- Email: [email protected]
Market equilibrium under the ‘threat’ of a VER
Journal of International
Economics 30 (1991) 137-152. North-Holland
Market equilibrium a VER
under the ‘threat’ of
Judith M. Dean Bowdoin College, Brunswick, ME
04011,
USA
Shubhashis Gangopadhyay* Indian Statistical Institute. Delhi Centre, 7. S.J.S. Sansanwal Marg, New Delhi, India 110016. and The Policy Group, W-17. Greater Kailash-I, New Delhi, India 110048
Received March 1988, revised version received January 1990
This paper characterizes market equilibrium under oligopoly, when a VER has introduced both asymmetry amongst exporters, and uncertainty. A restrained and an unrestrained exporter choose price strategically, under the ‘threat’ of a VER on the latter. A pure strategy equilibrium is shown to result only when the probability of the VER is high. Otherwise a unique mixed strategy equilibrium results. As the probability of the VER rises, the expected domestic price rises, &en If the VER is not imposed..
1. Introduction
Voluntary export restraints (VERs) have become a prevalent means of faces high levels of import restraining exports. When a domestic industry _ penetration or rapid growth of imports, the importing country may negotiate VERs with one or several major exporting countries. Ostensibly, this is to avoid disruption of the domestic market. Trade literature until recently has concentrated largely on the effects of a VER on the imposing country’s welfare. This has been contrasted with a tariff or a quota, under various assumptions on market structure [see Takacs (1978) and Murray, Schmidt and Walter (1983)]. With the recent emphasis on imperfect competition, much has been written on the use of trade restraints to capture monopoly *The initial version of this paper was written while Judith Dean was visiting the Indian Statistical Institute in the fall of 1987. Subsequently, revised versions were presented at the Eastern Economics Association meetings in March 1988, and the Econometric Society meetings in December 1988. We especially thank Kala Krishna for her helpful discussion of this paper at the Econometric Society meetings. We also thank the participants in seminars at Bowdoin College and Rutgers University. Finally, our thanks to two anonymous referees for very helpful suggestions. 0022-1996/91/SO3.50 0 1991-Elsevier
Science Publishers B.V. (North-Holland)
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profits from oligopolistic exporters. Again. this literature deals mainly with tariffs and subsidies [Brander and Spencer (1981), Dixit (1983), and Eaton and Grossman (1986)]. Recently, however, papers by Krishna (1983) and Harris (1985) have sought to examine the impact of a VER in the context of duopoly. In both these papers a game is played between the importing country’s firm and the exporting country’s firm, where these firms are Bertrand price competitors. In these studies, the asymmetry introduced by the VER actually ‘facilitates’ collusion between the two firms and higher profits for each. Two peculiar attributes of VERs necessitate further study. First, since VERs are bilateral and discriminatory, they are usually negotiated with several major exporters in the industry, leaving some exporters unrestrained. Secondly, the proliferation of VERs in an industry increases the likelihood that any new successful exporter will be asked to restrain its exports through a VER. The experience of many small exporters in the textile and clothing industries illustrates this problem. The United States recently negotiated a VER with Bangladesh under the Multitibre Arrangement (MFA), ostensibly for causing market disruption. This was despite the fact that Bangladesh accounted for less than 1 percent of total U.S. imports of these products. It is unlikely that Bangladesh would have been the target of protectionist sentiment without the MFA, and the numerous existing restraints on larger sellers in these industries. The existence of VERs signals not only pressure from the domestic industry for protection, but success in obtaining that protection. Thus, the presence of VERs on some exporters in an industry transmits to the unrestrained sellers both incentives to expand, since some competitors are restricted, and disincentives, since expansion could lead to their own sales being constrained. This paper, therefore, analyzes the impact of both the asymmetry amongst exporters and the uncertainty that a VER on one exporter introduces.’ We examine the interaction of a restrained and an unrestrained exporter, when the latter faces a positive probability of a VER. The restrained firm is the largest exporter, and therefore the most visible threat to the domestic industry. The unrestrained exporter is smaller, but is poised to expand. Now this unrestrained exporter may capture the entire export market from the restrained firm by undercutting the latter’s price (with appropriate assumptions on elasticity of supply). However, two problems emerge for the former if he follows this strategy. First, the domestic suppliers will be forced to lower price and will face a reduction in sales. This will be perceived as injury due to increased import penetration, and the unrestrained exporter will face ‘Bhagwati and Srinivasan (1976) do look at the output decision of a tirm facing the uncertainty of a VER. However, their analysis focuses on only one exporter who is presently unrestricted. It, therefore, does not incorporate the interaction amongst exporters when at least some are restrained (i.e. it ignores the asymmetry aspect of VERs).
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pressure to negotiate a VER. Secondly, the restrained firm may lower his price in response, in order to avoid losing his market. We therefore analyze the problem as a game, where these two firms choose price strategically in order to maximize expected profits under uncertainty. Uncertainty arises from the threat of a VER upon the presently unrestrained exporter. In this framework, we find that the type of equilibrium that emerges and the domestic price of the product both depend upon the likelihood of the VER on the unrestrained exporter. In particular, a pure strategy equilibrium results only when the probability of this VER is high. As this probability falls, a mixed strategy equilibrium results. Corresponding to this, the range for the domestic price is shown to rise as the probability of the VER rises. Thus, the stronger the threat of a VER being negotiated, the higher will be the range of the domestic price, even if the VER is not actually imposed. 2. The problem The home country produces a good that it also imports from abroad. We distinguish between three types of suppliers: a restrained exporter, A; an unrestrained exporter, B; and a group of suppliers that constitute the ‘competitive fringe’. The third group contains domestic producers as well as foreign firms who are too small to affect market outcomes. Let the aggregate supply curve of this group be denoted S(p), where s’(p)>O, and p is the price of the product. Pressure for protection in the home country comes from this third group, which contains domestic producers. It could be from workers who have experienced job losses due to competition from the more efficient exporter. Or one could think of the home country as being capacity constrained in the production of the good. Each small producer earns a rent, which declines with increasing imports. Being too small to compete strategically, these firms lobby for protection.2 Let home demand for the product be given by D(p), where D’(p) ~0. Then define ‘excess demand’, E(p), as
(1)
E(P) = D(P) -S(P),
where this is the demand to be met by exporters following assumption on E(p). Assumption
1.
E(p)
is twice
continuously
A and B. We make the
differentiable
and
E”(p) ~0.~
2We are indebted to a referee for pointing this out. -‘Henceforth we will work mainly with E(p), and S(p) will play no role other than determining the amount supplied by the smaller sellers. Assumption 1 is stronger than necessary. It is sullicient that 2E’+pE”
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E(0) c co, and there exists fi such that for all p>@, E(p)=O,
and for all
P E CO,iv, E(P) > 0.
To simplify the analysis we assume that A’s marginal cost is constant and equal to zero.4 We also treat the imported and domestic goods as perfect substitutes. Now exporter A is a major exporter who is the target of protectionist policy. Initially, exporter B is at a cost disadvantage with respect to A. In this context, B’s marginal cost, c, is such that c>O. Let B’s relative cost disadvantage be such that B is viewed as a small exporter by the home country, and therefore part of the competitive fringe. A VER is negotiated to restrain firm A, the visible major competitor with the domestic producers. Over time exporter B is able to lower costs sufficiently to match exporter A’s (i.e. exporter B’s marginal cost falls to zero). A and B then may be viewed as similar to Japan and South Korea in the automobile industry. In the early 1980s the United States negotiated a VER with Japan only. Despite the presence of other exporters, Japan was perceived as the major threat to the domestic industry. Once Japan was restrained, South Korea emerged as a significant competitor and began to capture a share of the U.S. market.’ Let p,, be defined as follows: p. = argmax pE(p).
(2)
Suppose initially that post. Then, in the absence of any restraints, A’s optimal choice is to charge po. The home country now negotiates a VER of the amount V, with country A, in order to reduce imports below the free trade level, i.e. V,cE(p,). Thus, the home country price rises to pI, where WP,) =
v,.
(3)
Suppose now that country B has succeeded in reducing its costs of production to the level of country A. B now has an incentive to undercut A and try to capture its market share. However, this will tend to drive down the price of the good. Home producers will perceive this as injury due to increased exports from B. Since home firms were successful in achieving a VER on A, B is aware that it, too, faces a positive probability of a VER if it undercuts A. As will become evident, the qualitative analysis is unaffected by the assumption that B’s costs fall. With its costs remaining at c, B could still
‘WC are indebted to a referee for this suggestion. ‘We do not attempt to model the technological changes that cause exporter B’s cost to fall. Our focus is on the interplay between exporters once B becomes a potentially large seller. We note below the changes in the analysis if exporter B’s costs do remain at c.
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make its presence felt in the market, and thus face the threat of a VER, if pi >c.6 We continue to assume that the home country desires to restrict imports below the free trade level (in order to keep the price above pO). Let Vs be the potential VER on B, where V,>O. We know then that (V,,+ Vs)
RP”) =
v*+ v,.
(4)
Then, we assume: Assumption 2.
p1 > pv > pO.
The imposition of both VERs, then, results in a price that is above the joint monopoly price of A and B acting in collusion (that is, pO). Country B knows V,, and hence pv, but it does not know whether the VER will actually be imposed on it or not. Let q be the probability that Vs is imposed, and (l-q) be the probability that it is not. If B pushes the price below pc, the home producers will lobby for a VER. One can think of q as the probability that the lobbyists will succeed in achieving the VER. We assume that both countries know the value of q. and that it is exogenously given.’ The game between A and B takes place in three stages: Stage I: A and B choose a price for their product. Stage II: The home country government, with probability q (and 1 -q) decides to impose (or not impose) a VER of Va on B. Stage III: The market clears with A and B selling at prices quoted in the first stage. Whether or not the VER is imposed, the other producers sell at a price p which solves S(p) = D(p) - QA - Qe, where QA and Qe are the amounts sold by A and B, respectively. The game as defined has the following features. (i) Domestic producers service customers first. This is in keeping with the ‘power’ enjoyed by the domestic suppliers when the consumer is indifferent between the imported and domestic good. (ii) Prices chosen in stage I cannot be changed after the decision by the importing country to impose or not impose a VER on country B. To complete the description of the game, we must make an assumption ‘If, however, p, >c>O, then Assumption 2 must be replaced with p, >p,>p,>c. ‘An extension of this would be to make q a function of the price charged by B. For example, one could assume that the lobbyists would be more successful, the lower B’s price. Alternatively, one could view q as the probability that a lobby group will push for a VER at all, making that explicitly dependent upon the behavior of B. Both types of modifications would make explicit characterization of the equilibria impossible, without making very special assumptions about the functional form of q. Hence, we have chosen to view q as the exogenous probability that the lobby group will be successful.
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regarding the division of the market when two suppliers charge the same price. Assumption 3.
Whenever A and B charge the same price p, and psp,,
A
always sells V,. This simplifies the analysis and has no qualitative bearing on the results. Countries A and B try to maximize their expected payoffs that accrue in stage III. These payoffs depend on the prices quoted by them in stage I, as well as the quantities they sell. Denote P=(p,,p,) as a price announcement, where pA (pe) is the price announced by A (B) in stage I. We will first show that these prices are always less then or equal to p,. Lemma 1. Price announcements anything strictly above pt..
are
such
that
neither
A nor
B charge
The intuition for this lemma is fairly straightforward. Given Assumptions 1 and 2, firm B’s profits at any price above pV are less than at p”. This is independent of whether the VER on B is imposed or not. Thus, B has no incentive to charge a price greater than p”. Given this, A will never consider prices above P,.~ Using Lemma 1, we can now define the quantities sold by each exporter for any price announcement, P. The amounts sold are determined by the price quoted by each exporter, whether V, is imposed or not, the demand and the supply of domestic producers, and Assumption 3. Let Qi be the amount sold by exporter i, i = A, B. I~PA$P,,
If PA > PB,
IfP,<
PA,
If PB 2 PAS
Q..t(f')= V,.
QA(
P)
=
VA with probability q, 0 with probability (l-q).
(5)
A?(&,) with probability (1 -q), Qe(P)= VBwith probability q. E(p,) Q,(P)
The payoff of exporter EA formal proof is available
=
-
VA
with probability (1 -q), q.
VBwith probability
i, i= A, B, is denoted
I&(P). This is the return
from the authors upon request.
(6) or
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profits to exporter i in stage III. When choosing prices, the exporter tries to maximize the expected payoff, which depends on 4 and the prices charged by the exporters. The expected payoff will be denoted ~r(P,q). Each firm chooses a strategy pi, i=A, B. /li is a cumulative probability distribution defined on [0, PJ. Firms are risk neutral, and for any p= (PA,PrI)r
An equilibrium strategy IL*= (&, P:) satisfies @‘(q,P?,pf) I @(q,Pi* Pf),
iJ= A, B.
(8)
This completes the description of the model. We now characterize the equilibria that will occur, and study some of the properties of these equilibria. In particular, we show how the expected payoffs, the nature of the equilibrium, and the expected minimum or maximum price paid by the consumers depend upon 4, the probability of a VER on B.
3. Results Making use of the equations in (5) and (6), we can examine the expected profit-maximization problem facing firm A and tit-m B. If pASpr,, country B’s expected return would be R&++& where
ah R(p) =
E(p)
would
be
(9)
4) =PBc4v,+(1-4)wB)l~ -
VA,
a,(p,,q),
and R(p) is maximized at where
pz.
If
pA>pB,
the best B could do
n,(p,, 4) = Per4 va+ (1---4)aPdl* Let the maximized values of rr3 and rr4 be denoted by respectively. When pA>pB, country A’s expected return is
(10) n;(q)
and
which is clearly maximized at pv, given Assumption 2. However, if the best A could do would be PAh-
n:(q),
pA spPe,
(12)
J.M. Dean and S. Gangopadhyay, Market equilibrium
14JI
Pv PA
undercuts
undercut
PB
P3
A
A
P4 PB Fig. 1
Figs. l(a) and l(b) are helpful in illustrating the problem facing these exporters. Fig. l(a) shows expected profits for A when A is undercut, expression (1 l), and when A is not undercut, expression (12), for a given value of q (O
solves
pV,=qp,V,.
(13)
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P I I I
I I I
Y 0
I
1 Fig. 2
9
Fig. l(b) shows the expected profits for firm B under the conditions of undercutting A, eq. (lo), and not undercutting A, eq. (9), again for a given value of 4, where O
so1ves %(p9d = n%d-
(14)
It is clear that both & and pA are well-defined and always exist in the intervals (O,p,] and [O,p,], respectively. In addition, it is easy to show that prices p4, p3, pB, and eA are all positive functions of q. The relationship between these prices is specified in Lemma 2. Lemma 2. Given Assumptions 1 and 2, the following are true: (i) p4 2 p3 > p2 (equality holding when q = I), (ii) p4~po (equality holding when q =O).
Using the definitions of llA, p4, and ~a, and using Lemma 2, we can draw the path of each of these price variables as q rises from zero to one. This is shown in fig. 2. The intersections of these curves divide the range of q into three well-defined blocks. From right to left these blocks correspond to p,,>p,+, p42&,h&, and &>E,,. They can be related t0 q as follows:
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J..M. Dean und S. Gangopudhxay,
P4~~A~PB+-~4>-~ -
P4
PB
PC
PC
Market
equilibrium
(15) Our first result is that the type of equilibrium that emerges in the above game depends on the value of 4. This is described in Proposition 1. Proposition 1. Under Assumptions 1, 2, and 3, the following are true: (i) A pure strategy equilibrium (PSE) exists if and only if
This PSE is unique and is characterized by A charging pv with probability 1 and B charging p4 with probability 1. A’s expected profit is qp,V, and B’s is G(q).
(ii) In all other cases there is a mixed strategy equilibrium (MSE). (iii) A’s expected profit rises with q and B’s falls with q, for given levels of V,
and V,.
(The nature of the equilibrium is stated formally in Theorems 1 and 2 in the appendix.)’ Given our unfolding of the game in stage III, as described in section 2, this result implies that under a PSE, the minimum price observed in the market will be p4. If the VER is imposed on B, then pv will also be observed; otherwise, only p4 is observed. This follows from the fact that domestic producers must match B’s price if B is unrestrained. The home country will, therefore, have an equilibrium price of p4 with probability (1 -q), and a price of pv with probability q. Very simply, this means that if q is large, price will tend to be high. Of course, when q= 1, p4 =p”, and the highest possible price will be observed. Proposition 1 also states that a PSE cannot exist if qsp4/pv. We show in the appendix that under such circumstances a mixed strategy equilibrium (MSE) occurs (Theorem 2), and give a constructive proof of the MSE. There are two MSE, each corresponding to a separate range of values of q, as given in (15) and shown in fig. 2. Combining (13), (14), and (15), it is easy to see ‘Proofs of Theorems 1, 2, and 3 are available from the authors upon request.
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that we need to consider two cases for constructing the MSE: (1) flAh~s, and (2) pAp4. This means that the return to A from matching B’s price is always less than its return from charging pV and being undercut. Hence here A charges p,. B will then undercut A, charging p4, and a PSE will occur. In the second and third blocks, pAspP4. Now, if B charges any price greater than Pi, A does better by matching B’s price, than by allowing itself to be undercut. If 4 takes any value in these two blocks, A will match B’s price. B will therefore have an incentive to charge a slightly lower price and undercut A. Hence, an MSE results. The second and third blocks of values for q give rise to MSE(i) and MSE(ii), where the range of values of price are [eA,pJ for MSE(i)” and [&,pJ for MSE(ii). At first glance the existence of a PSE appears unusual. In most analyses of Bertrand competition in the presence of capacity constraints it is assumed that the sum of the capacity constraints of the two firms is greater than the monopoly output level, and that neither firm alone can supply enough to ensure price equal to marginal cost. This would lead to an MSE. In our analysis, as 4 tends to one, we have a price game that is equivalent to a Bertrand game where the sum of the total capacity constraints is less than the monopoly output. This is due to the assumption that the home country is attempting to continue to restrict imports below the ‘free trade’ level, when B was not perceived as a threat (Assumption 2). It is easy to show that as Va increases, the range of 4 for which a PSE occurs shrinks. If V, becomes so large that Assumption 2 is violated, a PSE would not occur. However, as long as Assumption 2 holds, there exists a high enough value of q to generate a PSE.’ ’ “Note that in MSE(i), A charges no price between p4 and p. with any positive probability, though it does charge p. with positive probability. B charges prices only on the interval [eA,pJ. “Notice that B would also have been a viable competitor, with costs c>O, if originally p,,>c. In this case whether or not a PSE exists when q= 1 would again depend on whether ( v, + v,) P JW,).
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Increasing the size of V,, for a given level of 4 and V,, will lower the expected profit of A and raise the expected profit of B. This follows directly from observing the expected returns in each of the market equilibrium types (see the appendix, Theorems 1 and 2). This suggests that a decrease in 4 or an increase in VBhas the same qualitative effect on A and B. The special case in which q=O is similar in structure to that analyzed by Krishna (1983), if one interprets firms A and B as her foreign and domestic firms, respectively. However, the nature of the mixed strategy equilibrium that emerges here differs from Krishna’s due to the fact that A and B are assumed to produce perfectly substitutable products, while she assumes differentiated products. Consequently, her restrained exporter has a wellbehaved profit function, whereas neither firm A nor B possesses a continuous profit function. Yet, as in Krishna’s study, the existing VER serves to raise the profits of the two firms involved. This can be seen readily by noticing that the lower bound on prices played by both A and B is p,>O. Thus, given the VER on A, price is not competed down to equal marginal cost.
4. Expected price in the importing country The major reason why a VER may be imposed on an exporter by an importing country is because the domestic producers of the importing country are not sufficiently competitive to withstand pressure from the more efftcient foreign competitor. With the VER on the exporting country, the domestic producers increase their sales and charge a higher price for their product. The welfare implications for the home country depend upon the extent to which price rises due to the VER. Following from Proposition 1, however, the expected price in the home country depends upon the probability that a second VER is negotiated. In section 2, we described how in stage III of the game the domestic producers charge a price, p, which equates
S(P)= N-4 - QA - QB-
(16)
Clearly, given Lemma 1, if the home government imposes the VER on B, then the price which equates (16) is pv. Thus, the home country always has a probability 4 of obtaining p”. With probability (1 -q), it will obtain the price charged by B (again following from Lemma 1). The expected price in the home country for each equilibrium type is given in Theorem 3 in the appendix. Proposition 2. increases.
The
expected
price
in the home country
increases
as q
J.M. Dean and S. Gangopadhyay, .Llarket equilibrium
149
This proposition can be easily demonstrated, given Theorem 3. Suppose This, we know from Theorem 2, results in MSE case (ii), where the range of prices being played by A and B are [p,,p,]. Thus, with probability one, the domestic producers must charge B’s price which is a weighted average of prices from [p,,p,]. When q= 1, the expected equilibrium price in the home country has risen to pv. What can be said about the home country’s expected equilibrium price as q rises from zero to one? Since both err and p3 are positive functions of q, then for all values of q in which MSE(ii) occurs, B’s expected price rises with q. The same is true for all values of q which result in MSE(i). B’s price in MSE(i) is a weighted average of prices from [~~,p~]. Both e,, and p4 are also positive functions of q. When q rises such that a PSE occurs, B’s expected price is simply p4, which we know rises with q. Now the expected equilibrium price in the home country is [qp” +( 1 -q)pi], where pi is B’s expected price. Since pe is less than pc, and has been shown to increase with q, it is clear that the home country’s expected equilibrium price must rise with q. Together, Propositions 1 and 2 have important implications for policymaking. They suggest that given a VER of a specific amount, the greater is the threat of the VER, the higher is expected price in the home country. This is true even if the VER is never imposed. A strong threat to negotiate voluntary restrictions can, therefore, result in higher prices being observed than if a weaker threat is perceived. In his 1985 work, Harris made the assumption that the restrained firm behaves as a price follower and the other as a price leader. Such an assumption in the present framework would clearly lead to a PSE (and the elimination of the MSE). It is important, then, to analyze when such assumptions are valid. Dean and Gangophadhyay (1989) explore this issue by endogenizing the firms’ behavior. However, the qualitative results of this threat of a VER on expected equilibrium price remain valid under both assumptions of market behavior by A and B. q=O.
5. Conclusion
We have developed a model that examines two effects of a VER: (a) the asymmetry it introduces among exporters, since some exporters remain unrestrained; and (b) the uncertainty it introduces, since additional exporters may be restrained in the future. We then examined the impact of the VER in the context of oligopolistic exporters who are choosing price strategically, given this uncertainty. Our results indicate that a pure strategy equilibrium results only when the probability of a second VER is high. As this probability falls, a mixed strategy equilibrium results. Correspondingly, the range of prices played by the exporters rises as the probability of the VER rises. This suggests that the stronger the ‘threat’ of a VER on the
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unrestrained firm, the higher the expected domestic equilibrium price, even if the VER is never imposed. Some useful extensions of this analysis would be to (a) consider exporters’ goods as imperfect substitutes, and (b) endogenize the probability of the VER. Imperfect substitutability would obviously mean that if the unrestricted firm undercut the restrained exporter, the latter would not lose all customers. Endogeneity of the probability of the VER is suggested by the institutional framework itself. For example, restraints on new countries in apparel trade appear to be triggered by rapid growth of exports, even if the level of exports is low. However, the above analysis emphasizes the fact that the asymmetry and uncertainty introduced by the VER alter the behavior of both the directly restrained exporter and the unrestrained exporter. This leads to higher import (and domestic) prices for the imposing country than would prevail if the unrestrained exporter perceived no threat of a potential VER. Appendix
Theorem 1. Under Assumptions (PSE) exists if and only if q>
I, 2, and 3. a pure strategy equilibrium
b 0 P” ’
(*I
This PSE is unique and is characterked by A charging pv with probability I and B charging p4 with probability 1. A’s expected return is qpvVA and B’s is Mq). Theorem 2.
If q 5p,/p,, and (i) ~~~~~~ then there exists a unique mixed strategy equilibrium p*=
(,uX,&) which is given by: /G(P) = 07
P,$P*
P*(P) = 19 l&P) =Q
1
/G(P) = 1-q [
l-p”, 1 P
P
~A5PcP4,
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151
The expected payofffor A is equal to p*V,= qpcVA. The expected payofffor B is equal to n,(p,,q). then there exists a unique mixed strategy equilibirum, p* = (ii) fA
/G(P) = 1 -
nf- X,(Pv4)
p(l _q)VA ’
_p+p-=p37
/G(P) = 19
P32P7
/G(P) = 09
P
1
&(P) = ~ 1-q
[
1-L!!, 1 P
,4(P) = 1,
eBi5P
P3 SP*
The expected payofffor A is equal to PAVE. The expected payofffor B is equal to x:(q). Theorem 3. equal to
(iii)
Let pe be the expected
qp ” +pBln&
b’
if
price in the home country. Then p’ is
o
Note that (i)-(iii) correspond exactly fo the pure strategy equilibrium, the MSE case (i), and the MSE (ii), respectioely. References Bhagwati, J. and T.N. Srinivasan, 1976, Optimal trade policy and compensation under endogenous uncertainty: The phenomenon of market disruption, Journal of International Economics 6, 3 17-336.
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Brander, J.A. and B.J. Spencer, 1981. Tariffs and the extraction of foreign monopoly rents under potential entry, Canadian Journal of Economics 14. 371-389. Dean. J. and S. Gangopadhyay, 1989, Strategic trade practices in the presence of a VER. manuscript. Dixit, A., 1984. International trade policy for oligopolistic industries. Economic Journal Conference Papers 94. I-16. Eaton. J. and G. Grossman. 1986, Optimal trade and industrial policy under oligopoly, Quarterly Journal of Economics 101, 383-406. Harris, R., 1985, Why voluntary export restraints are ‘voluntary’, Canadian Journal of Economics 18, 799-809. Krishna, K.. 1983, Trade restrictions as facilitating practices, Woodrow Wilson School, Princeton University 1983 Discussion Paper no. 55. Murray. T., W. Schmidt and 1. Walter, 1983, On the equivalence of import quotas and voluntary export restraints, Journal of International Economics 14, 191-194. Takacs. W., 1978. The non-equivalence of tariffs, import quotas and voluntary export restraints, Journal of International Economics 8, 565-573.
Economics 30 (1991) 137-152. North-Holland
Market equilibrium a VER
under the ‘threat’ of
Judith M. Dean Bowdoin College, Brunswick, ME
04011,
USA
Shubhashis Gangopadhyay* Indian Statistical Institute. Delhi Centre, 7. S.J.S. Sansanwal Marg, New Delhi, India 110016. and The Policy Group, W-17. Greater Kailash-I, New Delhi, India 110048
Received March 1988, revised version received January 1990
This paper characterizes market equilibrium under oligopoly, when a VER has introduced both asymmetry amongst exporters, and uncertainty. A restrained and an unrestrained exporter choose price strategically, under the ‘threat’ of a VER on the latter. A pure strategy equilibrium is shown to result only when the probability of the VER is high. Otherwise a unique mixed strategy equilibrium results. As the probability of the VER rises, the expected domestic price rises, &en If the VER is not imposed..
1. Introduction
Voluntary export restraints (VERs) have become a prevalent means of faces high levels of import restraining exports. When a domestic industry _ penetration or rapid growth of imports, the importing country may negotiate VERs with one or several major exporting countries. Ostensibly, this is to avoid disruption of the domestic market. Trade literature until recently has concentrated largely on the effects of a VER on the imposing country’s welfare. This has been contrasted with a tariff or a quota, under various assumptions on market structure [see Takacs (1978) and Murray, Schmidt and Walter (1983)]. With the recent emphasis on imperfect competition, much has been written on the use of trade restraints to capture monopoly *The initial version of this paper was written while Judith Dean was visiting the Indian Statistical Institute in the fall of 1987. Subsequently, revised versions were presented at the Eastern Economics Association meetings in March 1988, and the Econometric Society meetings in December 1988. We especially thank Kala Krishna for her helpful discussion of this paper at the Econometric Society meetings. We also thank the participants in seminars at Bowdoin College and Rutgers University. Finally, our thanks to two anonymous referees for very helpful suggestions. 0022-1996/91/SO3.50 0 1991-Elsevier
Science Publishers B.V. (North-Holland)
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profits from oligopolistic exporters. Again. this literature deals mainly with tariffs and subsidies [Brander and Spencer (1981), Dixit (1983), and Eaton and Grossman (1986)]. Recently, however, papers by Krishna (1983) and Harris (1985) have sought to examine the impact of a VER in the context of duopoly. In both these papers a game is played between the importing country’s firm and the exporting country’s firm, where these firms are Bertrand price competitors. In these studies, the asymmetry introduced by the VER actually ‘facilitates’ collusion between the two firms and higher profits for each. Two peculiar attributes of VERs necessitate further study. First, since VERs are bilateral and discriminatory, they are usually negotiated with several major exporters in the industry, leaving some exporters unrestrained. Secondly, the proliferation of VERs in an industry increases the likelihood that any new successful exporter will be asked to restrain its exports through a VER. The experience of many small exporters in the textile and clothing industries illustrates this problem. The United States recently negotiated a VER with Bangladesh under the Multitibre Arrangement (MFA), ostensibly for causing market disruption. This was despite the fact that Bangladesh accounted for less than 1 percent of total U.S. imports of these products. It is unlikely that Bangladesh would have been the target of protectionist sentiment without the MFA, and the numerous existing restraints on larger sellers in these industries. The existence of VERs signals not only pressure from the domestic industry for protection, but success in obtaining that protection. Thus, the presence of VERs on some exporters in an industry transmits to the unrestrained sellers both incentives to expand, since some competitors are restricted, and disincentives, since expansion could lead to their own sales being constrained. This paper, therefore, analyzes the impact of both the asymmetry amongst exporters and the uncertainty that a VER on one exporter introduces.’ We examine the interaction of a restrained and an unrestrained exporter, when the latter faces a positive probability of a VER. The restrained firm is the largest exporter, and therefore the most visible threat to the domestic industry. The unrestrained exporter is smaller, but is poised to expand. Now this unrestrained exporter may capture the entire export market from the restrained firm by undercutting the latter’s price (with appropriate assumptions on elasticity of supply). However, two problems emerge for the former if he follows this strategy. First, the domestic suppliers will be forced to lower price and will face a reduction in sales. This will be perceived as injury due to increased import penetration, and the unrestrained exporter will face ‘Bhagwati and Srinivasan (1976) do look at the output decision of a tirm facing the uncertainty of a VER. However, their analysis focuses on only one exporter who is presently unrestricted. It, therefore, does not incorporate the interaction amongst exporters when at least some are restrained (i.e. it ignores the asymmetry aspect of VERs).
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pressure to negotiate a VER. Secondly, the restrained firm may lower his price in response, in order to avoid losing his market. We therefore analyze the problem as a game, where these two firms choose price strategically in order to maximize expected profits under uncertainty. Uncertainty arises from the threat of a VER upon the presently unrestrained exporter. In this framework, we find that the type of equilibrium that emerges and the domestic price of the product both depend upon the likelihood of the VER on the unrestrained exporter. In particular, a pure strategy equilibrium results only when the probability of this VER is high. As this probability falls, a mixed strategy equilibrium results. Corresponding to this, the range for the domestic price is shown to rise as the probability of the VER rises. Thus, the stronger the threat of a VER being negotiated, the higher will be the range of the domestic price, even if the VER is not actually imposed. 2. The problem The home country produces a good that it also imports from abroad. We distinguish between three types of suppliers: a restrained exporter, A; an unrestrained exporter, B; and a group of suppliers that constitute the ‘competitive fringe’. The third group contains domestic producers as well as foreign firms who are too small to affect market outcomes. Let the aggregate supply curve of this group be denoted S(p), where s’(p)>O, and p is the price of the product. Pressure for protection in the home country comes from this third group, which contains domestic producers. It could be from workers who have experienced job losses due to competition from the more efficient exporter. Or one could think of the home country as being capacity constrained in the production of the good. Each small producer earns a rent, which declines with increasing imports. Being too small to compete strategically, these firms lobby for protection.2 Let home demand for the product be given by D(p), where D’(p) ~0. Then define ‘excess demand’, E(p), as
(1)
E(P) = D(P) -S(P),
where this is the demand to be met by exporters following assumption on E(p). Assumption
1.
E(p)
is twice
continuously
A and B. We make the
differentiable
and
E”(p) ~0.~
2We are indebted to a referee for pointing this out. -‘Henceforth we will work mainly with E(p), and S(p) will play no role other than determining the amount supplied by the smaller sellers. Assumption 1 is stronger than necessary. It is sullicient that 2E’+pE”
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E(0) c co, and there exists fi such that for all p>@, E(p)=O,
and for all
P E CO,iv, E(P) > 0.
To simplify the analysis we assume that A’s marginal cost is constant and equal to zero.4 We also treat the imported and domestic goods as perfect substitutes. Now exporter A is a major exporter who is the target of protectionist policy. Initially, exporter B is at a cost disadvantage with respect to A. In this context, B’s marginal cost, c, is such that c>O. Let B’s relative cost disadvantage be such that B is viewed as a small exporter by the home country, and therefore part of the competitive fringe. A VER is negotiated to restrain firm A, the visible major competitor with the domestic producers. Over time exporter B is able to lower costs sufficiently to match exporter A’s (i.e. exporter B’s marginal cost falls to zero). A and B then may be viewed as similar to Japan and South Korea in the automobile industry. In the early 1980s the United States negotiated a VER with Japan only. Despite the presence of other exporters, Japan was perceived as the major threat to the domestic industry. Once Japan was restrained, South Korea emerged as a significant competitor and began to capture a share of the U.S. market.’ Let p,, be defined as follows: p. = argmax pE(p).
(2)
Suppose initially that post. Then, in the absence of any restraints, A’s optimal choice is to charge po. The home country now negotiates a VER of the amount V, with country A, in order to reduce imports below the free trade level, i.e. V,cE(p,). Thus, the home country price rises to pI, where WP,) =
v,.
(3)
Suppose now that country B has succeeded in reducing its costs of production to the level of country A. B now has an incentive to undercut A and try to capture its market share. However, this will tend to drive down the price of the good. Home producers will perceive this as injury due to increased exports from B. Since home firms were successful in achieving a VER on A, B is aware that it, too, faces a positive probability of a VER if it undercuts A. As will become evident, the qualitative analysis is unaffected by the assumption that B’s costs fall. With its costs remaining at c, B could still
‘WC are indebted to a referee for this suggestion. ‘We do not attempt to model the technological changes that cause exporter B’s cost to fall. Our focus is on the interplay between exporters once B becomes a potentially large seller. We note below the changes in the analysis if exporter B’s costs do remain at c.
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make its presence felt in the market, and thus face the threat of a VER, if pi >c.6 We continue to assume that the home country desires to restrict imports below the free trade level (in order to keep the price above pO). Let Vs be the potential VER on B, where V,>O. We know then that (V,,+ Vs)
RP”) =
v*+ v,.
(4)
Then, we assume: Assumption 2.
p1 > pv > pO.
The imposition of both VERs, then, results in a price that is above the joint monopoly price of A and B acting in collusion (that is, pO). Country B knows V,, and hence pv, but it does not know whether the VER will actually be imposed on it or not. Let q be the probability that Vs is imposed, and (l-q) be the probability that it is not. If B pushes the price below pc, the home producers will lobby for a VER. One can think of q as the probability that the lobbyists will succeed in achieving the VER. We assume that both countries know the value of q. and that it is exogenously given.’ The game between A and B takes place in three stages: Stage I: A and B choose a price for their product. Stage II: The home country government, with probability q (and 1 -q) decides to impose (or not impose) a VER of Va on B. Stage III: The market clears with A and B selling at prices quoted in the first stage. Whether or not the VER is imposed, the other producers sell at a price p which solves S(p) = D(p) - QA - Qe, where QA and Qe are the amounts sold by A and B, respectively. The game as defined has the following features. (i) Domestic producers service customers first. This is in keeping with the ‘power’ enjoyed by the domestic suppliers when the consumer is indifferent between the imported and domestic good. (ii) Prices chosen in stage I cannot be changed after the decision by the importing country to impose or not impose a VER on country B. To complete the description of the game, we must make an assumption ‘If, however, p, >c>O, then Assumption 2 must be replaced with p, >p,>p,>c. ‘An extension of this would be to make q a function of the price charged by B. For example, one could assume that the lobbyists would be more successful, the lower B’s price. Alternatively, one could view q as the probability that a lobby group will push for a VER at all, making that explicitly dependent upon the behavior of B. Both types of modifications would make explicit characterization of the equilibria impossible, without making very special assumptions about the functional form of q. Hence, we have chosen to view q as the exogenous probability that the lobby group will be successful.
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regarding the division of the market when two suppliers charge the same price. Assumption 3.
Whenever A and B charge the same price p, and psp,,
A
always sells V,. This simplifies the analysis and has no qualitative bearing on the results. Countries A and B try to maximize their expected payoffs that accrue in stage III. These payoffs depend on the prices quoted by them in stage I, as well as the quantities they sell. Denote P=(p,,p,) as a price announcement, where pA (pe) is the price announced by A (B) in stage I. We will first show that these prices are always less then or equal to p,. Lemma 1. Price announcements anything strictly above pt..
are
such
that
neither
A nor
B charge
The intuition for this lemma is fairly straightforward. Given Assumptions 1 and 2, firm B’s profits at any price above pV are less than at p”. This is independent of whether the VER on B is imposed or not. Thus, B has no incentive to charge a price greater than p”. Given this, A will never consider prices above P,.~ Using Lemma 1, we can now define the quantities sold by each exporter for any price announcement, P. The amounts sold are determined by the price quoted by each exporter, whether V, is imposed or not, the demand and the supply of domestic producers, and Assumption 3. Let Qi be the amount sold by exporter i, i = A, B. I~PA$P,,
If PA > PB,
IfP,<
PA,
If PB 2 PAS
Q..t(f')= V,.
QA(
P)
=
VA with probability q, 0 with probability (l-q).
(5)
A?(&,) with probability (1 -q), Qe(P)= VBwith probability q. E(p,) Q,(P)
The payoff of exporter EA formal proof is available
=
-
VA
with probability (1 -q), q.
VBwith probability
i, i= A, B, is denoted
I&(P). This is the return
from the authors upon request.
(6) or
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profits to exporter i in stage III. When choosing prices, the exporter tries to maximize the expected payoff, which depends on 4 and the prices charged by the exporters. The expected payoff will be denoted ~r(P,q). Each firm chooses a strategy pi, i=A, B. /li is a cumulative probability distribution defined on [0, PJ. Firms are risk neutral, and for any p= (PA,PrI)r
An equilibrium strategy IL*= (&, P:) satisfies @‘(q,P?,pf) I @(q,Pi* Pf),
iJ= A, B.
(8)
This completes the description of the model. We now characterize the equilibria that will occur, and study some of the properties of these equilibria. In particular, we show how the expected payoffs, the nature of the equilibrium, and the expected minimum or maximum price paid by the consumers depend upon 4, the probability of a VER on B.
3. Results Making use of the equations in (5) and (6), we can examine the expected profit-maximization problem facing firm A and tit-m B. If pASpr,, country B’s expected return would be R&++& where
ah R(p) =
E(p)
would
be
(9)
4) =PBc4v,+(1-4)wB)l~ -
VA,
a,(p,,q),
and R(p) is maximized at where
pz.
If
pA>pB,
the best B could do
n,(p,, 4) = Per4 va+ (1---4)aPdl* Let the maximized values of rr3 and rr4 be denoted by respectively. When pA>pB, country A’s expected return is
(10) n;(q)
and
which is clearly maximized at pv, given Assumption 2. However, if the best A could do would be PAh-
n:(q),
pA spPe,
(12)
J.M. Dean and S. Gangopadhyay, Market equilibrium
14JI
Pv PA
undercuts
undercut
PB
P3
A
A
P4 PB Fig. 1
Figs. l(a) and l(b) are helpful in illustrating the problem facing these exporters. Fig. l(a) shows expected profits for A when A is undercut, expression (1 l), and when A is not undercut, expression (12), for a given value of q (O
solves
pV,=qp,V,.
(13)
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P I I I
I I I
Y 0
I
1 Fig. 2
9
Fig. l(b) shows the expected profits for firm B under the conditions of undercutting A, eq. (lo), and not undercutting A, eq. (9), again for a given value of 4, where O
so1ves %(p9d = n%d-
(14)
It is clear that both & and pA are well-defined and always exist in the intervals (O,p,] and [O,p,], respectively. In addition, it is easy to show that prices p4, p3, pB, and eA are all positive functions of q. The relationship between these prices is specified in Lemma 2. Lemma 2. Given Assumptions 1 and 2, the following are true: (i) p4 2 p3 > p2 (equality holding when q = I), (ii) p4~po (equality holding when q =O).
Using the definitions of llA, p4, and ~a, and using Lemma 2, we can draw the path of each of these price variables as q rises from zero to one. This is shown in fig. 2. The intersections of these curves divide the range of q into three well-defined blocks. From right to left these blocks correspond to p,,>p,+, p42&,h&, and &>E,,. They can be related t0 q as follows:
146
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P4~~A~PB+-~4>-~ -
P4
PB
PC
PC
Market
equilibrium
(15) Our first result is that the type of equilibrium that emerges in the above game depends on the value of 4. This is described in Proposition 1. Proposition 1. Under Assumptions 1, 2, and 3, the following are true: (i) A pure strategy equilibrium (PSE) exists if and only if
This PSE is unique and is characterized by A charging pv with probability 1 and B charging p4 with probability 1. A’s expected profit is qp,V, and B’s is G(q).
(ii) In all other cases there is a mixed strategy equilibrium (MSE). (iii) A’s expected profit rises with q and B’s falls with q, for given levels of V,
and V,.
(The nature of the equilibrium is stated formally in Theorems 1 and 2 in the appendix.)’ Given our unfolding of the game in stage III, as described in section 2, this result implies that under a PSE, the minimum price observed in the market will be p4. If the VER is imposed on B, then pv will also be observed; otherwise, only p4 is observed. This follows from the fact that domestic producers must match B’s price if B is unrestrained. The home country will, therefore, have an equilibrium price of p4 with probability (1 -q), and a price of pv with probability q. Very simply, this means that if q is large, price will tend to be high. Of course, when q= 1, p4 =p”, and the highest possible price will be observed. Proposition 1 also states that a PSE cannot exist if qsp4/pv. We show in the appendix that under such circumstances a mixed strategy equilibrium (MSE) occurs (Theorem 2), and give a constructive proof of the MSE. There are two MSE, each corresponding to a separate range of values of q, as given in (15) and shown in fig. 2. Combining (13), (14), and (15), it is easy to see ‘Proofs of Theorems 1, 2, and 3 are available from the authors upon request.
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that we need to consider two cases for constructing the MSE: (1) flAh~s, and (2) pA
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Increasing the size of V,, for a given level of 4 and V,, will lower the expected profit of A and raise the expected profit of B. This follows directly from observing the expected returns in each of the market equilibrium types (see the appendix, Theorems 1 and 2). This suggests that a decrease in 4 or an increase in VBhas the same qualitative effect on A and B. The special case in which q=O is similar in structure to that analyzed by Krishna (1983), if one interprets firms A and B as her foreign and domestic firms, respectively. However, the nature of the mixed strategy equilibrium that emerges here differs from Krishna’s due to the fact that A and B are assumed to produce perfectly substitutable products, while she assumes differentiated products. Consequently, her restrained exporter has a wellbehaved profit function, whereas neither firm A nor B possesses a continuous profit function. Yet, as in Krishna’s study, the existing VER serves to raise the profits of the two firms involved. This can be seen readily by noticing that the lower bound on prices played by both A and B is p,>O. Thus, given the VER on A, price is not competed down to equal marginal cost.
4. Expected price in the importing country The major reason why a VER may be imposed on an exporter by an importing country is because the domestic producers of the importing country are not sufficiently competitive to withstand pressure from the more efftcient foreign competitor. With the VER on the exporting country, the domestic producers increase their sales and charge a higher price for their product. The welfare implications for the home country depend upon the extent to which price rises due to the VER. Following from Proposition 1, however, the expected price in the home country depends upon the probability that a second VER is negotiated. In section 2, we described how in stage III of the game the domestic producers charge a price, p, which equates
S(P)= N-4 - QA - QB-
(16)
Clearly, given Lemma 1, if the home government imposes the VER on B, then the price which equates (16) is pv. Thus, the home country always has a probability 4 of obtaining p”. With probability (1 -q), it will obtain the price charged by B (again following from Lemma 1). The expected price in the home country for each equilibrium type is given in Theorem 3 in the appendix. Proposition 2. increases.
The
expected
price
in the home country
increases
as q
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This proposition can be easily demonstrated, given Theorem 3. Suppose This, we know from Theorem 2, results in MSE case (ii), where the range of prices being played by A and B are [p,,p,]. Thus, with probability one, the domestic producers must charge B’s price which is a weighted average of prices from [p,,p,]. When q= 1, the expected equilibrium price in the home country has risen to pv. What can be said about the home country’s expected equilibrium price as q rises from zero to one? Since both err and p3 are positive functions of q, then for all values of q in which MSE(ii) occurs, B’s expected price rises with q. The same is true for all values of q which result in MSE(i). B’s price in MSE(i) is a weighted average of prices from [~~,p~]. Both e,, and p4 are also positive functions of q. When q rises such that a PSE occurs, B’s expected price is simply p4, which we know rises with q. Now the expected equilibrium price in the home country is [qp” +( 1 -q)pi], where pi is B’s expected price. Since pe is less than pc, and has been shown to increase with q, it is clear that the home country’s expected equilibrium price must rise with q. Together, Propositions 1 and 2 have important implications for policymaking. They suggest that given a VER of a specific amount, the greater is the threat of the VER, the higher is expected price in the home country. This is true even if the VER is never imposed. A strong threat to negotiate voluntary restrictions can, therefore, result in higher prices being observed than if a weaker threat is perceived. In his 1985 work, Harris made the assumption that the restrained firm behaves as a price follower and the other as a price leader. Such an assumption in the present framework would clearly lead to a PSE (and the elimination of the MSE). It is important, then, to analyze when such assumptions are valid. Dean and Gangophadhyay (1989) explore this issue by endogenizing the firms’ behavior. However, the qualitative results of this threat of a VER on expected equilibrium price remain valid under both assumptions of market behavior by A and B. q=O.
5. Conclusion
We have developed a model that examines two effects of a VER: (a) the asymmetry it introduces among exporters, since some exporters remain unrestrained; and (b) the uncertainty it introduces, since additional exporters may be restrained in the future. We then examined the impact of the VER in the context of oligopolistic exporters who are choosing price strategically, given this uncertainty. Our results indicate that a pure strategy equilibrium results only when the probability of a second VER is high. As this probability falls, a mixed strategy equilibrium results. Correspondingly, the range of prices played by the exporters rises as the probability of the VER rises. This suggests that the stronger the ‘threat’ of a VER on the
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unrestrained firm, the higher the expected domestic equilibrium price, even if the VER is never imposed. Some useful extensions of this analysis would be to (a) consider exporters’ goods as imperfect substitutes, and (b) endogenize the probability of the VER. Imperfect substitutability would obviously mean that if the unrestricted firm undercut the restrained exporter, the latter would not lose all customers. Endogeneity of the probability of the VER is suggested by the institutional framework itself. For example, restraints on new countries in apparel trade appear to be triggered by rapid growth of exports, even if the level of exports is low. However, the above analysis emphasizes the fact that the asymmetry and uncertainty introduced by the VER alter the behavior of both the directly restrained exporter and the unrestrained exporter. This leads to higher import (and domestic) prices for the imposing country than would prevail if the unrestrained exporter perceived no threat of a potential VER. Appendix
Theorem 1. Under Assumptions (PSE) exists if and only if q>
I, 2, and 3. a pure strategy equilibrium
b 0 P” ’
(*I
This PSE is unique and is characterked by A charging pv with probability I and B charging p4 with probability 1. A’s expected return is qpvVA and B’s is Mq). Theorem 2.
If q 5p,/p,, and (i) ~~~~~~ then there exists a unique mixed strategy equilibrium p*=
(,uX,&) which is given by: /G(P) = 07
P,$P*
P*(P) = 19 l&P) =Q
1
/G(P) = 1-q [
l-p”, 1 P
P
~A5PcP4,
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The expected payofffor A is equal to p*V,= qpcVA. The expected payofffor B is equal to n,(p,,q). then there exists a unique mixed strategy equilibirum, p* = (ii) fA
/G(P) = 1 -
nf- X,(Pv4)
p(l _q)VA ’
_p+p-=p37
/G(P) = 19
P32P7
/G(P) = 09
P
1
&(P) = ~ 1-q
[
1-L!!, 1 P
,4(P) = 1,
eBi5P
P3 SP*
The expected payofffor A is equal to PAVE. The expected payofffor B is equal to x:(q). Theorem 3. equal to
(iii)
Let pe be the expected
qp ” +pBln&
b’
if
price in the home country. Then p’ is
o
Note that (i)-(iii) correspond exactly fo the pure strategy equilibrium, the MSE case (i), and the MSE (ii), respectioely. References Bhagwati, J. and T.N. Srinivasan, 1976, Optimal trade policy and compensation under endogenous uncertainty: The phenomenon of market disruption, Journal of International Economics 6, 3 17-336.
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Brander, J.A. and B.J. Spencer, 1981. Tariffs and the extraction of foreign monopoly rents under potential entry, Canadian Journal of Economics 14. 371-389. Dean. J. and S. Gangopadhyay, 1989, Strategic trade practices in the presence of a VER. manuscript. Dixit, A., 1984. International trade policy for oligopolistic industries. Economic Journal Conference Papers 94. I-16. Eaton. J. and G. Grossman. 1986, Optimal trade and industrial policy under oligopoly, Quarterly Journal of Economics 101, 383-406. Harris, R., 1985, Why voluntary export restraints are ‘voluntary’, Canadian Journal of Economics 18, 799-809. Krishna, K.. 1983, Trade restrictions as facilitating practices, Woodrow Wilson School, Princeton University 1983 Discussion Paper no. 55. Murray. T., W. Schmidt and 1. Walter, 1983, On the equivalence of import quotas and voluntary export restraints, Journal of International Economics 14, 191-194. Takacs. W., 1978. The non-equivalence of tariffs, import quotas and voluntary export restraints, Journal of International Economics 8, 565-573.