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Federal Reserve Bank of Chicago
Do Safeguard Tariffs and Antidumping
Duties Open or Close Technology
Gaps?
Meredith A. Crowley
Revised February 10, 2003
WP 2002-13
Do Safeguard Tariffs and Antidumping Duties Open
or Close Technology Gaps?
Meredith A. Crowley
Economic Research
Federal Reserve Bank of Chicago
mcrowley@frbchi.org
First version: July 30, 2002
This version:
February 10, 2003
Abstract
This paper examines how the country-breadth of tari protection can a ect the technology adoption decisions of both domestic import-competing and foreign exporting rms. The
analysis is novel in that shows how rm-level technology adoption changes under tari s of different country-breadth. I show that a country-speci c tari like an antidumping duty induces
both domestic import-competing rms and foreign exporting rms to adopt a new technology
earlier than they would under free trade. In contrast, a broadly-applied tari like a safeguard
can accelerate technology adoption by a domestic import-competing rm, but will slow-down
technology adoption by foreign exporting rms. Because safeguard tari s can delay the foreign
rm's adoption of new technology, the worldwide welfare costs associated with using them may
be larger than is generally believed.
I
thank Bob Staiger, Scott Taylor and Yuichi Kitamura for detailed comments and encouragement. I also
thank Bob Baldwin, Eric French, Tom Prusa and seminar participants at the University of Wisconsin-Madison, the
Federal Reserve Bank of Chicago, the Federal Reserve Board of Governors, Purdue University, SUNY - Stony Brook,
the Bureau of Labor Statistics, the Federal Reserve System Committee on International Economic Analysis Spring
2001 Meetings, the Midwest International Economics Group Fall 2001 Meetings and the NBER's 2002 Universities'
Research Conference on Firm-level Responses to Trade Polices. The opinions expressed in this paper are those of the
author and do not necessarily re ect those of the Federal Reserve Bank of Chicago or the Federal Reserve System.
1
1
Introduction
Over the last twenty years, the world has witnessed a dramatic increase in the use of industryspeci c import restraints like antidumping duties, safeguard measures, and voluntary restraint
agreements. Although protection-seeking industries often claim that they are the victims of \unfair"
trade, in many cases, it is clear that a domestic industry's falling market share is due to its
technological inferiority relative to its foreign competitors. This paper explores how the countrybreadth of tari protection a ects the technology adoption decisions of import-competing and
exporting rms.
For example, the US saw steel imports increase from 7.3% of the US market in 1964 to 16.7%
in 1968 after European and Japanese steel producers adopted a major technological innovation,
the basic oxygen furnace.1 From 1969 to 1974, the US government responded to this import surge
with country-speci c import restraints. In this instance, the US negotiated voluntary restraint
agreements with the EC and Japan. These import restrictions had two notable e ects. First, steel
imports from countries not covered by the agreement rose. Second, the US industry failed to catchup technologically. In 1974, when 80.9% of Japanese production and 68.8% of German production
utilized the basic oxygen furnace, only 56.0% of US steel production utilized the new technology.2
In the 1980s and 1990s, technology in steel production continued to improve with the development of continuous casting, another cost-reducing production technology. The US government
again responded to import surges from technological leaders with country-speci c antidumping
duties and voluntary restraint agreements.3 The results of protection were the same as before.
Imports from countries not covered by the import restraints rose.4 Moreover, the US remained
technologically behind. In 1982, only 26.9% of US production utilized continuous casting compared
to 78.7% of Japanese production and 61.9% of German production. By 1992, the absolute technology position of the US was much better; 79.3% of US production utilized continuous casting.
However, the US was still behind its traditional competitors - 92.0% of German production and
1
See Moore, 1996.
OECD, 1974.
3
An exception to the general practice of country-speci c protection was the use of the Trigger Price Mechanism
from 1977 to 1982 which imposed a price oor on imports from all countries.
4
See Prusa, 2001 and Moore, 1996.
2
2
95.4% of Japanese production now used continuous casting - and had been leapfrogged by Turkey
and Korea which used continuous casting for 82.2% and 96.8% of production, respectively.
Despite the dismal history of steel, the American experience with trade protection and technology adoption has not been universally bad. In 1983, in the face of rising imports of Japanese
motorcycles, the US government temporarily raised its tari on motorcycles. The goal was to
help the American producer, Harley-Davidson, implement its plan to introduce \innovative new
management and manufacturing techniques, many of which were learned from [Harley-Davidson's]
Japanese competitors."5 This experiment in using the multi-country \safeguard tari " to assist a
rm in adopting the technology of its foreign rivals turned out to be a success - by 1986 HarleyDavidson had closed the technology gap. It had \revitalized its manufacturing and streamlined
its operations"6 , had reclaimed the top spot in the US superheavyweight motorcycle market, and
had begun a resurgence in which the rm has steadily increased both its pro tability and market
share up to the present day. Interestingly, unlike the US experience with steel protection, the
comprehensive safeguard tari didn't lead to trade diversion. In fact, under the safeguard tari ,
imports of motorcycles from Japan grew 17.6% between 1984 and 1985 while growth of imports
from Germany was only 7% and imports from Italy fell 11.0%.7
Why were the outcomes of trade protection so di erent? This paper attempts to explain how
di erences in the breadth of trade protection could have a ected technology adoption by these
two industries. Speci cally, it analyzes technology adoption decisions under country-speci c tari s,
like antidumping duties and voluntary restraint agreements, and broadly-applied, multicountry
protection, like safeguard tari s.8 Moreover, it examines how these tari s a ect the technologyadoption decisions of both domestic import-competing and the foreign exporting rms they compete
against.
5
Harley-Davidson Motor Company, 2000, p. 2.
Ibid.
7
Author's calculation for motorcycles with engines 700 cc's or larger from \US Imports for Consumption and
General Imports, TSUSA Commodity by Country of Origin, FT246," Bureau of the Census, Washington, DC 19721988. Because the safeguard was imposed in mid-1983, 1984 is the rst year for which data on imports under the
safeguard are available.
8
In this paper, I use the term antidumping duty to refer to country-speci c trade protection and use the term
safeguard tari to refer to multicountry protection. In practice, there are exceptions to this general rule. After
1984, antidumping protection could be comprehensively applied to all import sources if multiple petitions were led
simultaneously. Also, prior to 1994, safeguard protection could be applied to a single country.
6
3
This is the rst paper to analyze the relationship between the breadth of trade protection
and technology adoption. In exploring how tari s a ect technology adoption, I draw from the
technology adoption literature (Reinganum, 1981a, 1981b; Fudenberg and Tirole, 1985) in which
ex ante identical rms compete in the dates at which they adopt an existing, widely available
technology whose cost of adoption is decreasing with time. My research complements Matsuyama
(1990) and Miyagiwa and Ohno (1995, 1999) who study how the duration of trade protection can
a ect the adoption of an existing technology. They show that when the duration of protection is
endogenous to the domestic rm's decision of when to adopt the new technology, the new technology
is never adopted. I abstract from this problem by examining permanent protection. Miyagiwa and
Ohno (1995) show that permanent protection is equivalent to temporary protection with a minimum
duration and a termination date that is exogenous to the domestic rm's technology adoption
decision. Because safeguards face WTO-enforced time limits and the duration of antidumping
protection depends on foreign rms' behavior and, since 1994, is limited to 5 years in most cases,
analyzing permanent protection is a reasonable simpli cation. Lastly, by examining the welfare
consequences of technology adoption under country-speci c and broadly-applied tari s, this paper
contributes to a large literature (Bagwell and Staiger, 1999; Ethier, 1998) which analyzes the welfare
properties of country-speci c tari s in the context of regional and multilateral trade agreements.
This paper uses a segmented markets model in which three rms in three di erent countries one importing country and two exporting countries - compete on quantity. At some time, the rm in
one foreign exporting country discovers and adopts a new technology. The import-competing rm
and the rm in the second foreign country then decide when to adopt the new technology. When
the cost of technology adoption is decreasing with time but is a xed cost at any moment in time,
a rm that faces a large worldwide market has an incentive to adopt the new technology relatively
early. I show that when the import-competing rm and the rm in the second foreign country are
suÆciently similar in terms of the size of the worldwide market they face, it is indeterminate which
country will adopt the new technology rst in the pure strategy Nash equilibrium under free trade.
If one rm faces a worldwide market that is suÆciently larger than its competitor's, it will adopt
the new technology rst.
Protection under a multicountry safeguard tari and a country-speci c antidumping duty
4
changes the equilibrium in the technology adoption game. Country-speci c antidumping duties
advance the date of technology adoption for both the import-competing rm and the second foreign rm. They do this by reducing the market share of the technologically superior foreign rm
and increasing the market shares of both the domestic rm and the second foreign rm. By increasing both rms' market shares, the antidumping duty creates an incentive for both rms to
adopt the new technology earlier than they would under free trade. Because the antidumping duty
doesn't change the relative market shares of these two rms, it doesn't alter the equilibrium order
of technology adoption. In contrast, a multicountry safeguard tari advances the date of technology
adoption by the import-competing rm and delays the date of technology adoption by the second
foreign rm. This happens because the safeguard tari increases the market share of the domestic
rm and reduces the market shares of both foreign rms. Moreover, the safeguard tari changes
the relative market shares of the domestic rm and the foreign rm that does not have the new
technology. By changing the relative market shares of these two rms, the safeguard tari can
alter the equilibrium order of adoption. When the safeguard tari increases the domestic rm's
market share above a critical threshold, the domestic rm \leap-frogs" the second foreign rm in
the technology adoption race.
In summary, tari s of di erent country-breadth have di erent e ects on technology adoption.
The safeguard tari closes one technology gap - that between the domestic import-competing rm
and foreign rm that precedes it in technology adoption - but, it also opens a second technology
gap by delaying the second foreign rm's technology adoption. Although a safeguard tari can
improve the welfare of an importing country by accelerating its technological progress, it can also
cause worldwide welfare losses by delaying technology adoption among foreign exporting rms. In
contrast, if an importing country imposes an antidumping duty against a technologically superior
foreign rm, this closes the technology gap between the initial foreign innovator and the rms in all
other countries that are technologically behind it. In terms of worldwide welfare, earlier technology
adoption by rms in all countries yields dynamic gains but the antidumping duty itself imposes
static costs.
Another motivation behind this paper is to question a conventional wisdom that has arisen
among some economists and trade policy makers. It is widely understood that antidumping duties
5
impose a high welfare cost on consumers (see Gallaway, Blonigen and Flynn, 2000; Staiger and
Wolak, 1994 and Prusa, 2001) and are a tax that addresses no fundamental market failure.9 Gruenspecht (1988), Anderson (1992), and Clarida (1993) suggest that dumping is a pro t-maximizing
strategy for a foreign rm and imply that antidumping duties are welfare-reducing. However, safeguard tari s have been less costly to consumers (Baldwin, 1985; Finger, Hall and Nelson, 1982;
and Hansen and Prusa, 1995), less distortionary to worldwide trade ows, and may be bene cial to
importing countries because they allow governments some exibility in setting policy (Bagwell and
Staiger, 1990; Ethier, 1998; Fischer and Prusa, 1999). Trade lawyers and policymakers like Bhala
(1996) and Jackson (1989) have developed this viewpoint to suggest that reform of trade policy
include elimination of antidumping policy and expansion of the safeguard policy.10
However, the arguments that safeguards are somehow better than antidumping duties tend
to rest on static measures of the welfare consequences of trade protection. The di erence in the
dynamic welfare costs of these policies has not been thoroughly examined. This paper suggests
that by delaying technology adoption in foreign countries, the dynamic costs of using safeguard
tari s may be larger than those associated with antidumping duties.
Section 2 outlines the model. Section 3 presents the technology adoption game and the equilibrium technology adoption dates under di erent trade policies. Section 4 analyzes the importing
country's welfare under di erent trade policies. Section 5 concludes.
2
The Model
To study how the breadth of tari protection a ects the decisions of rms, I construct a partial
equilibrium model of a world with three countries, two foreign countries (denoted A and B) and
one domestic country (called home and indexed H). I restrict my attention to imperfectly competitive industries because antidumping duties and safeguard tari s are often used in industries with
9
An exception to this general rule is Hartigan (1996) which examines predatory dumping arising from a capital
market imperfection.
10
Bhala (1996) has argued, \antidumping law is unnecessary. Injury to an industry in an importing country caused
by imports can be addressed by safeguard actions... Applying [safeguard actions] in the context of dumping is
legitimate because dumping is not necessarily unfair." Jackson (1989) supports this by claiming that \...unfair trade
[i.e. dumping] also causes burdens of adjustment and so arguably quali es for safeguards policies."
6
relatively small numbers of producers.11 By assuming there is one rm in each country, markets
are segmented, and the goods produced in each country are perfect substitutes, I can tie-down the
country-speci c volume of trade and simplify analysis of the strategic behavior of rms. To further
simplify the analysis, I assume the foreign markets are closed to each other and to the home rm.
The rms in the foreign countries sell their output in their own market and in the home country's
market, but the home rm sells its output in only its own market. See gure 1 for a diagram of
trade ows.
Initially, the three rms have identical technologies. I assume the rm in country A discovers
and adopts a new, low-cost technology. This new technology is widely available to rms everywhere
and its cost of adoption is falling over time. For example, cost-reducing process innovations like the
basic oxygen furnace, continuous casting, industrial robots, computers and machine vision would
satisfy this assumption. The advent of this new technology induces a technology adoption race
between the import-competing rm in the home country and the rm in country B. I characterize
the Nash equilibrium of this game under free trade, safeguard tari s, and antidumping duties.12
2.1 Instantaneous Pro ts
The three rms, called A, B, and home, play an in nitely-repeated quantity-setting game. At
every moment in time, rms choose their quantities simultaneously to maximize pro ts given their
current technology level. I assume that rms follow Markov strategies in order to restrict my
attention to the non-cooperative equilibrium in the repeated quantity-setting game.
The technology level of a rm at any point in time is simply its marginal cost of production at
that time,
i
where i = a; b; h. The technology level of any rm can take on two values,
i
2f
; g
11
Under US trade law, an industry must pay legal fees in order to request trade protection. The free-rider problem
could explain why protection is most often sought by industries with relatively few producers. Alternatively, in
industries with many producers, management quality may vary widely across domestic rms and the government
may be less likely to nd injury is caused by imports.
12
The Nash equilibrium rules out by assumption the possibility of pre-emption in technology adoption. Fudenberg
and Tirole (1985) have shown that, in a continuous time technology adoption game with two identical rms, allowing
for pre-emption causes the equilibrium dates of technology adoption to occur earlier and rents to be equalized between
the two rms. When rents are equalized, rms are indi erent between being the leader or follower in technology
adoption. In this paper, I analyze what Fudenberg and Tirole call a \precommitment equilibrium." Oster (1982)
nds that plant-speci c characteristics are important determinants of the dates at which US steel rms adopted the
basic oxygen furnace and continuous casting. Thus, plant-speci c characteristics may act as pre-commitment devices.
7
where is the new or low-cost technology and is the old or high cost technology ( < ). Initially,
all three rms have the old, high-cost technology.
Inverse demand in the home country is given by p(q; M a ; M b ) where q is the home rm's output
and M i is imports from rm i into the home country. In order to derive a precise analytic relationship among any tari , each rm's equilibrium quantity, and the order of technology adoption, I
assume inverse demand is linear and that the domestically-produced good and the foreign-produced
goods are perfect substitutes, p(q; M a ; M b ) = a (q + M a + M b ). Similarly, inverse demand in each
foreign country i is linear, pi (qi ) = ai
q i . Thus, the instantaneous equilibrium pro ts of rms are
given by the following.
1
(a
16
1
= (ai
4
h =
i
3
h
i 2
+
) +
i
+
j
1
(a
16
+ i + j )2
3( i + i ) +
(1)
h
+
j
+ j )2
(2)
for i = a; b, i =
6 j where i is the tari imposed by the home country against imports from
country i.
The pro ts of each rm are increasing in the size of the market(s) it serves. Because the cost
of adoption at any point in time is a xed cost, the rm the serves the larger market(s) and can
spread the cost of adoption over more units will have an incentive to adopt earlier.
2.2
A technological improvement in a foreign country
At some time denoted t = 0, rm A experiences a positive technology shock; its marginal cost
of production falls to . This causes rm A to increase its exports to the home country. At any
time t > 0, the new technology of rm A can be acquired by the home rm and the rm in country
B at a cost C (t) that decreases with time C 0 (t) < 0 and C 00 (t) 0. Thus, the advent of the new
technology kicks-o a technology adoption race between the home country's rm and the rm in
country B in which each rm must choose its date of technology adoption, th and tb , respectively.
To simplify notation, let i ( h ; b ) denote the instantaneous pro ts of rm i = h; b when both
the home rm and rm B have the old technology, i ( h ; b ) denote rm i = h; b's pro ts when
8
the home rm has the old technology and rm B has the new technology, i ( h ; b ) denote rm
i = h; b's pro ts when the home rm has the new technology and rm B has the old technology,
and i ( h; b ) denote rm i = h; b's pro ts when both rms have the new technology. Firm A's
new technology level is given by
a
=
after t = 0 and is suppressed for clarity. Lastly, the
tari s imposed against country A and country B are permanent and are suppressed for clarity of
notation.13
Linear demand and constant marginal cost imply the following relationships about instantaneous pro ts under di erent technology levels for any set of non-prohibitive tari s ( a ; b ) that
are constant over time. First, the pro ts of being a technological leader exceed the pro ts earned
when both rms have the new technology which, in turn, exceed the pro ts of being a technological
follower. Formally, i ( i ; j ) > i ( i ; j ) > i ( i ; j ) for i = h; b, i =
6 j . Second, the pro ts of
leading in the technology adoption race exceed the pro ts earned when both rms have the old
technology, which in turn, exceed the pro ts of being a follower. i ( i ; j ) > i ( i ; j ) > i ( i ; j )
for i = h; b, i 6= j .
Thirdly and most importantly, the bene t to a rm of being the leader in adopting the new
technology exceeds the bene t to the rm when it's the follower in adopting the new technology.
i ( i ; j )
i ( i ; j ) > i ( i ;
j
)
i ( i ;
j
)>0
(3)
Equation (3) is the critical condition that ensures that the two rms, home and rm B, will
never want to adopt the new technology at the same moment in time, even if their instantaneous
pro t functions are identical.
3
The technology adoption game
The home rm and the rm in country B strategically choose dates at which to adopt the new
technology, th and tb , in order to maximize the discounted present value of net pro ts. The rm
in country A, which already has the new technology, has no strategic choice to make regarding
13
In sections 3.2 and 3.3, I discuss how relaxing the assumption that tari s are constant over time will alter the
results.
9
technology. It does, however, continue to strategically choose the quantity of output to sell in
the home country. The discounted present value of net pro ts to rm i = h; b, i =
6 j depends on
whether it is a leader or follower in technology adoption and is given by the following:
i
i
j
V (t ; t ) =
8
>
>
<g `i (ti ; tj )
>
>
:g fi (ti ; tj )
if ti tj
if
ti
(4)
tj
where
`i
i
j
g (t ; t ) =
g fi (ti ; tj ) =
Z ti
0
Z tj
0
e
e
rs i
i
j
( ; )ds +
rs i
( i ; j )ds +
Z tj
t
i
Z ti
t
j
e
e
rs i
i
j
( ; )ds +
rs i
( i ;
j
)ds +
Z
1
t
Z
j
t
1
i
e
rs i
( i;
j
)ds
e
rti
C (ti )
e
rs i
j
)ds
e
rti
C (ti )
( i;
The function g`i represents the discounted present value of net pro ts to rm i if it adopts the
new technology before rm j does. The rst term in g`i represents the discounted present value
of rm i's pro ts over the period in which both rm i and rm j have the old technology. The
second term represents the discounted present value of rm i's pro ts over the period in which it
has the new low-cost technology and rm j has the old high-cost technology. The third term is
the discounted present value of rm i's pro ts over the period in which both rms have the new
technology. Finally, the last term represents the discounted present value of installing the new
technology at time ti . The function gfi di ers from g`i in that the second term in gfi represents
the discounted present value of pro ts earned for the period in which rm i lags behind rm j in
adopting the new technology.
In the next section, I characterize the Nash equilibrium in the technology adoption game under
free trade. In section 3.2 I characterize the Nash equilibrium under a safeguard tari and in section
3.3 I characterize the Nash equilibrium under an antidumping duty.
10
3.1 Technology Adoption under Free Trade
When the home rm sets tari s against both countries equal to zero, it experiences an increase
in imports from country A and a decrease in imports from country B in the wake of country
A's discovery and adoption of the new technology. Moreover, the price of the good in the home
country's market will fall. Thus, in a broad sense, the home country is eligible for trade protection
under a variety of WTO provisions. When will the home rm and its foreign competitor, rm B,
adopt the new technology if the home country maintains a policy of free trade?
The discounted present value of net pro ts to each rm, V i is strictly concave and continuous in
ti for a given tj but is not di erentiable at ti = tj . The strict concavity and continuity of g `i (ti ; tj )
and gfi (ti ; tj ) imply that each function has a unique maximum that is independent of tj .
De nition 1 Let t^i = arg max g`i (ti ; tj ) and let t~i = arg max gfi (ti ; tj ) for every tj for i = h; b,
i 6= j .
Each rm's optimal dates for technology adoption have two important features. First, because
there are larger gains from being the rst to adopt the new technology, see (3), the optimal dates
of adoption for each rm depend only on the order of adoption. If a rm is the leader, its optimal
date is strictly earlier than if it's a follower t^i < t~i for i = B; H . Second, the optimal dates for the
two rms will di er according to the total size of the worldwide market each rm faces.
Proposition 1 Optimal adoption dates under free trade. Under free trade, the optimal dates for
technology adoption by each rm are (a) di used over time (i.e., t^i < t~i for i = h; b) and (b) the
relationships between the optimal dates of adoption for the two rms can be summarized as follows
where qb =
1
2
ab
1
2 (
+ ) , the average quantity produced for sale in country B:
3
8
3
b
if q = (
8
t^b < t~b <t^h <t~h
if 0 < (
t^b < t~b =t^h <t~h
) < qb
)
3
8
t^b <t^h < t~b <t~h
if 0 < qb < (
t^b =t^h < t~b =t~h
if 0 = qb
11
(5)
(6)
)
(7)
(8)
Proof:
Part (a): Di usion over time. For all tj ,
(3). Since
@gf i (t~i ;tj )
@ti
@gf i (t^i ;tj )
@ti
>
@g`i (t^i ;tj )
@ti
= 0 by the de nition of t^i and by
= 0 and gfi (ti ; tj ) is strictly concave, then t^i < t~i for i = h; b.
Part (b): Ordering of optimal dates. The partial derivatives of g`i with respect to ti and of gfi
with respect to ti are as follows:
@g `i
@ti
@g fi
@ti
= e
= e
rti i
( i ; j )
rti
i i j
( ; )
i ( i ; j )
C 0 (ti ) + rC (ti )
i ( i ;
C 0 (ti ) + rC (ti )
j
)
(9)
(10)
From the proof of part (a), t^i < t~i for i = h; b in expressions (5), (7), and (8) . Consider
expression (5). I need to show t~b < t^h .
By de nition 1, evaluating (10) for i = b at its optimal value t~b implies C 0(t~b ) + rC (t~b) =
b ( b ;
h (
h)
h ; b )
b ( b ;
h ).
+ b ( b ;
Thus, evaluating (9) for i = h at t~b yields,
h)
b ( b ;
h)
> 0 for q b > 83 (
@g`h
@th
t~
=e
rt~b
h ( h ; b )
b
). By the strict concavity of g`h , it
follows that t~b < t^h.
Turning to expression (7), it is necessary to show (i) t^b < t^h, (ii) t^h < t~b , and (iii) t~b < t~h . From
the proof of expression (5), it follows that (ii) is true for qb < 83 (
evaluating (9) for i = b at t^b implies C 0(t^b ) + rC (t^b ) = b ( b ; h )
into (9) for i = h yields
@g`h
@th
t^b
> 0 for q b < 38 (
). For (i), by de nition 1,
b ( b ; b ). Substituting this
). By the strict concavity of g`h , it follows that
t^b < t^h . For (iii), by de nition 1, evaluating (10) for i = b at t~b and substituting this expression
into (10) for i = h yields
@gf h
@th
t~b
> 0 for q b < 83 (
). By the strict concavity of gfh , t~b < t~h .
For expression (8), if qb = 0, then g`h = g`b and gfh = gfb . Thus, the value of t^ that maximizes
g `h and g `b and the value of t~ that maximizes g fh and g fb must be the same. QED.
Proposition 1 summarizes the relationship between a rm's optimal dates for technology adoption and the size of the worldwide market it faces. Because country B's market is closed to imports
and the home country's market is open, if the home country maintains a free trade policy, rm B
will serve a larger market and its optimal dates for adoption will precede the home rm's. Because
12
country B's market is closed, it can spread its costs of adoption over a larger number of units and
thus has an incentive to adopt the technology at relatively early dates.14 Intuitively, condition (5)
tells us that when the average quantity rm B sells in its own market is suÆciently large relative
to the cost savings generated by the new technology, its optimal dates for technology adoption
precede those of the home rm. As the size of country B's market decreases, the pro t-maximizing
quantity rm B produces for its own market decreases, as given by (7), and the gaps between its
optimal dates for adoption and the home rm's optimal dates decrease. Finally, when rm B sells
no output in its own market, the optimal dates for adoption for the two rms are the same.
Having identi ed the optimal dates for adoption under di erent parameter values, I now turn
to each rm's best response function. Given the optimal dates of adoption presented in proposition
1, the best response function of rm i can be written as
tiR (tj ) =
8
>
>
>
t^i
>
>
>
<
if tj > tj
f^i ~ig
j
t ; t if t
>
>
>
>
>
>
:t~i if tj < tj
(11)
= tj
for i = h; b, i =
6 j and where tj is de ned as the value of tj such that g`i(t^i ; tj ) = gfi (t~i ; tj ).
The best response function of each rm i = h; b consists of the two dates (t^i and t~i ) that are the
candidates for maximizing the discounted present value of net pro ts V i . For rm i, the bene t of
being a leader in technology adoption is just equal to the bene t of being a follower in technology
adoption if its opponent chooses to adopt the new technology at a date tj
2 (t^i; t~i ). If
rm j chooses
to adopt at any time before this cuto date (tj < tj ), then rm i earns a higher discounted present
value of net pro ts when it delays its technology adoption until the relatively late date t~i . Hence,
rm i's best response to rm j adopting at any date tj < tj is to choose to adopt the new technology
at the later date, t~i . Similarly, if rm j adopts the new technology at any date tj > tj , the home
rm maximizes its discounted present value of net pro ts by adopting quickly at date t^i .
14
Relaxing the assumption that foreign markets are closed to each other and the home rm causes the equilibrium
to change in an obvious way. If the home rm and rm B have the same access to all markets, the size of their
worldwide markets will be identical and their optimal dates for technology adoption will be the same. Consequently,
there will be two pure strategy Nash equilibria in which either rm can be the rst to adopt the new technology.
13
Proposition 2 Technology Adoption under free trade. In the technology adoption game, there is
one pure strategy Nash equilibrium (t^b ; t~h ) in which the rm in country B always adopts the new
technology rst if the quantity rm B sells in country B is suÆciently large, qb > k where k 2
(0; 83 (
)). There are two pure strategy Nash equilibria (t^b ; t~h ) and (t^h ; t~b ) in which either rm
can be the rst to adopt the new technology if the quantity rm B sells in country B is suÆciently
small, qb < k .
Proof: Consider two cases.
Case 1: Suppose qb 83 (
). Then, t~b < t^h by proposition 1. Inspection of the best response
functions shows that the only possible intersection is at (t^b ; t~h ).
Case 2: Suppose 0 qb < 83 (
). Then t^b < t^h < t~b < t~h by proposition 1. If t^h < th and
tb < t~b , then the best response functions intersect at (t^b ; t~h ) and (t^h ; t~b ). By lemma 3 in appendix
A, for all qb < k , t^h < th and tb < t~b so there are two pure strategy Nash equilibria. For all
q b > k , t^h > th or tb > t~b or both. Thus, inspection of the best response functions shows that the
only possible intersection is at (t^b ; t~h ). QED.
Two interesting observations can be drawn from proposition 2. First, the order of technology
adoption is indeterminate when the foreign rm's domestic market is suÆciently small or does not
exist.15 This suggests that if a very small country with perfect access to foreign markets keeps its
own market completely closed in order to promote an infant industry, it can still lose the technology
race. Alternatively, it also suggests a rm in a small country like Korea could beat a rm in a
large country like the EU or US in adopting a new technology if the large country allows imports
to enter freely. If the Korean market were closed and the US market were open, the Korean rm's
worldwide market share would be larger than that of a rm in the US. Thus, in equilibrium, the
Korean rm could adopt rst. Second, if the foreign rm's closed domestic market is suÆciently
large and the home country's market is open, the home rm will always lose the technology race.
This could explain why rms in a country like Japan have historically beat American rms in
adopting widely-available new technologies during periods when American markets were relatively
15
Intuitively, allowing for pre-emption as in Fudenberg and Tirole (1985) should make the results more extreme.
The rm with the larger worldwide market should always adopt the new technology rst in equilibrium. If the two
rms are identical in terms of the size of their worldwide markets, the indeterminacy in the order of adoption remains.
14
open to imports and Japanese markets were relatively closed.
3.2 Technology Adoption under a safeguard tari
The home country could respond to the increase in imports from country A that follows rm
A's positive technology-shock with a WTO-authorized safeguard tari . Applying a safeguard tari
in this context is legitimate because it satis es the two WTO criteria. First, the equilibrium in the
instantaneous quantity setting game involves an increase in imports from country A. Second, the
domestic rm su ers \injury" in the form of a loss of market share and reduced pro ts. I follow
the WTO rules and model the safeguard as a tari that is equally applied to imports from all
countries. Although the WTO speci es that a safeguard is a temporary tari that can be imposed
for a maximum duration of ve years, I simplify the analysis by analyzing a permanent safeguard
tari .16
Under a safeguard tari policy, the home country imposes a positive, non-prohibitive tari (i.e.,
sg < 21 (a
3
h
+
a
+
b ))
on imports from country A and country B, sg = i for i = A; B .
From the instantaneous pro t functions (1) and (2), we can see that the safeguard tari increases
the home rm's instantaneous pro ts and decreases the foreign rms' pro ts, regardless of their
technology levels. Under a safeguard tari , for a given ti , the discounted present value of pro ts
V i for i = h; b is strictly concave and continuous, but it is not di erentiable at ti = tj .
De nition 2 Let t^i;sg = arg max g`i (ti ; tj ; sg ) and let t~i;sg = arg max gfi (ti ; tj ; sg ) for every tj for
i = h; b, i 6= j .
The bene t to the home rm of adopting the new technology is larger under a safeguard
tari than it is under free trade both when it's a leader in adopting and when it's a follower,
h (
h ; b ; sg )
h ( h ;
b ; sg )
> h (
h; b; i
= 0)
h ( h ;
b; i
= 0) for
b
= ; and i = a; b.
The safeguard tari raises the marginal cost of exporting to the home country for rms A and
B. For the home rm, under Cournot competition, the marginal bene t of reducing its costs is
16
Miyagiwa and Ohno (1995) have shown that if a temporary tari has a certain minimum duration and an
credible, exogenous termination date, it is equivalent to a permanent tari in terms of providing an incentive for
earlier technology adoption.
15
larger when its competitors' costs are higher. For the rm in country B, the safeguard tari has
the opposite e ect. The safeguard tari leads rm B to export less and, consequently, produce
less. Because the xed cost of technology adoption must now be spread over a smaller quantity of
output, rm B will delay technology adoption relative to its optimal date under free trade.
Lemma 1 The home rm's optimal dates for technology adoption under a safeguard tari are
earlier than under free trade, t^h;sg < t^h and t~h;sg < t~h. Firm B's optimal dates for adopting the
new technology are later under the safeguard tari than they are under free trade t^b;sg > t^b and
t~b;sg > t~b .
Proof: From (9), the rst order condition of g`i with respect to ti can be written i ( i ; j )
i ( i ; j ) = rC (ti ) C 0 (ti ). By de nition 1, t^i = arg max g `i under free trade for i = h; b and by
de nition 2 t^isg = arg max g`i (ti ; tj ; sg ) under a safeguard tari for i = h; b. For all nonprohibitive
safeguard tari s, 0 < sg < 21 (a 3 h + a + b ) , the marginal bene t of the new technology is higher
under the safeguard tari for the home rm, h ( h ; b ; sg )
h ( h ; b ; sg ) > h (
h ( h ; b ; = 0) and lower under the safeguard tari for rm B, b ( b ; h ; sg )
b ( b ; h ; = 0)
h ; b ;
= 0)
b ( b ; h ; sg ) <
b ( b ; h ; = 0). Thus, t^h;sg < t^h and t^b;sg > t^b . From the rst order condition
of gfi with respect to ti , it can be shown that t~h;sg < t~h and t~b;sg > t~b . QED.
Proposition 3 Optimal dates under a safeguard tari . Under a safeguard tari , the relationships
among the optimal dates of adoption for the two rms and the relative magnitudes of the home
country's safeguard tari , sg , the cost savings generated by the new technology 83 (
average quantity sold by rm B in its own market, qb = 21 (ab
2
3
1
2 (
3
(
8
+ )) are as follows:
t^bsg < t~bsg <t^hsg <t~hsg
if sg < (qb
t^bsg <t^hsg < t~bsg <t~hsg
if (qb
t^bsg =t^hsg < t~bsg =t~hsg
if sg = qb
t^hsg < t^bsg <t~hsg < t~bsg
2
2
3
3
3
8
2 b 3
)) < sg
if (q + (
3
8
t^hsg <t~hsg < t^bsg < t~bsg
2
3
2
3
3
(
8
))
(12)
2
)) < sg < qb
3
(13)
if qb < sg < (qb + (
16
), and the
(14)
))
(15)
(16)
Proof: For di usion over time, (t^i;sg < t~i;sg ), see the proof of proposition 1 (a). For the order
of adoption, as for proposition 1(b), the proof relies on the de nitions of t^isg and t~isg and on the
concavity of g`i and gfi . The full proof is presented in appendix A.
Overall, expressions (12) through (16) show that when the safeguard tari is relatively small,
rm B's optimal dates are earlier; when the safeguard tari is relatively large, the home rm's
optimal dates are earlier.
More precisely, inequality (12) shows that when the additional cost imposed by the safeguard
tari and the reduction in production costs associated with the new technology are small relative
to the equilibrium average quantity sold by rm B in its own market, rm B will have optimal
adoption dates that are earlier than the home rm. Although the safeguard tari increases the
home rm's domestic market share and decreases rm B's market share, if country B's own market
is suÆciently large, it will still have a stronger incentive to adopt relatively early. Equation (14) can
be thought of as the breakeven tari that makes the two rms identical in terms of their worldwide
market share. When the safeguard tari is suÆciently large relative to the average quantity sold
by rm B in country B, the safeguard tari e ectively confers a large domestic market share on the
home rm and a small share of the home country's market on rm B. This makes the two rms
identical in terms of their worldwide market shares. Thus, they have the same incentives to adopt
the new technology. As the magnitude of the safeguard tari increases beyond this breakeven tari ,
the home rm's market share increases to the point that its optimal dates precede rm B's.
Because the equilibrium average quantity sold by rm B increases with the size of the market
in country B, inequalities (12) through (16) can be interpreted to explain how the safeguard tari
will a ect technology adoption by rms in large versus small countries. For example, if country
B is so small that qb = 0, even a small safeguard tari causes the home rm's optimal dates to
precede rm B's. Conversely, if country B is very large, even a prohibitive safeguard tari may be
too small to cause the home rm's optimal dates to precede rm B's.
As in the case of free trade, the best response function of rm i is given by (11) with the optimal
dates for technology adoption under a safeguard tari given by proposition 3.
Proposition 4 Technology adoption under a safeguard tari . In the technology adoption game, if
17
the home country's tari is suÆciently small relative to the average quantity rm B sells in its own
market and the cost savings generated by the new technology ( sg < where 2 ( 2 (qb 3 (
1
1
3
8
)); 32 qb )), then the rm in country B adopts the new technology rst in the pure strategy Nash
equilibrium (t^bsg ; t~hsg ). Over an intermediate range of tari s ( < sg < ), there are two pure
1
2
strategy Nash equilibria in which either rm can be the rst to adopt the new technology (t^hsg ; t~bsg )
or (t^bsg ; t~hsg ). If the home country's government imposes a safeguard tari that is suÆciently large
))), then the
relative to the size of country B's market ( sg > where 2 ( 2 qb ; 2 (qb + 3 (
2
2
3
3
8
home rm adopts the new technology rst in the pure strategy Nash equilibrium (t^hsg ; t~bsg ).
The proof of proposition 4 is similar to the proof of proposition 2 and is presented in appendix
A.
See gure 2 for a graph of the Nash equilibrium under di erent values of the tari . Panel A
depicts the Nash equilibrium when the average quantity sold in country B's market is very large
relative to the safeguard tari and the cost savings generated by the new technology. The bene t
of technology adoption to rm B is much larger than the bene t of technology adoption to the
home rm because rm B's total output is larger. Therefore, rm B is willing to incur a much
larger cost in adopting the new technology. Because the cost of technology adoption is decreasing
with time, this translates into rm B's willingness to adopt the new technology at a much earlier
date. Consequently, in equilibrium, rm B adopts the new technology rst.
Figure 2 also indicates how increasing the tari above threshold values ( 1 and 2 ) can alter
the equilibrium order of adoption. Of particular interest is an increase in the size of the tari
from a value just below 2 to a value just above this cuto . For values of sg < 2 , the two
pure-strategy Nash equilibria are presented in panel B of gure 2. In this panel, although the sizes
of the worldwide markets served by the two rms are not identical, the tari is suÆciently large
relative to the size of the market in country B that the two rms' total market shares are similar.
This means that the bene t of technology adoption is almost the same for the two rms and implies
that in equilibrium, either rm can lead in technology adoption. Interestingly, the home country's
government can eliminate this indeterminacy by raising the tari above and, thus, increasing
2
the home rm's total market share. For tari s in the range sg > 2 , as depicted in panel C, the
home rm's market share is so much larger than that of the total market share of rm B that the
18
home rm will always adopt the new technology rst.
Another question to consider is how does changing the size of a tari within an interval a ect
the equilibrium dates of adoption. Figure 3 presents a graph of how changing the size of sg within
the interval ( ; ) will a ect equilibrium adoption dates. In this case, for small increases in the
1
2
tari from to 0 , there are still two pure-strategy Nash equilibria. However, an increase in the
tari causes the home rm's optimal adoption dates (t^hsg and t~hsg ) to shift forward in time and
causes rm B's optimal adoption dates to shift backward in time.
If the home rm is a technological leader, the safeguard tari will close the gap between the
home rm and rm A. If the home rm is a technological follower, the safeguard tari will close
the gap between the home rm and rm B. For rm B, the safeguard tari reduces the marginal
value of the new technology. Thus, it delays technology adoption and opens a gap between rm B
and its predecessor in technology adoption.
3.3 Technology adoption under an antidumping duty
Lastly, consider what would happen if the home country imposed a permanent country-speci c
tari , similar to an antidumping duty, on imports from country A, but imposed no tari on imports
from country B. Under WTO rules, an antidumping duty could be imposed because the low price
that would prevail in the home country immediately after the introduction of the new technology
in country A could be compared to rm A's historical data on the costs of producing under the old
technology in such a way as to show that rm A was pricing below it average historical cost.
A permanent, non-prohibitive tari on imports from A, (i.e., ad < 31 (a
)), raises the cost
to rm A of exporting to the home country. From (1) and (2), we see that this tari increases the
instantaneous pro ts of the home rm and rm B regardless of their technology levels. Under an
antidumping duty, for a given ti , the discounted present value of pro ts V i for i = h; b is strictly
concave and continuous, but it is not di erentiable at ti = tj .
De nition 3 Let t^i;ad = arg max g`i (ti ; tj ; ad ) and let t~i;ad = arg max gfi (ti ; tj ; ad ) for every tj
for i = h; b, i 6= j .
19
For both the home rm and rm B, the marginal bene t of adopting the new technology is
larger under an antidumping duty than it is under free trade.
Lemma 2 The optimal dates for technology adoption of the home rm and rm B are earlier under
a antidumping duty than they are under free trade, t^i;ad < t^i and t~i;ad < t~i .
Proof: From (9), the rst order condition of g`i with respect to ti can be written i ( i ; j )
i ( i ; j ) = rC (ti ) C 0 (ti ). By de nition 1, t^i = arg max g `i under free trade for i = h; b and
by de nition 3 t^iad = arg max g`i (ti ; tj ; ad ) under an antidumping duty for i = h; b. For all
nonprohibitive, permanent antidumping duties against A, 0 < ad < 31 (a
) , the marginal
bene t of the new technology is higher under the antidumping duty for i = h; b, i ( i ; j ; ad )
i ( i ; i ; ad ) > i ( i ; j ; = 0)
i ( i ; j ; = 0). Thus, t^i;ad < t^i for i = h; b. From the rst
order condition of gfi with respect to ti , it can be shown that t~i;ad < t~i for i = h; b. QED.
From the instantaneous pro t functions (1) and (2), we can see that the pro ts earned by the
home rm and rm B from sales in the home country are identical under an antidumping duty
against country A. By targeting its tari protection against the import surge from country A, the
home country inadvertently helps rm B. The antidumping duty generates some (static) rents for
the home rm and provides an incentive for the home rm to acquire the new technology earlier
than it would under free trade. However, whereas the safeguard tari conferred a dynamic gain
to the home rm by slowing down rm B's technology adoption, the antidumping duty creates a
dynamic cost to the home rm by speeding up its rival's technology adoption.
Proposition 5 Optimal dates under an antidumping duty. Under an antidumping duty, the optimal dates for technology adoption by each rm are (a) earlier than they are under free trade but
(b) the relative ordering of the optimal dates is the same as that under free trade.
20
3
8
3
b
if q = (
8
t^b;ad < t~b;ad <t^h;ad <t~h;ad
if 0 < (
t^b;ad < t~b;ad =t^h;ad <t~h;ad
) < qb
(17)
)
3
8
t^b;ad <t^h;ad < t~b;ad <t~h;ad
if 0 < qb < (
t^b;ad =t^h;ad < t~b;ad =t~h;ad
if 0 = qb
(18)
)
(19)
(20)
Proof: The proof is identical to the proof of proposition 1 except that the instantaneous pro ts
under an antidumping duty i ( i ; j ; ad ) replace the instantaneous pro ts under free trade. Under
an antidumping duty, the marginal bene t of technology adoption, i ( i ; j ; ad )
increases by the same amount for the home rm and rm B (
0 for i = h; b and
j
@ (i ( i ;
j
; ad ) i ( i ;
@ ad
j
; ad ))
i ( i ; j ; ad )
= 83 (
)>
= ; . Because the antidumping duty provides the same incentive for early
adoption to each rm, it doesn't alter the ordering of the optimal dates, even though it does cause
the optimal dates to be earlier than they are under free trade. QED.
As in the case of free trade, the best response function of rm i is given by (11) with the
optimal dates for technology adoption under an antidumping duty described by lemma 2 and given
by proposition 5.
Proposition 6 Technology Adoption under an antidumping duty. In the technology adoption game,
there is one pure strategy Nash equilibrium (t^bad ; t~had ) in which the rm in country B always adopts
the new technology rst if the quantity rm B sells in country B is suÆciently large, qb > k where
k
2 (0; 83 (
)). There are two pure strategy Nash equilibria (t^bad ; t~had ) and (t^had ; t~bad ) in which
either rm can be the rst to adopt the new technology if the quantity rm B sells in country B is
suÆciently small, qb k .
Proof: The proof is identical to the proof of proposition 2.
Although the idea that antidumping duties could accelerate technology adoption may appear
surprising, it is consistent with the empirical evidence. It is well-known that US steel rms have
often lagged behind their foreign competitors in adopting new technologies. Proposition 6 could
explain this as either (1) the foreign competitors had larger worldwide markets shares and therefore
21
adopted rst or (2) the foreign and US rms had similar worldwide market shares, but although
either rm could have been the rst to adopt the new technology, the foreign rm adopted rst
and thus, it was an optimal strategy for the US rm to postpone adoption until the price of the
new equipment or technology fell further.
Proposition 6 relies on the assumption that the country-speci c antidumping duty is a permanent tari . Or, more precisely, it relies on the assumption that the duration of the antidumping
duty is independent of the home rm's behavior. Earlier work by Matsuyama (1990) and Miyagiwa
and Ohno (1995) has shown that a temporary tari whose termination date is endogenous, i.e. will
be removed as soon as the domestic rm adopts the new technology, delays technology adoption. In
practice, the duration of antidumping protection is supposed to depend on the behavior of foreign
exporting rms, not domestic import-competing ones. However, the output and pricing decisions
of domestic rms might play a role in the magnitude and duration of antidumping duties. If the
duration of antidumping duties depends on domestic rm behavior, Matsuyama's (1990) analysis
is applicable and it may be that domestic rms delay technology adoption to maintain protection.
4
The importing country's welfare
Section 3 demonstrated that both antidumping duties and safeguard tari s can alter the technology adoption decisions of rms. We have seen that both safeguard tari s and antidumping
duties can accelerate an import-competing rm's adoption of a new technology. The question that
remains is do safeguard tari s and antidumping duties improve an importing country's welfare?
Analyzing the welfare implications of a tari in this model is complicated because di erent equilibria arise under di erent parameter values. The government's maximization problem will depend
on whether the home rm or the rm in country B adopts the new technology rst. Moreover, a
small change in a safeguard tari above or below certain threshold values ( and ) can potentially
1
2
change the equilibrium order of technology adoption. Thus, the government's objective function
need not be continuous in the tari . In this section, I brie y explore the importing country's welfare
under antidumping duties and safeguard tari s for one equilibrium order of adoption. I outline how
small changes in tari s can a ect the home country's welfare when the home rm is the rst to
22
adopt the new technology. This same approach could be used to examine how a safeguard tari or
antidumping duty a ects worldwide welfare and see how the two policies generate gains and losses
for di erent groups in the foreign countries.
4.1 Welfare under a safeguard tari
The government's problem in choosing a safeguard tari in the equilibrium in which the home
rm adopts the technology rst (t^h;sg < t~b;sg ) is given by:
max W =
sg
+
Z t^h;sg
Z0 1
t~b;sg
e
e
rs
rs
h
b
sg
w( ; ; )ds +
w(
h
;
b
; sg )ds
e
Z t~b;sg
t^
h;sg
rt^h;sg
e
rs
w(
h
C (t^h;sg )
; b ; sg )ds
(21)
where w() is the within-period welfare of the home country, equal to the sum of consumer's
surplus, pro ts and tari revenue.
The change in the home country's welfare with respect to a small change in the safeguard tari
when the home rm adopts the new technology rst is:
(+)
( )
( )
(+)
(+)
@W
@W @ t^h;sg
@W @ t~b;sg
dW
=
+
+
>0
d sg
@ sg @ t^h;sg @ sg
@ t~b;sg @ sg
(22)
Overall, a small increase in the safeguard tari improves the home country's welfare. This
welfare improvement can be broken into three components, a direct e ect, a technology incentive
e ect, and a technology disincentive e ect. These e ects are described below. The direct e ect
essentially captures the rent-shifting gains of a safeguard tari . Because the rms compete on
quantity, the home country can improve welfare by imposing a tari that shifts rents from foreign
rms to the home rm and home country's government.
The second term in (22), which I call the technology-incentive component, is also positive.
Recall from lemma 1 that the home rm adopts the new technology at an earlier date as the tari
increases
@ t^h;sg
@ sg
< 0. The e ect of a change in the date of adoption on the discounted present value
23
of welfare can be expanded as follows:
(+)
z }| {z
rt^h;sg
@W
=e
@ t^h;sg
( )
C 0 (t^h;sg ) + rC (t^h;sg )
}|
w(
h
; b ; sg )
{
w( h ; b ; sg )
The di erence w( h ; b ; sg ) w( h ; b ; sg ) is the marginal gain in instantaneous welfare associated with the home rm's adoption of the new technology. The term C 0 (t^h;sg ) + rC (t^h;sg ) is the
marginal cost of technology adoption at time t^h;sg . Because adoption of the new technology leads
to a fall in the domestic price, there are gains to domestic consumers when the home rm adopts
the new technology. Because the home rm doesn't internalize these gains to consumers when it
chooses its date of adoption, the marginal bene t to the home country of technology adoption exceeds the marginal cost to the home rm of technology adoption. Thus, the term
@W
@ t^h;sg
is negative;
the discounted present value of welfare increases if the home rm adopts the new technology at an
earlier date. As the safeguard tari causes the home rm to adopt earlier, the overall contribution
of the technology incentive component is positive.
The third term in (22), which I call the technology disincentive component, is also positive
because the home country's welfare increases when rm B delays its technology adoption. The
e ect on the home country's welfare of a change in the date of technology adoption by rm B can
be expanded as follows.
(+)
z }| {z
rt~b
@W
=e
@ t~b;sg
(+)
}|
(w( h ; b ; sg )
w(
h
{
; b ; sg ))
The di erence w( h; b ; sg ) w( h ; b ; sg ) represents the marginal decrease in the home country's instantaneous welfare when rm B adopts the new technology. Although adoption of a new
technology by the rm in country B will increase the home country's consumer's surplus, the loss
to the home rm's pro ts is larger. Thus, the term
@W
@ t~b;sg
> 0. Because the safeguard tari delays
rm B's technology adoption, the overall contribution of the technology disincentive component is
positive.
In summary, a safeguard tari improves the home country's welfare in three ways. First, it shifts
rents to the home country. Second, it accelerates technology adoption by the home rm. Third,
24
it delays foreign technology adoption. It is interesting that the safeguard tari , widely perceived
as a more \fair" instrument of protection that an antidumping duty, actually generates some of
its welfare gains for the home country by slowing down technology adoption in countries that are
technologically behind.
4.2 Welfare under an antidumping duty
In the equilibrium in which the home rm adopts the new technology before rm B, the home
country's government's problem is:
max W =
ad
+
Z t^h;ad
Z0
1
t~b;ad
e
e
rs
rs
h
b
ad
w( ; ; )ds +
w(
h
;
b
; ad )ds
e
Z t~b;ad
t^h;ad
rt^h;ad
e
rs
w(
C (t^h;ad )
h
; b ; ad )ds
(23)
where w() is the home country's welfare under an antidumping duty against imports from
country A.
The change in the home country's welfare with respect to a small change in the antidumping
duty is given by the following:
(+)
( )
( )
(+)
( )
@W
@W @ t^h;ad
@W @ t~b;ad
dW
=
+
+
d ad
@ ad @ t^h;ad @ ad
@ t~b;ad @ ad
(24)
Equation (24) is qualitatively very similar to equation (22), the change in the home country's
welfare with respect to a change in the safeguard tari . Although the magnitudes of the direct
e ect and the technology incentive e ect are di erent under an antidumping duty, the direction
is the same. Both components contribute positively to the home country's welfare. The third
term in (24) is now a foreign technology incentive rather than a disincentive. Recall from lemma
2 that the antidumping duty accelerates rm B's technology adoption. Because earlier adoption
by rm B reduces the home rm's pro ts (and the government's tari revenue) more than it
increases consumer's surplus, the term
@W
@ t~b;ad
is positive. Therefore, the foreign technology incentive
25
component is negative. Thus, the welfare e ect of a small increase in the antidumping duty depends
on which terms dominate. As the direct, rent-shifting component is likely to be larger than the
other two e ects, the overall e ect on welfare is likely positive.
Interestingly, the policy favored by domestic import-competing rms, the antidumping duty,
appears to o er smaller welfare gains to the importing country than the safeguard tari . Moreover,
although antidumping policy is often criticized as harmful to worldwide welfare, it appears to be
less harmful to foreign rms than safeguards policy.
5
Conclusion
This paper explores how the breadth of trade protection a ects the technology adoption decisions of domestic import-competing and foreign exporting rms. I nd that targeted countryspeci c tari s, like antidumping duties, can close the technology gap that arises when an exporting
rm in one country discovers and implements a new technology. Importantly, the antidumping duty
accelerates adoption by both the protected domestic rm and its foreign competitors. In contrast,
safeguard tari s can close the technology gap for domestic import-competing rms, but also open
the gap for foreign exporting rms.
One way to understand the historical pattern of the US industry's failure to innovate is to
argue that in selectively restricting imports from technologically-superior countries like the EU and
Japan, the US opened its market to rms in smaller countries that were technologically behind. By
increasing the market share of rms in countries like Korea, Turkey, and Brazil, the US increased
the incentive for rms in these countries to develop new, innovative steel plants.
A more important policy conclusion to be drawn from this paper is that broad safeguard tari s
create incentives for foreign rms to delay their technology adoption relative to what they would
choose under free trade or an antidumping duty. Interestingly, an across-the-board tari increase
could result in a loss to worldwide welfare by delaying the adoption of a new technology in other
exporting countries. This tends to lend merit to the argument of many countries that lobbied for
the creation of country-speci c safeguards tari s during the Uruguay round. Countries that have
small domestic markets and are technological followers could nd themselves falling even further
26
behind technologically if they are subjected to a safeguards tari which was instituted in the wake
of their competitor's technological improvement. Policymakers have been dismayed with the variety
of negative welfare consequences of antidumping duties and have suggested that safeguard tari s
would somehow be less prone to political abuse and would distort trade ows less than antidumping
duties. This paper suggests that multicountry safeguard tari s are not a panacea.
27
Appendix A: Proofs
Lemma 3 There exists a k 2 (0; 38 (
)) such that th < t^h and t~b < tb if qb < k .
Proof: De ne k = min[k1 ; k2 ]. The instantaneous pro t function of rm B and the rst order
conditions for g`b and gfb imply that
function of qb . For all qb
de nition of tb ,
2 (0; 38 (
@ t^b
@qb
< 0 and
@ t~b
@qb
< 0. Thus, by de nition th is a decreasing
)), t^b < t^h < t~b . By de nition of V h , de nition 1 and
@ t = 0. By the continuity and monotonicity of t^h , it follows that
= 0 and @q
there exists some qb = k1 such that t^h = th . Thus, for qb > k1 , t^h > th. By the continuity
and monotonicity of t~b , it follows that there exists some qb = k2 such that t~b = tb . Thus, for
@ t^h
@qb
b
b
q b > k 2 , tb > t~b . QED.
Proof of proposition 3
(b) Order of optimal dates under a safeguard tari . Let 1 = 32 [qb
3
8 (
)], 2 = 23 qb , and
)]. From the proof of part (a), we know that t^bsg < t~bsg and t^hsg < t~hsg
let 3 = 23 [qb + 38 (
for expressions (12), (13), (14), (15) and (16). Taking each expression in turn, consider expression
(12). I need to show t~bsg < t^hsg . By de nition 1, evaluating the partial derivative of gfb with
respect to tb (10) at its optimal value t~bsg implies C 0 (t~bsg ) + rC (t~bsg ) = B ( B ; H ) B ( B ; H ).
Thus, evaluating
H ( B ;
H)
@g`h
@th
at t~bsg yields
@g`h
@th
j
t~bsg
=e
rt~bsg
H ( H ; B )
H (
H ; B )
+ B (
B; H)
> 0 for sg < 1 . By the strict concavity of g `h (), it follows that t~bsg < t^hsg for
sg < 1 .
Turning to expression (13), it is necessary to show (i) t^bsg < t^hsg , (ii) t^hsg < t~bsg , and (iii)
t~bsg < t~hsg . From the proof of expression (12), it follows that (ii) is true for sg > 1 . For (i), by
de nition 1, evaluating (9) for i = b at t^bsg implies C 0 (t^bsg ) + rC (t^bsg ) = b ( b ; h )
Thus, substitution and direct calculation imply
@g`h
@th
t^bsg
b ( b ; b ).
> 0 for sg < 2 . By the strict concavity
of g`H (), it follows that t^bsg < t^hsg . For (iii), the partial derivative of gfh with respect to th and
the partial derivative of gfb with respect to tb is given by (10) for i = h and b, respectively. By
de nition 1, evaluating (10) for i = b at t~bsg and substituting this expression into (10) for i = h
enables one to evaluate
@gf h
@th
t~bsg
> 0 for sg < 2 . By the strict concavity of g fh , t~bsg < t~hsg .
Turning to expression (15), I must show (iv) t^hsg < t^bsg , (v) t^bsg < t~hsg , and (vi) t~hsg < t~bsg .
From the proof of expression (13) (i), (iv) is true for sg > 2 and from the proof of (13) (iii), (vi)
28
is true for sg > 2 . For (v), recall that the partial of g`b with respect to tb is given by (9) for i = b
and the partial of gfh with respect to th is given by (10) for i = h. By de nition 1, evaluating
at t^bsg and substituting this expression into (9) for i = h yields
strict concavity of gfh , t^bsg < t~hsg .
@gf h
@th
t^
@g`b
@tb
> 0 for sg < 3 . By the
bsg
Finally, turning to expression (16), I need to show t~hsg < t^bsg . From the proof of expression
(15) (v), this holds for sg > 3 . QED.
Proof of proposition 4
I proceed by analyzing a series of cases.
Case 1: Suppose sg < 1 < 1 . Then, t~b;sg < t^h;sg by proposition 3. Inspection of the best
response functions shows that the only possible intersection is at (t^b;sg ; t~h;sg ).
Case 2: Suppose sg > 3 > 2 . Then, t~h;sg < t^b;sg by proposition 3 and the only possible
intersection of the best response functions is at (t^h;sg ; t~b;sg ).
Case 3: Suppose 1 < sg < 2 . Then t^b;sg < t^h;sg < t~b;sg < t~h;sg by proposition 3. By lemma
4, for smaller tari s ( sg < 1 ) within this interval, t^h;sg > th;sg . Inspection of the best response
functions reveals that the only intersection for t^h;sg > th;sg occurs at (t^b;sg ; t~h;sg ). By lemma 4, for
larger tari s ( sg > ) within this interval, t^h;sg < th;sg . Thus, there are two pure strategy Nash
1
equilibria,
(t^b;sg ; t~h;sg )
and (t^h;sg ; t~b;sg ).
Case 4: Suppose 2 < sg < 3 . Then t^h;sg < t^b;sg < t~h;sg < t~b;sg by proposition 3. By lemma
5, for larger tari s ( sg > 2 ) within this interval, tb;sg < t^b;sg and the best response functions
can only intersect at (t^b;sg ; t~h;sg ). By lemma 5, for smaller tari s ( sg < ) within this interval,
2
t^b;sg
<
tb;sg .
Thus, there are two pure strategy Nash equilibria,
Lemma 4 There exists a 1
sg > 1 .
2
(t^b;sg ; t~h;sg )
and (t^h;sg ; t~b;sg ). QED.
( 1 ; 2 ) such that th;sg < t^h;sg if sg < 1 and t^h;sg < th;sg if
Proof: For all sg 2 ( 1 ; 2 ), t^b;sg < t^h;sg < t~b;sg by proposition 3. Further, t^h;sg = t~b;sg at 1 and
t^h;sg = t^b;sg at 2 by proposition 3. By the de nition of V h () and de nition 1,
@ t^h
@ sg
< 0. From the
best response function (11), we know th;sg 2 (t^b;sg ; t~b;sg ) 8 sg . By the continuity and monotonicity
29
of th;sg , it follows that there exists at 1 2 ( 1 ; 2 ) such that t^h;sg = th;sg . For sg < 1 , t^h;sg > th;sg
and for sg > , t^h;sg < th;sg . QED.
1
Lemma 5 There exists a 1 2 ( 2 ; 3 ) such that t^b;sg < tb;sg if sg < 2 and tb;sg < t^b;sg if sg > 2 .
Proof: For all sg 2 ( 2 ; 3 ), t^h;sg < t^b;sg < t~h;sg by proposition 3. Further, t^b;sg = t^h;sg at 2 and
t^b;sg = t~h;sg at 3 by proposition 3. By the de nition of V b () and de nition 1,
@ t^b
@
> 0. From the
best response function (11), we know tb;sg 2 (t^h;sg ; t~h;sg ) 8 sg . By the continuity and monotonicity
of tb;sg , it follows that there exists at 2 ( 2 ; 3 ) such that t^b;sg = tb;sg . For sg < , t^b;sg < tb;sg
and for
sg
> 2 , t^b;sg > tb;sg . QED.
2
2
30
Figure 1: Trade Flows in the Model
Firm A
Country A
Firm B
-
qa
qb
Ma
Mb
?
?
Home Country
6
q
Home Firm
31
Country B
Figure 2: Nash Equilibria under a safeguard tari
Panel A
t~h;sg
t^h;sg
th;sg
t^b;sg t~b;sg tb;sg
Panel C
th;sg
t~h;sg
t^h;sg
tb;sg t^b;sg
Panel B
t~b;sg
Key:
t~h;sg
thR (tb )
th;sg
tbR (th )
t^h;sg
t^b;sg
tb;sg
t~b;sg
Panel A: One pure-strategy Nash equilibrium at (t^b ; t~h ) for sg < 1
Panel B: Two pure-strategy Nash equilibria at (t^b ; t~h ) and (t^h ; t~b ) for 1 < sg < 2
Panel C: One pure-strategy Nash equilibrium at (t^h ; t~b ) for 2 < sg
32
Figure 3: A small change in the safeguard tari
thsg
tbR (th ; )
tbR (th ; 0 )
t~hsg ( )
thR (tb ; )
t~hsg ( 0 )
thR (tb ; 0 )
tbR (th ; ) tbR (th ; 0 )
tbsg
t^hsg ( )
thR (tb ; )
t^hsg ( 0 )
thR (tb ; 0 )
t^bsg ( ) t^bsg ( 0 )
thsg
33
t~bsg ( ) t~bsg ( 0 )
tbsg
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Regulatory Incentives and Consolidation: The Case of Commercial Bank Mergers
and the Community Reinvestment Act
Raphael Bostic, Hamid Mehran, Anna Paulson and Marc Saidenberg
WP-02-06
Technological Progress and the Geographic Expansion of the Banking Industry
Allen N. Berger and Robert DeYoung
WP-02-07
Choosing the Right Parents: Changes in the Intergenerational Transmission
of Inequality Between 1980 and the Early 1990s
David I. Levine and Bhashkar Mazumder
WP-02-08
6
Working Paper Series (continued)
The Immediacy Implications of Exchange Organization
James T. Moser
WP-02-09
Maternal Employment and Overweight Children
Patricia M. Anderson, Kristin F. Butcher and Phillip B. Levine
WP-02-10
The Costs and Benefits of Moral Suasion: Evidence from the Rescue of
Long-Term Capital Management
Craig Furfine
WP-02-11
On the Cyclical Behavior of Employment, Unemployment and Labor Force Participation
Marcelo Veracierto
WP-02-12
Do Safeguard Tariffs and Antidumping Duties Open or Close Technology Gaps?
Meredith A. Crowley
WP-02-13
7
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