠ (0)/r – C(K).
Differentiating the above with respect to K yields
e-rt*(K)[M(s) - Π (s)]dt*/dK – C’(K).
Given that t*(s) < T, and the fact that the permanent subsidy results in entry later than T = t*(0),we conclude that the above derivative is positive. Thus, a further decrease in investment below~

K decreases the profit to the foreign firm.

27
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s

W*

D

s*

A2
so

T
~
T(s*)

Figure 1

2

B

C

A
$(0)

$(s)

t
T1

T0 = t*(0)Figure 2