Is the Tariff the ‘Mother of Trusts’?
Reciprocal Trade Liberalization with
Multimarket Collusion
by
Eric W. Bond
(Vanderbilt University)andConstantinos Syropoulos(Florida International University)

Current Version: February 2005

Abstract
In this paper we examine the impact of trade liberalization on collusive conduct between domestic and foreign
firms interacting in multiple markets. We establish a non-monotonic relationship between trade barriers andthe sustainability and profitability of collusion in a homogeneous product Cournot oligopoly with symmetriccountries. We show that when trade barriers are sufficiently low, the efficient cartel outcome will involvecross-hauling of goods. As a result, an increase in trade barriers makes the cartel less profitable and harder
to sustain. In particular, increases in trade barriers (from very low initial levels) may be welfare increasing
because of their pro-competitive effect. We also show that when trade barriers are sufficiently high, theefficient cartel will involve no trade. In this region, increases in trade barriers will be pro-collusive because
they protect markets from deviations by foreign firms. We also extend the analysis to consider the
implications of product differentiation.

___________________________
Eric W. Bond, Department of Economics, Vanderbilt University, VU Station B #351819, 2301 Vanderbilt
Place, Nashville, TN, 37235-1819, USA, Phone: (615) 322-3237, eric.bond@vanderbilt.edu
Constantinos Syropoulos, Department of Economics, Florida International University, University Park,
DM-321, Miami, FL 33199; Phone: (305) 348-2592; E-mail: syropoul@fiu.edu

I. Introduction
In 1899 the president of the American Sugar Refining Company, Harry Havemeyer, asserted that “The motherof all trusts is the customs tariff bill.” Havermayer’s argument was that tariff protection excludes competition
from foreign firms, and hence makes it easier for domestic firms to collude behind protective tariff walls.
Since then this remark has been frequently interjected in discussions concerning the possible benefits ofreducing tariffs as an argument in support of the pro-competitive effects of trade liberalization. However,evidence from the 1990s suggests that cartels continue to be a significant policy problem, despite thesubstantial degree of global market integration due to multilateral trade liberalization and declining
transportation costs. In particular, these cartels have frequently involved firms located in a number of different
countries and allocating their market shares internationally.1
In light of the failure of declining trade barriers to eliminate international cartel activity, we think it isappropriate to re-examine the relationship between trade liberalization and collusive activity. Although thisquestion has been addressed in the literature, the primary focus has been on the case of single market
collusion. However, the evidence suggests that multimarket agreements are prominent features of international
cartels.2 In the spirit of Bernheim and Whinston (1990), we focus on the case in which firms use multimarket

1

A report by the WTO (1997, Chapter 4) concluded that “...while the extent of cartel activities is
intrinsically difficult to assess ... there are some indications that a growing proportion of cartel agreements areinternational in scope.” An additional source of evidence is the significant number of international cartels prosecutedby the US Department of Justice in the 1990's. Examples of international cartels involving U.S. and foreign firms thatwere successfully prosecuted include a food and food additive cartel (operating from 1991 to 1995), a vitamin cartel(1990-1999), and a graphite electrodes cartel (1992-1997). The U.S. Department of Justice (2000) reports thatprosecution of participants in the food and feed additives cartel resulted in the imposition of a $100 million fine on theArcher-Daniel Midlands company, a U.S. firm, and a $50 million fine on a subsidiary of a German firm. In 1999, thegovernment collected a record fine of $500 million from F. Hoffman-La Roche, a Swiss company involved in aconspiracy to fix the price of vitamins. The significance of these cartels is reflected in the fact that the fines fromthese prosecutions accounted for more than 90% of the fines imposed in criminal antitrust cases annually.
2

The citric acid cartel, which consisted of 5 firms from 4 different countries, illustrates the sophistication ofsome recent cartel arrangements. Top executives of the companies initially met to set up the cartel; then, lower level
executives worked out the details on product prices and market shares (to the tenth of a decimal point) that eachcompany was allowed to earn in each market; companies then shared market information to verify that participating
members had complied with the agreement. If firms exceeded their market shares, they were required to purchase theexcess from another firm that had not met its assigned market share.
It is also worth noting that the use of multimarket collusive agreements in international cartels is not new. For1contact to sustain more profitable outcomes than would be possible by separate agreements covering
individual markets. More specifically, we study the relationship between trade barriers (i.e., imports tariffs
or transportation costs) and the profitability of collusion in the context of a symmetric, two-country modelof homogeneous-goods oligopoly with firms interacting in their (segmented) domestic and export markets (asin Brander and Krugman (1983)). We treat the trade barriers that separate the two markets as parameters, andexamine how (equal) changes in their (common) level affect the maximum global profits firms can sustain
in a collusive multimarket agreement.
An important feature of our work is its emphasis on how efficient output allocations vary with the levelof trade barriers. When trade barriers are high, the most profitable cartels are those that adopt a geographic
allocation of outputs in which each country’s firms serve only their own market. At that level, increases intrade costs typically enhance the profitability of collusion because they make deviations in foreign export
markets less appealing. When trade barriers are low and deviation constraints are not binding, the mostprofitable allocations necessitate the “cross-hauling” of goods. This finding is driven by the fact that firms’
deviation incentives are convex in their output assignments to domestic and foreign markets, which implies
that the agreements with the lowest deviation incentives “smooth” output levels across markets by allocating
firms similar market shares in each market. We show that this tension between the sustainability andprofitability of agreements generates a non-monotonic relationship between trade costs and cartel profits whenfirms punish deviations through reversion to the Nash equilibrium of the single-period game. When goods
are perfect substitutes and the incentive constraint is binding under free trade, an increase in trade costs causes
cartel profits to decline because trade becomes more costly under the agreement. However, higher trade costs
also increase the likelihood of firms being able to sustain an agreement with no trade, the most profitableagreement. Thus, when trade barriers are sufficiently high, further increases in them facilitate collusion.

example, one of the earliest international collusion cases was a tobacco cartel in which U.S. and British firms agreed
to stay out of each other’s domestic market and divide shares in third country markets (U.S. vs. American Tobacco(1911)). See Bond (2002) for additional discussion of some of the legal and antitrust issues involved in international
cartels.
2

These findings suggest that reciprocal trade liberalization in the presence of multimarket collusion canhave important implications for welfare.

We show that when trade barriers are initially low, tradeliberalization may be welfare-reducing due to its pro-collusive effect. Interestingly, this result holds no matter
whether trade costs take the form of tariffs or transportation costs; therefore, trade liberalization and market
integration are not substitutes for active competition policy. In contrast, when barriers are initially high, tradeliberalization is welfare-improving because cartel members find it less appealing to specialize in selling totheir local markets; that is, it is more difficult for firms to engage in geographic collusion. In short, therelationship between national welfare and trade barriers is non-monotonic.
Our results on the effects of reciprocal trade liberalization differ from those obtained when home andforeign firms collude in a single market. A prominent paper in this area is Davidson (1984), which examined
the impact of tariff policy on collusion with firms interacting in quantities in a single homogeneous goods
market. In this setting, tariffs affect firm incentives asymmetrically because they render deviations more
attractive for the home country firm but not for the foreign firm. To maintain collusion, a unilateral tariff
reduction requires cartel output to be reallocated from home firms to foreign firms. Assuming that firms adjust
quantities to maintain total output at the monopoly level, Davidson showed that a tariff reduction at high tariff
levels facilitates collusion. The reason for this is that foreign firms do not earn enough profits at such tariff
levels to be able to compensate domestic firms for their increased incentive to violate the cartel agreement;
however, at low tariff rates they do.3 Our analysis differs from Davidson’s in that, with multimarket contact,
reciprocal trade liberalization affects collusive incentives symmetrically, with each firm thus being favorably
affected in its export market but not in its home market. Reciprocal tariff changes do not have redistributive
effects within the cartel, but they may change the efficient market-sharing agreement.

3

Our model also

In similar spirit, Rotemberg and Saloner (1989) compared the effects of tariffs and quotas with repeatedprice interactions between a domestic and a foreign firm. Placing cost asymmetries between firms at center stage,
Fung (1992) studied the effects of economic integration (captured by a unilateral tariff reduction) on critical discountrates and through that on collusive conduct in a differentiated-goods model with price competition. Syropoulos(1992) examined how tariffs and quotas affect the sustainability of collusion among quantity-setting foreignoligopolists (with no domestic producers).
3extends existing work on multimarket collusion by providing a comprehensive analysis of how tradeliberalization affects the profitability of cartels and welfare. Bernheim and Whinston (1990) established thatthe presence of trade barriers between markets may render multimarket agreements more profitable thanagreements arranged on a market by market basis.4 Our analysis differs in that we take as given the benefitsof multimarket collusion and consider how market shares, profits and welfare respond to changes in the levelof trade barriers.5
Section II of the paper presents the basic model for the case of homogeneous goods. We begin byanalyzing the case of an international duopoly under very weak restrictions on punishment schemes. In thissetting, we generate two main results. The first is that the minimum discount factor (i.e., the smallest discountfactor that is capable of sustaining the monopoly profit level) is discontinuous at zero trade costs. This isimportant because it implies the existence of a range of actual discount factors under which the eliminationof trade barriers enables firms to sustain full collusion. The second result is that the minimum discount factor
approaches zero when trade barriers approach their prohibitive level. These results establish a collusion
facilitating effect of trade liberalization at low levels of trade barriers and a collusion undermining effect at
sufficiently high trade barrier levels. To ascertain the robustness of these findings, we then extend the analysis

4

Pinto (1986) extended the Brander-Krugman framework to study how repeated firm interactions may
affect collusive conduct and showed that, in the presence of trade costs, the monopoly payoffs can be sustained bygeographic allocation of markets.
5

In a related paper, Colonescu and Schmitt (2000) investigated how the move from a regime of “market
segmentation” (where firms can price discriminate between domestic and export markets) to a regime of “economic
integration” (where price discrimination is impossible) affects competitive conduct via its impact on minimum
discount factors. Their analysis revealed that the transition to market integration is pro-competitive or anticompetitive depending on the degree of (dis)similarity of product markets. Our analysis differs in that we areconcerned with the implications of reciprocal cuts in trade costs on incentive constraints and collusive outcomes, andconsider circumstances under which collusion does not necessarily lead to the elimination of trade flows. Lommerud
and Sørgard (2000) also investigated the effects of reciprocal tariff cuts on multimarket collusion under repeatedquantity- and price-setting games by symmetric homogeneous good duopolists. However, these authors were mainly
concerned with the effects of trade liberalization on minimum discount factors and did not study the exact
circumstances under which incentive constraints are binding for firms and what that may mean for geographic
collusion and welfare. Olson and Mason (1996), considered a model similar to ours to explore the effects of a priceceiling in one market on multimarket collusion when incentive constraints are binding. They showed that a mild priceceiling in one market can cause firms to behave more collusively in the unregulated market.
4

to the oligopoly case with an arbitrary number of firms in each country. We conclude Section II with asimulation analysis (using permanent reversion to the Nash equilibrium of the single-period game aspunishment) that illustrates further the effects of trade liberalization on minimum discount factors, global
profit levels, and national welfare. Section III extends the analysis to the case of imperfect substitutes, andSection IV concludes. The formal proofs of propositions can be found in the Appendix.

II. The Model with Homogeneous Goods and Quantity Competition
To examine the issue of reciprocal trade liberalization with multimarket contact, we consider a symmetric twocountry Cournot oligopoly model of trade. For clarity, we label the two countries “home” and “foreign”. We
begin with the case in which there is a single firm in each country producing a homogeneous good. Later we
extend the analysis to consider more firms and product differentiation. Our assumption of symmetry is
embodied in the assumptions that all firms have constant and identical marginal costs, and each country i hasa linear inverse demand function, whererepresents the total quantity sold in it. Without lossof generality, we normalize marginal costs to zero. However, a firm’s involvement in world trade is costly:for each unit of output a firm ships abroad, it incurs a trade cost t.6 The important point is that trade barriers
segment national markets and introduce an asymmetry in the costs of delivering goods at home and abroad.
Letdenote the quantity a firm from country i sells in its own market andexport market. It readily follows that firm i will earn a profit of
in its export market, for given quantities
cooperative equilibrium, firm i chooses

in its own market andchosen by its rival firm

to maximize global profits, given

to show that, under the above assumptions, we will have6

the quantity it sells in its

and. In a non-

. It is straightforwardin the one-shot Nash equilibrium,

Trade costs could be identified either with specific import tariffs or with transportation costs. We abstractfrom the unilateral use of trade barriers for strategic policy purposes and assume that changes in trade costs are due toeither due to technological change or to reciprocal tariff reductions that affect trade partners symmetrically.
5

so we may drop country subscripts and focus on the output decisions of a representative firm. Thus, letting
superscript N identify Nash equilibrium values, we obtain

Lemma 1: The Nash equilibrium outputs,

and global profits,, can be described asfollows:
If

a)

then

in t and minimized at
Ifb)

Furthermore,is strictly convex

.

then

As in Brander and Krugman (1983), the Nash equilibrium is characterized by the cross-hauling ofidentical products, provided, of course, the trade cost t is less than the prohibitive level,. For low trade

cost levels, an increase in t reduces global profits because export markets are sufficiently important to firms.
However, when trade cost levels are high, firms earn most of their profits in their home market and thus
benefit from increased protection. Global profits are maximized when the trade cost level is at or beyond
because firms are better off with a monopoly in their own market than with a duopoly in every market.

A. Collusion with Multimarket Contact - The Duopoly Case
We now consider the possibility of tacit collusion with firms setting quantities in domestic and export markets.
As in Bernheim and Whinston (1990), we suppose firms engage in multimarket collusion by allocating to eachfirm a pairthat reflects the outputs q and x targeted for sale in the domestic and export markets,

respectively. 7 Since all firms face identical conditions in the two markets, once again, we may treat firms from

7

Spagnolo (2001) showed that, in cases where a deviation in one market raises the payoff to deviation inanother market, multimarket agreements may yield lower profits than single market collusive arrangements. Thispossibility does not arise in our model because the assumption of constant marginal costs makes deviation payoffs
independent across markets.
6different countries symmetrically and focus on the payoff of a representative firm. In particular, if a firm
deviates from the collusive arrangement in any one market it gets punished in all markets.
The global profit of a firm under an agreement

is

,

where

is concave in(1)

and decreasing in t. It is straightforward to verify that, in the special case ofno trade barriers (i.e., when t = 0), cartel profits are maximized for any combination of output levels that
. However, for any t > 0, cartel profits are maximized by choosing

satisfy

and x = 0.

Since under this arrangement every firm produces the monopoly output is its home market and sells nothingabroad, we refer to it as maximal geographic collusion. A key benefit of multimarket contact is that firms
can reallocate shares across markets to the lowest cost producer so as to minimize total cartel costs.
If firm i deviates from a collusive agreement in its own (export) market that specifies an output of x (q)for its rival, firm i’s deviation profit in that market will be. Since a firm that violates a collusive agreement has an incentive
to do that in all markets, its payoff to deviating from a cartel output paircan be obtained by summing

the deviation payoffs across all markets; that is,.

Clearly,

is decreasing in t and strictly convex in(2)

for all output pairs that yield non-negative profits

in each market.
We assume that, in the event of a deviation, an agreement calls for a “credible” punishment in whichfirms switch to a subgame perfect equilibrium of the repeated game that forces the deviating firm to attain a7

lower payoff. Denote withthe representative firm’s discount factor, and with

global payoff during the punishment phase. Then, for a given t, an agreement

its per period

will be sustainable if.
(3)

The Nash equilibrium payoff characterized in Lemma 1 is a natural punishment. However, as has beenemphasized by Abreu (1988) and others, the cartel could support more profitable agreements by choosing
more severe punishments. In order to identify results that do not depend on the particular form of punishment
considered, at this point we assume that the chosen punishment payoff satisfies. (We examine thecase of Nash punishments later.)
An efficient cartel agreement will maximize the payoff to a representative firm over the setof incentive-compatible output levels. The following
result, proven in the Appendix, establishes that efficient agreements can be characterized using standard
Lagrangian methods and provides some useful properties of efficient cartel agreements.

Lemma 2: If
with
a)

for

,

is a convex set and contains a collusive agreement.
The first-order conditions (FOCs) for maximizing.

are necessary and sufficient for a cartel agreement to be efficient.
b)

The efficient cartel agreement,(i)

If t > 0, then, has the following properties:

.

8

(4)

(ii)
c)

If t = 0, then q * = x * $ A/4, with strict equality if.

The maximum sustainable profits for a cartel member,, is continuous

in t.

At an interior solution with a binding incentive constraint, the FOCs associated with the Lagrangian in. (Subscripts q and x denote partial derivatives.) It can be seen from direct(4) requiredifferentiation ofin (1) and ofwhen t = 0. Intuitively, this is so because the strictin (2) thatconvexity of the deviation payoff inmakes it attractive for the cartel to “smooth” outputs across markets

when the incentive constraint is binding. As a result, there is cross-hauling of identical products in a collusive
agreement when t = 0 and the incentive constraint is binding. When t > 0, this cross-hauling becomes costly
and thus the cartel finds it more profitable to assign larger output shares to the domestic firm in each market.
However, for small trade costs, the no deviation constraint may prevent the representative firm from going
all the way to the most profitable collusive agreement associated with complete geographic specialization.
This suggests the existence of a trade-off between incentive compatibility and profitability in the allocationof market shares when t > 0. The continuity of global profit,, in t follows from Berge’s maximum

theorem.
Having established the existence and form of profitable cartel agreements, we now turn to the questionof how the sustainability and profitability of cartels are affected by the level of trade costs. We begin byexamining how the trade cost level affects the ability to sustain the monopoly profit level,, in eachmarket. When t > 0, cross-hauling is costly and the only way to capture the monopoly profit level is to choose
and x = 0. Since

maximal geographic collusion, i.e.,itfollows

from

(3)

that

the

monopoly

output9

is increasing in
will

be

sustainable

for

for

,

. We refer toas the minimum discount factor that isnecessary to sustain the monopoly output level. For the case in which punishment involves permanent
reversion to the Nash equilibrium,. In that case the minimum discount factor

is monotonically decreasing in t, withas

. For the more general case, where thepunishments are only required to be continuous in t and to satisfy, the minimum discount factor

will not necessarily be monotonic in t. However, we can establish that, even in this more general case, we will
have

as

The result thatcollusion. For any.8asestablishes a sense in which very high trade cost levels facilitate, it is possible to find a trade cost level in the neighborhood ofthat allows firms

to attain the maximal collusive profits. High trade costs facilitate collusion because they discourage theforeign firm from entering the market when the home firm charges the monopoly price. The observation thatvery high trade costs (tariffs) facilitate multimarket collusion is in line with the conventional wisdom aboutprotectionism and collusion. What may be more surprising is that there is also a sense in which tradeliberalization can facilitate collusion when trade barriers are low. To see this note that, for t = 0, cross haulingof goods is costless and. Lemma 2b(ii)can be attained with any allocation that satisfies

shows that with t = 0, the most efficient cartel agreement requires setting q = x = A/4 when the no deviation
constraint is binding.

8This means that at t = 0 the minimum discount factor for supportingis. It follows from the strict convexity ofand, thenIf, thenfollows from the observation that

follows from the fact that
10

and

. If
.

its symmetry at t = 0 that

. Therefore,punishments, we have<

. With Nash

. The downward jump in the minimum

discount factor at t = 0 reveals a sense in which trade liberalization may facilitate collusion: collusion can besustained for a wider range of discount factors at t = 0 than for positive tariff rates in the neighborhood of t
= 0.
Since some transportation cost frictions are likely to remain even when tariff barriers are completely
eliminated, one might be tempted to view this discontinuity in the minimum discount factor at t = 0 as atheoretical curiosum. However, this discontinuity reflects the fact that cross-hauling of goods makes acollusive agreement easier to sustain. When the incentive constraint is binding and t is not too high, theefficient collusive agreement characterized in Lemma 2 will involve x > 0. As a result, a reduction in t shouldmake the collusive agreement more profitable for the cartel in this region. This intuition can be formalized
by considering. Since,in this interval. However, the fact thatis continuous in t means that there will exist aandsuch thatfor;9 thus, starting from any t in this interval, the elimination of trade costs will raise cartel profits.
We may summarize these results as follows:

Proposition 1: Assume thatis continuous in t andfor any discount factora)sustainable for

9

The continuity of. Choosing. Then,, there will exist an

such that the monopoly profit,;

and the result thatasensures the existence of a t such thatto be the smallest value of t satisfying this condition, it follows from the definition of theminimum discount factor that monopoly profits will be unsustainable for
11

.

, is

b)

there exists a set of discount factors,

costs,

for any, and a non-empty interval of trade, such thatis sustainable for t = 0 but not for

The elimination of trade barriers will raise cartel profits if

and

.

.

The intuition for part (b) follows from the fact that the easiest agreements to sustain are those thatinvolve cross-hauling of goods in order to reduce the deviation incentives, which follows from the convexityof the deviation payoffs. If trade costs are not too high, the firm will still find it profitable to engage in crosshauling in an efficient agreement. Trade liberalization will thus benefit the cartel members by reducing thecost of this cross-hauling. When trade costs become sufficiently high, however, the cartel will find it
profitable to use maximal geographic collusion. With only one firm in each market, maximal geographic
collusion can be used to sustain

for sufficiently high t.

It is important to point out that Proposition 1 is robust to relaxation in the assumption that the demand
curve is linear. For the case of a general inverse demand function,, we can express a firm’s deviation, where Y is the aggregate output of all other firms, and y and t are

payoff as

the firm’s output and trade cost, respectively, in a given market. Let
deviation. Differentiation ofyieldssinceconvexity of the deviation payoff follows from the fact thatgeneral case,denote the firm’s optimal. When demand is linear, theis constant andis decreasing in Y. In the> 0 because the denominator is negative by the second-ordercondition on the choice of y. It follows that the deviation payoff will be convex in the general demand caseas well. Thus, as long as the inverse demand function is such thatis concave, the results of Lemma

2 and Proposition 1 will hold.
We can also use Lemma 2 to say something about the effect of trade liberalization on profits in the12neighborhood of t = 0 forwhen t = 0 and. Lemma 2(b) establishes that the efficient cartel agreement will have
. Through appropriate differentiation of the Lagrangian in (4), the effect of a change

in trade costs on global profits is,where payoffs are evaluated at the constrained efficient pair
expression are conflicting when

(5)

. The first two terms of the above. An increase in trade costs reduces the payoff under the collusive

agreement, but it also reduces the incentive to deviate from it. We know from the first-order condition forthe choice of q that

. If we substituted this expression into the first two terms andevaluated expressions in the neighborhood of the efficient cartel at free trade, we would obtain.

(6)

Clearly, the above expression will be negative for cartel output levels that are below the Nash equilibrium
level. Therefore, in the neighborhood of unimpeded free trade, the negative effect of the trade cost increaseon the agreement payoff dominates the effect on the deviation payoff. It then follows from (5) that an increasein the trade cost, t, will reduce global profits as long as t does not force the punishment payoff to fall too
rapidly. Stronger results on the effects of tariff on cartel payoffs require explicit assumptions about thepunishment payoffs.

B. Collusion with Multimarket Contact - The Oligopoly Case
The analysis above can be readily extended to the case in which there are n > 1 firms operating in eachcountry. We retain symmetry by assuming that the number of firms in each country is the same, and let q (x)13denote the output of a representative firm from each country in its domestic (export) market. The total output
in each market will then be Q = n(q + x). In this section we indicate how the results of Proposition 1 areaffected when n > 1.

Lemma 3: The Nash equilibrium withfirms can be characterized as follows:a), thenandb), thenand.

As in the duopoly case, profits in the Nash equilibrium will be convex in t and the maximum Nash profit
will occur when

. Furthermore, firms may benefit from multimarket collusion whenever the Nashequilibrium profit

is less than the monopoly profit

Lemma 1 is that

. The primary difference from the findings inwhen n > 1. This means that there will continue to exist gains from collusion

even when the tariff is prohibitive, because there is still room for the domestic firms to coordinate theirproduction plans (i.e., reduce domestic output).
The agreement and deviation payoffs for this case are given by

(7)

14

The agreement payoff,, is concave inand the deviation payoff,, is convex in. It is shownin the Appendix that the results of Lemma 2 extend directly to the case of n > 1 firms in each country. In> A/(4n) for t =particular, when the no deviation constraint is binding, the efficient cartel will have

0. Cross-hauling of goods will continue to be a component of efficient cartel agreements when trade costs
are low in order to facilitate collusion. This suggests that trade-liberalization will continue to have a procollusive effects when tariffs are low and the no deviation constraint is binding on the cartel. It can be shownfor n > 1. Thus, as in Proposition 1(b), we can construct an interval such that thethatelimination of trade barriers will raise cartel profits.10
The result that a trade costs allow the cartel to sustain monopoly profits in an international duopoly wasfor n=1 and sufficiently high t. This result followed from the fact that aobtained by showing thatprohibitive tariff eliminates the incentive to deviate from the cartel equilibrium with maximal geographic
collusion when n = 1 (i.e.,as). With n > 1, a deviating firm will

earn profits by cheating both on its allocation in the export market and on its allocation in the domestic market.
A sufficiently high trade cost can drive the gain to deviating in the foreign market to zero, but there will still
exist gains from deviating against the other domestic firms in the local market. As a result,must besufficiently high to sustain collusion between domestic firms even when trade costs are prohibitive. Because
the cartel has to worry only about deviations by the n domestic firms when dividing up the market, this doessuggest a sense in which prohibitive tariffs make collusion easier. This idea can be formalized if we assume

10

For t = 0, the cartel that yields

allocates each firm

units in each market and the minimum. When t > 0, thediscount factor isefficient cartel allocates each firm

units in its domestic market and 0 in the export market. In this case, theminimum discount is. The result

follows from the convexity ofin. It should be noted that the construction of an interval
analogous tothe one in Proposition 1(b) involves a slightly different argument for n > 1, because we cannot be sure that there
exists a t satisfying

for all. If no such
15

exists, then=.

that the punishment involves permanent reversion to the Nash equilibrium. With t = 0, we can use Lemma
3 and (7) to obtain. The trade cost required to deter deviations iswhich yields. Utilizing this result andyields,from Lemma 3. Comparing these two discount factors we have

for

, so

is easier to sustain for sufficiently high tariffs.

The above ideas can be used to obtain the following result on the pro-collusive effects of tradeliberalization when trade costs are low, and the collusive effects of protectionism when trade costs are high.

Proposition 2: Suppose there are n > 1 firms in each country.

a)

If

b)

If

, the monopoly profit,and, is easier to sustain foris continuous in t, there will exist a set of discount factors,, and a non-empty interval of trade costs,

such thatthan for t = 0.

is sustainable for t = 0 but not forwill raise cartel profits if

andfor any,. The elimination of trade barriers.

It is worth noting that the trade costs that is required to deter deviation in the export market with n = 1). In contrast, when n > 1, theis equal to the prohibitive tariff in the Nash equilibrium (i.e.,tariff required to deter deviation in the export market exceeds the tariff that prohibits trade in the Nashequilibrium described in Lemma 3 (i.e.,).

with n > 1.

16

This follows from the fact that

C. Multimarket Collusion with Nash Punishments
The results so far have concentrated on the analysis of the effects of trade barriers on collusion in theneighborhood of the extreme value of t = 0 and. It is clear from (5) that in order to derive results on

the effects of trade barriers on firm profits for

we must make a specific assumption about thepunishment payoffs. In this section, we suppose the punishment takes the form of permanent reversion to the
Nash equilibrium of the one-shot game. We first establish that trade liberalization facilitates collusion in theneighborhood of t = 0. Then, we use simulations to illustrate how changes in trade costs, t, affect theminimum discount factor that supports the maximum sustainable global profit,
welfare for, and the level of national. Since tariffs generate revenues while transportation costs do not our discussion of

welfare explicitly considers both types of trade costs.

Proposition 3: If the no deviation constraint is binding and punishments take the form of permanent
reversion to the Nash equilibrium of the one shot game, then the constrained-efficient global profit isdecreasing in t in the neighborhood of t = 0 (i.e.,).

Fig. 1(a) illustrates how the minimum discount factor varies with t for n = 1, 2, 3 under the assumptionthat A = 10. For n = 1, the minimum discount factor is discontinuous at t = 0, and, as pointed out

in Proposition 1. With Nash punishments, we obtain the further result that the minimum discount factor ismonotonically decreasing infor n =1. Fig. 1(a) also illustrates that there is also a discontinuity

at t = 0 when n = 2, 3, as noted in Proposition 2. However, the size of the range of this discontinuity decreases
with n.11 This suggests that, with Nash punishments, the favorable effect of trade liberalization on collusion

11

For example, when n = 5, the aforementioned range becomes (.7515, .7538).
17

is most important when the number of firms in the market is fairly small. Furthermore, Fig. 1(a) reveals that,for n = 2, 3, the minimum discount factor at A/2 is less than that at t = 0, as indicated by Proposition 2(a).
is not monotonic on (0, A/2) for n = 2, 3. The reason for this can be seen by

Note, however, thatdifferentiatingin the case of complete geographic specialization, which yields(8)Since there is no trade with geographic specialization, increases in t have no effect on. Higher levelsof t reduce the gains from cheating by selling in the export market, and this tends to reduce the minimum
discount factor. However, this effect could be offset if the punishment payoff is increasing in t. It can be seenfrom Lemma 3 that the Nash equilibrium payoff is increasing in t in the neighborhood of the prohibitive tariff,, in the Nash equilibrium. This accounts for the spikes in the minimum discount factor at

A/(n+1) for n = 2, 3. For

and, the minimum discount factor must be decreasing in t because.

A second way to characterize the effect of trade costs on collusion is to identify the dependence of(constrained optimal) global profits,, on trade costs t. Fig. 1(b) illustrates the relationship between

and t for a sufficiently low discount factor

that ensures the monopoly output is not sustainable at t

= 0. This value lies below the ranges identified in Propositions 1(b) and 2(b) under which the elimination of
trade barriers raises profits for some interval of t. The impact of trade barriers on profits in this case was
identified in (5) and (6), which showed that an increase in t will reduce profits in the neighborhood of t = 0
if the punishment payoff is non-decreasing in t. However, Lemmas 1 and 3 showed that the Nash equilibrium
18

payoff is strictly decreasing in t for. Therefore, these two effects are conflicting in the case of

Nash punishments. Numerical analysis reveals that profits are decreasing in t in this region, so the former
effect dominates. The simulations also reveal that the negative effect of trade costs on cartel profits isstrongest when the number of firms is small. This is consistent with the result obtained for the minimum
discount factors that the pro-collusive effect of trade liberalization is largest when the number of firms issmall.
The efficient agreements underlying the payoffs in Fig. 1(b) involve export sales for t = 0, as establishedin Lemma 2. The optimal level of export sales will be decreasing in t up to the point where exports are
eliminated, which occurs at t = .775 for n = 1 and t = .275 for n = 3. Since

for t exceeding the value

for which exports are eliminated, it can be seen from (5) that a sufficient condition for global cartel profits
to be increasing in t when firms sell only in their own market is that the punishment payoff be non-increasing
in t. Since the Nash payoffs are decreasing in t in the neighborhood of these critical values for t, cartel profits
will be increasing in t. This is captured in Fig. 1(b) by the fact that increases in trade costs raise cartel profits
for intermediate values of trade cost levels. For n=1, geographic specialization yields the monopoly profit
level for. For n=2 monopoly profits can also be attained for some values of t, but for n=3 theincentive to deviate is sufficiently large that constrained-efficient profits are below the monopoly profit level
for all t.

Also note that for n=2 and n=3, profits have a local minimum at the respective values of. This is due to the sharp increase in the punishment payoff in the neighborhood of> 1, which was also responsible for the local maximum infor nin Fig. 1(a) for n > 1.

Overall, these results indicate a non-monotonic relationship between the level of trade costs and the
maximum sustainable profits under collusion when firms use reversion to the static Nash equilibrium as thepunishment. One feature of these figures is the U-shaped relationship between profits and trade costs
suggested by the discussion of (6) for cases where the effects of tariffs on punishments is not too large. Trade19cost increases reduce profits in the neighborhood of t = 0, where there is significant trade, but raise profits
when t is sufficiently high and, as a consequence, there is substantial geographic specialization.
The simulations also illustrate an additional effect resulting from the use of Nash punishments for n >1, which is that profits have a local minimum at. In this neighborhood, the punishment effect in (5)dominates the first two terms. Finally, the simulations capture the idea that the global maximum for the cartel
will occur at trade costs that are sufficiently high to permit a large degree of geographic collusion.
We conclude our analysis by considering the impact of reciprocal trade liberalization on national welfare
when firms engage in multimarket collusion. These results can then be compared with the benchmark case of
the one-shot Nash equilibrium explored in Brander and Krugman (1983). We consider two cases: one inwhich the trade cost t represents tariffs, and another in which t represents transportation costs.
When trade barriers take the form of tariffs, national welfare, W, can be expressed as the sum of
consumer surplus, global profits, and tariff revenue:(9)

The second equality in (9) is due to the fact that, with symmetric countries, the tariff revenues collected by
the home country government from foreign firms is exactly equal to the loss of export profits to the foreign
treasury in the export market. Thus, in equilibrium, the aggregate welfare measure is simply the area under
the home market demand curve. Trade liberalization will raise domestic welfare if and only if it results in a
reduction in the domestic price. It immediately follows from Lemmas 1 and 3 that welfare in the one-shot
Nash equilibrium is monotonically decreasing in t, because industry output
in t.
20

is decreasing

Fig. 2 illustrates the relationship between welfare and tariff levels under constrained efficient
multimarket collusion using the same parameter values as in Fig. 1. One particularly interesting feature is thatfor

, national welfare is maximized at a positive tariff. In the neighborhood of t = 0, increases in thetariff have two conflicting effects on output. One is that the total cost of exports rises, which tends to reduce
output. The other is that the tariff makes it more difficult to sustain the cartel, which tends to increase output.
The simulations illustrate that, for, this effect is non-monotonic, with total output initially falling andthen rising to a higher level as the tariff increases. This non-monotonicity is also present for, but inthese cases global welfare is maximized at t = 0. These results yield a significant difference between the noncooperative case, where welfare is monotonically decreasing in t, and the constrained-collusive case becauseof the effects of changes in tariffs on the sustainability of collusion.
In the case where trade barriers take the form of transportation costs, national welfare will equal thevalue in (9) less the transportation costs associated with imports; that is,. The cross-hauling ofgoods is more costly to national welfare in this case, because trade uses up real resources and no longer
transfers revenues to the government. Brander and Krugman (1983) find that this yields a non-monotonic
relationship between welfare and trade barriers under non-cooperation. In this case, trade is beneficial because
it makes markets more competitive; however, trade is also socially costly because it absorbs resources for twoway trade in identical products. Brander and Krugman prove that: (i) the former effect dominates when t islow (thus, welfare is decreasing in t in the neighborhood to t = 0); (ii) the latter effect dominates fortransportation costs close to the prohibitive level (thus, welfare is increasing in t in the neighborhood of);and (iii) welfare is maximized at t = 0.
The relationship between national welfare and transportation costs under multimarket collusion isdepicted in Fig. 2 for the same parameter values considered in Fig. 1. When trade costs are sufficiently high,so that firms choose to engage in maximal geographic collusion, there is no essential distinction between

21

tariffs and transportation costs because there are no tariff revenues. Consequently, in this case, the relationshipbetween national welfare and transportation costs is identical to the obtained earlier with tariffs. However,when trade costs are sufficiently low, so that cross-hauling is absent (i.e.,), welfare in the presence oftransportation costs is strictly lower than welfare in the presence of tariffs, as indicated in Fig. 2 by the thinnercurves labeled. As in Krugman and Brander (1993), welfare is increasing in t in the neighborhood of theprohibitive level. However, unlike Krugman and Brander, welfare is not necessarily maximized at t = 0, or
decreasing in transportation costs in the neighborhood of t = 0 because, as was pointed out earlier, tradeliberalization at low trade costs facilitates collusion.12
Fig. 2 reveals that, when firms engage in multimarket collusion and the number of firms is small, totally
free trade may not yield the highest level of welfare, regardless of whether trade barriers take the form oftariffs or transportation costs. This contrasts with the case in which firms behave non-cooperatively (where
welfare is maximized at t = 0), and thus substantiates the potentially adverse welfare effect of globalization
due to its pro-collusive effect when t is small. Of course, these exercises have assumed the absence of acompetition policy aimed at deterring collusion. If an effective competition policy, capable of detecting
collusion is in place, the Nash equilibrium quantities described in Lemma 1 will be observed and welfare will
be maximized at t = 0. 13 These results suggest that reciprocal trade liberalization will not be a substitute forcompetition policy in the presence of collusive behavior of this type. To realize the gains from tradeliberalization countries will have to use an appropriate competition policy.

12

For the simulations with n = 1, the point that minimizes global profit occurs when transportation costs are
7.9% of the collusive price. The maximum welfare point occurs when transportation costs are 11.7% of themonopoly price. These values are above the average freight rates that are typically calculated for the U.S. (forexample, Hummels (2001) calculates a weighted average freight rate of 3.8% for all U.S. trade), which suggests thatcurrent transport cost barriers are sufficiently low for this effect to be important.
13

An even higher welfare level than under free trade could be achieved by using subsidies that induce firms
to produce at the competitive level, A/n.
22

III. Imperfect Substitutes
We now extend the model to consider the case in which products are imperfect substitutes on the demand side.
As before, there are two countries with n firms in each country and each firm having a zero marginal
production cost. The inverse demand function of good i sold in market k is

, wherecaptures the degree of substitutability between any two goods. This demand function maintains theequal size of the two markets and imposes symmetry between home and foreign firms by requiring an equal
degree of substitutability between all products.
The following lemma summarizes the key properties of the payoff functions:Lemma 4: In the Cournot oligopoly model with symmetric trade barriers anda)global profits,

in the Nash equilibrium, are strictly convex in t and minimized at

;

b)

;

c)

global profits

under an agreementd)global profits

under the optimal deviation from an agreement

convex inare strictly concave in;are strictly.

Lemma 4 indicates that the convexity and concavity properties of the payoff functions are preserved
when we allow for imperfect substitutability. However, there are two differences that deserve some emphasis
23here because they play an important role in the results we report below. The first is that, with imperfect
substitutability, the Nash equilibrium profits could be maximized at free trade if

is sufficiently small. When

products are relatively poor substitutes, the gain in profits on domestic sales from a prohibitive tariff is not
as great as the loss of sales in the foreign market. The second difference is that, for t > 0, the agreement thatmaximizes cartel profits will not necessarily involve complete geographic specialization. Specifically, theprofit-maximizing cartel outputs are(10)

The strict concavity offormakes it desirable for the representative firm to continue selling inboth markets when t is not too large. In this case, the elimination of trade is more costly for the cartel because
the goods of domestic suppliers are imperfect substitutes for the goods of foreign suppliers. It can be shown
that, with, the Nash equilibrium quantities will exceed the constrained-efficient quantities for all n

and t.
As in the previous section, we can define

to be the set ofpairs satisfying the no

deviation constraint (3). Arguments similar to those used in Lemma 2 can also be used here to establish that
there will exist a unique agreement that maximizes cartel profits subject to the incentive constraint. Thisagreement will have the property that

if t > 0, andif t = 0. With imperfect

substitutability and t = 0 there are two reasons for firms to equalize their market shares: deviation incentives

24

are lower and payoffs are maximized when market shares are equal. For, the cartel will choose toallocate larger output shares to domestic firms in each market, as in the case with perfect substitutability.
One difference that arises between the results of Propositions 1 and 2 and those obtained withis that the minimum discount factor that is necessary to support the most profitable level of collusion no longer
has a discontinuity at t = 0. However, we can identify similar effects by illustrating how the minimum
discount factor varies with t in the case of Nash punishments. Increases in tariffs facilitate collusion if they
reduce the minimum discount factor. It can be shown, by differentiating the expression for the minimum
discount factor, that if n=1,

will have a local minimum at t = 0, so that trade liberalization will facilitatecollusion in this case. For n > 1, the minimum discount factor will attain a local minimum (maximum) at t
= 0 for. Fig. 3(a) shows the relationship between the minimum discount factor

and trade costs t for= .95, .8, .65, when n=2. For

values of .95 and .8, there is a local minimum at t =0 and a local maximum at the value of t for which. At the value of t at which, increases

in the trade costs will not affect the agreement payoff but will deter deviations from the collusive outcomes
and reduce the Nash punishment. Therefore, increases in the trade costs must unambiguously facilitatecollusion in this region. For=.65 the minimum discount factor has a local maximum at t = 0. The decline

in the minimum discount parameter becomes quite rapid at the point where. In summary, theseresults indicate that trade liberalization will facilitate collusion in the neighborhood of t = 0 if n=1 or if n >1 and the degree of product differentiation is not too large with linear demand.
A second aspect of the effect of tariffs on collusion that can be examined is the effect on the(constrained) efficient profit level when the discount factor is less than the minimum discount factor. Withimperfect substitutability a result analogous to (6) will hold: profits will be decreasing in the neighborhoodof t = 0 when the incentive constraint binds. Fig. 3(b) illustrates the impact of trade barriers on profits for thevalues ofillustrated in Fig. 3(a). Since the maximum profit levels attainable under collusion will vary with25

, these results have been normalized by dividing the agreement profits by the maximum sustainable profits
available at t = 0. In all cases there is a pronounced U-shaped relationship between protection and cartel
profits, because profits initially decline with tariffs but eventually increase as complete geographic
specialization becomes optimal. The simulations indicate that whenis close to 1 the global maximum forprofits occurs with geographic specialization of firms, so that the most collusive agreement involves tradebarriers high enough to keep foreign sellers out of the market. Whenis lower, the global maximum occurs

at t = 0. When product differentiation becomes sufficiently large, geographic specialization in sales insubstantially lower profits.
A comparison of Figs 3(a) and 3(b) illustrates the importance of considering both the minimum discountfactor and the level of cartel profits in considering the effects of the tariff on cartel activity. Fig. 4 illustrates
howvaries with t under the assumption that trade barriers take the form of tariffs. For reasons

similar to those associated with Figs. 2(a), and 2(b), the relationship between welfare and trade costs is nonmonotonic. Note, however, that in all of the cases illustrated the welfare level is decreasing in the trade costin the neighborhood of free trade.

IV. Concluding Remarks
In this paper, we have established that in general there is a non-monotonic relationship between the level oftrade barriers and the profitability of cartels in the case of symmetric Cournot oligopolies.

Thus, therelationship between tariffs and cartel activity is more subtle than suggested by Havemeyer’s remark.
One sense in which high tariffs facilitate collusion is that they generally make it easier to sustain
agreements with maximal geographic collusion in which firms specialize in selling in their own market. Thisis reflected in the result that the minimum discount factor associated with maximal geographic collusion isdecreasing in the level of trade barriers as long as trade barriers do not have too large an effect on thepunishment payoff. When the goods produced by cartel members are very good substitutes, the cartel profits

26

will be highest when trade costs are high enough to facilitate the sustainability of maximal geographic
collusion. However, geographic collusion is not attractive when the degree of substitutability between goods
is low because profits are relatively low when firms sell only in their own markets. Therefore, cartel members
will not benefit from high tariffs in this case, even though the minimum discount factor may be relatively low.

We also established that collusion is easier to support at free trade when cartel members have equalmarket shares across markets. This finding accounted for the result that cartel profits are decreasing in thelevel of the trade costs in the neighborhood of free trade when the no deviation constraint is binding. An
increase in the trade cost level reduces the profit of cartel members for two reasons: (i) it taxes trade, and (ii)it makes it more difficult for firms to sustain collusion. If the latter effect is sufficiently large, the trade cost
increase may result in a reduction in domestic price and an increase in national welfare. Numerical analysis
indicated that this case is most likely to occur when goods are very close substitutes and the number of firms
is small.
Our findings unveil the important role of substitutability in determining the linkage between tradeliberalization and collusion. For homogeneous product cartels, profits will be highest in the extreme casesof free trade and high tariffs. When products are more heterogeneous, however, the highest profits will most
likely be earned under free trade because the benefits of high tariff protection to geographically segmented
markets are relatively small.
Our findings also unveil several questions concerning cartel activity that should be addressed. The
observation that cartel deviation incentives are smallest when firms have symmetric costs suggest that firms
might have an incentive to locate plants in each market in order to make collusion easier to sustain. This could
give rise to a interesting relationship between foreign direct investment and the level of collusion. A second
issue to be addressed is the extent to which the benefits of symmetric market shares extend to the case inwhich firms compete in prices rather than quantities. These remain areas for future research.

27

Figure 1a: Minimum Discount Factors as Functions of Trade Costs (Homogeneous Goods)

Figure 1b: Constrained-Efficient Global Profits and Their Dependence on Trade Costs(Homogeneous Goods)
28

Figure 2: Welfare as a Function of Reciprocal Tariffs and Transport Costs (Homogeneous Goods)

29Figure 3a: Minimum Discount Factors as Functions of Trade Costs (Imperfect Substitutes)

30

Figure 3b: Constraint-Efficient Relative Profits as Functions of Trade Costs(Imperfect Substitutes)

31Appendix
The proofs in this section will be derived for the general demand function

most general case with
with

and

for the. The results of Section II.A are obtained from the special caseand those for II.B with.

Proof of Lemmas 1, 3, 4: Letbe the profit of a representative firm with output

y when all other firms produce Y and marginal cost is c. The best response function isand maximum profit is. Solvingwith the requirement thatand

, we can characterize the Nash equilibrium outputs.

This yields:

C

If

,

then

(A.1)

C

If

,

then

The proofs to all parts of these lemmas readily follows from the above.
A-1||

To prepare the ground for proof of Lemma 2, we first establish the following properties of the functions
and Z in Lemma A.1 below.

Lemma A.1:a)If

, thenIf t > 0, thenis strictly quasi-concave.

Ifis strictly concave.

, thenis concave.

b)c)is concave in (q, x).

For, there exists (q, x) such that

> 0 if either (i) n > 1 or (ii) n = 1 and.

Proof: Using the definition ofand, we have(A.2).

Parts (a) and (b) follow from evaluation ofof

andfrom (A.2). The concavity ofand the convexity

also imply the concavity of Z in {q, x}, and hence the convexity of the feasible set F. To establish part(c), note thatsince

. Differentiationof the payoff functions gives, which from (A.1) will

A-2

be negative if

and

and

. Similarly,

. For

,

> 0 and0, so there will exist an
hand, ifand>by the continuity of Z. On the othersuch that, then there will exist an

such thatwhen n > 1.

||

Proof of Lemma 2:
Part (a): Lemma A.1 showed that our optimization problem (4) satisfies the conditions for Theorems 2.1-2.2
in Takayama (1993). Since

is a concave function and F is a convex set satisfying the Slater condition,

the FOCs are necessary and sufficient for an agreement (q, x) to be a global maximum to the efficient cartel
problem. In the case of Lemma 2 whereconcavity ofof, the solution will also be unique if t > 0 by the strict quasi-. In the case of Section III with, the solution will be unique from the strict concavity.
Part (b):The necessary conditions for a maximum of the Lagrangian at an interior solution can be

expressed as

(A.3)

where

is the Lagrange multiplier. Using the fact that

A-3

and

,

(A.4)

the first equality in (A.3) can equivalently be written as

.

Since

and

(A.5)

will both be negative at an interior solution where the no deviation constraint binds, (A.5)

will require that q = x if t = 0. For the case ofSolving (A.3) withmonopoly profits are attained with an allocation A/(4n).

and t = 0 yields, with strict equality holding for. For t > 0, (A.5) can be rewritten as(A.6)

where the inequality follows from (A.3). In order for the right-hand side to satisfy the inequality for t > 0, wemust have q > x.
This characterizes the quantities at interior solutions. We conclude by showing that there cannot be acorner solution with q = 0. If a corner solution with q = 0 is a maximum to the optimization problem, there
will exist a

and an x such that

and.

Subtracting the former condition from the latter and using (A.4), we have that a corner solution with q = 0
requires. Simplifying this expression and rearranging

A-4

terms gives

which is clearly positive. This

contradicts our supposition that q = 0; therefore, q = 0 cannot be part of an efficient cartel agreement.

Proof of Proposition 3: Noting thatand that the Lagrangian in (4) is valid for||, we maysolve the constrained optimization problem for t=0 to obtain.

It can be verified that

. Moreover,the expressions forandfor all, which implies

and, as expected. Substitutingin (5) and manipulating the resulting expression yields

.

||

A-5

References
Abreu, Dilip, (1986), “Extremal Equilibria of Oligopolistic Supergames,” Journal of Economic Theory 39,
191-225.
Bernheim, B. Douglas and Michael D. Whinston, (1990), “Multimarket Contact and Collusive Behavior,”
RAND Journal of Economics 21, 1-26.
Bond, Eric W., (2004), “Antitrust Policy in Open Economies: Price Fixing and International Cartels,” inJames C. Hartigan and E. Kwan Choi (eds), Handbook of International Trade, Volume II: Economic
and Legal Analyses of Trade Policy and Institutions, Blackwell Handbooks in Economics.
Brander, James and Paul Krugman, (1983), “A Model of Reciprocal Dumping,” Journal of International
Economics 15, 313-323.
Colonescu, Constantin and Nicolas Schmitt, (2003), “Market Integration, Market Segmentation and Tacit
Collusion,” Review of International Economics 11, 175-193.
Davidson, Carl, (1984), “Cartel Stability and Tariff Policy,” Journal of International Economics 17, 219-237.
Friedman, James, (1971), “A Non-cooperative Equilibrium for Supergames,” Review of Economic Studies
38, 1-12.
Fung, K.C., (1992), “Economic Integration as Competitive Discipline,” International Economic Review
33, 837-847.
Hummels, David (2001), "Toward a Geography of Trade Costs?” Manuscript, Purdue University,(http://www.mgmt.purdue.edu/faculty/hummelsd/)
Lommerud, Kjell Erik and Lars Sørgard, (2001), “Trade Liberalization and Cartel Stability,” Review ofInternational Economics 9(2), 343-355.
Nussbaum, Helga, (1986), “International Cartels and Multinational Enterprises” in Multinational Enterprisein Historical Perspective, Teichova, Levy-Leboyer, and Nussbaum (eds), Cambridge University Press(Cambridge).
Phillips, Owen R. and Charles F. Mason, (1996), “Market Regulation and Multimarket Rivalry,” RAND
Journal of Economics 27:3, 596-617.
Pinto, Brian, (1986), “Repeated Games and the ‘Reciprocal Dumping’ Model of Trade,” Journal ofInternational Economics 20, 357-366.
Rotemberg, Julio J. and Garth Saloner, (1989), “Tariff vs Quotas with Implicit Collusion,” Canadian Journalof Economics 22, 237-444.
Spagnolo, Giancarlo, (2001), “Issue Linkage, Credible Delegation, and Policy Cooperation,” CEPR
Discussion Paper No. 2778.

R-1

Syropoulos, Constantinos, (1992), “Quantitative Restrictions and Tariffs with Endogenous Firm Behavior,”
European Economic Review 36, 1627-1646.
Takayama, Akira, (1993), Analytical Methods in Economics, University of Michigan Press (Ann Arbor).
U.S. Department of Justice, (2000), International Competition Policy Advisory Committee, Final Report,(http://www.usdoj.gov/atr/icpac/finalreport.htm)
World Trade Organization, (1997), Annual Report for 1997.

R-2

R-3