This note qualifies the statement made in Bouët (2001), European Economic Review 45, 323-336, by showing that within the model proposed by the author the effect of a VER on research and development does depend on the mode of competitionprice competition

Xavier Wauthy

English

Research Papers in Economics

A note on Research and Development and Voluntary Export
Restrictions". 
Xavier Wauthy
CEREC, facultés Saint−Louis, Bruxelles and CORE
Abstract
This note qualifies the statement made in Bouët (2001), European Economic Review 45,
323−336, by showing that within the model proposed by the author the effect of a VER on
research and development does depend on the mode of competition
Citation: Wauthy, Xavier, (2002) "A note on Research and Development and Voluntary Export Restrictions".." Economics
Bulletin, Vol. 6, No. 1 pp. 1−6
Submitted: November 8, 2001.  Accepted: February 5, 2002.
URL: http://www.economicsbulletin.com/2002/volume6/EB−01F10002A.pdf1 Introduction
In a recent issue of the European Economic Review, Bou¨ et (2001) oﬀers yet a new contri-
bution to the strategic trade policy literature. The main result of his paper is that under
Cournot competition, a VER decreases R-D expenses while a tariﬀ increases innovation.
Then, this result is generalized to Bertrand competition. Quoting the paper’s abstract, we
are indeed told that ”When the R-D investment has uncertain consequences on marginal
cost, a voluntary export restriction (VER) decreases innovation by the domestic producer
as compared to the free trade level. This result holds both under Cournot and Bertrand
competition” (p.323).
The aim of the present note is to qualify the above claim: contrary to the above
statement, the qualitative impact of the VER on R-D investment does depend on the
mode of market competition in Bou¨ et’s model. To support our claim, we shall proceed
in three steps. First, we brieﬂy recall of the argument underlying Bou¨ et’s result. Then
we consider two examples in which the presence of the VER increases R-D investment,
instead of decreasing it. Last, we brieﬂy sketch the economic intuition which underlies
our result.
2 Bou¨ et (2001)
The part of Bou¨ et’s paper that is relevant for the present comment can be summarized
as follows.
• Think of a domestic ﬁrm (denoted N, for Northern) being challenged in its domestic
market by a foreign one (denoted S, for Southern). Firm S produces at low marginal
cost. Before entry takes place, ﬁrm N may invest in R-D. If the R-D program is
successful, N produces at low marginal cost whereas if it is not successful, the
domestic ﬁrm produces at a higher marginal cost. R-D expenses therefore results
from a willingness to remain competitive against a low cost entrant.
• Firm N may thus engage in R-D. However, the outcome of the R-D activity is
uncertain and by investing more, ﬁrm N increases the probability of success for its
R-D program. In equilibrium, the optimal R-D investment level reﬂects the trade-
oﬀ between higher R-D expenses sunk in stage one and the increased prospects for
high proﬁts that are associated with producing at low cost in stage 2.
• Suppose now that the game is altered in a way such that ﬁrm N’s payoﬀs increase in
the case of an unsuccessful R-D activity but are not aﬀected in the case of a successful
program. Since the domestic payoﬀ in case of ex post wasteful R-D expenses has
increased while remaining unchanged in case of successful R-D, the marginal beneﬁt
of R-D investment has decreased in this modiﬁed game, so that ﬁrm N invests less
in equilibrium.
Bou¨ et (2001) shows that, under Cournot competition, any VER which is binding in
case of unsuccessful program and not binding otherwise, alters the game precisely in the
way alluded to here above. So that the VER induces less R-D.
Then, the author claims that a similar result obtains under Bertrand competition. In
order to make his point, he replicates the argument developed under Cournot competition.
1The argument runs as follows. Suppose the quota is set exactly at the equilibrium level
of foreign’s sales in the unsuccessful R-D price subgame. This quota is not binding at the
equilibrium of the price subgame that follows a successfull R-D program. Relying on the
analysis of Krishna (1989), we know that the quota set at the free trade level will increase
ﬁrm N’s proﬁt (more precisely both ﬁrms’ proﬁts) in the unsuccessful R-D price game.
If it leaves ﬁrm N’s equilibrium proﬁts in the successful R-D game untouched, this quota
will induce less R-D in equilibrium, exactly as under Cournot competition. Bou¨ et argues
that if the VER is set at the free trade level of the unsuccessful R-D price subgame, this
last condition is satisﬁed.
We provide hereafter two examples which show that the last part of the above argument
is not correct in general. In fact, Krishna (1989)’s main contribution is to show that
under price competition a VER tends to be eﬀective even if set above the free trade
equilibrium level, i.e. in the two subgames. In other words, we may expect that a quota
set at a level corresponding to the free trade equilibrium sales of the foreign ﬁrm in the
unsuccessful R-D game will increase domestic proﬁts whatever the outcome of the R-D
program. Accordingly, nothing can be said in general about the eﬀect of the VER on R-D
investment under price competition. In the nest two examples, the presence of the quota
increases the R-D investment of the domestic ﬁrm.
3 Example 1
Let us ﬁrst consider the linear example developed in Bou¨ et (2001), section 5, when il-
lustrating Cournot competition. We apply it to Bertrand competition, so that the only
diﬀerence between our treatment of the example and his is the mode of competition.
Market demand is given by p = a − (qN + qS) and we assume that a = 24. Firm S
faces a marginal cost cN = 3. Firm N faces a marginal cost ch = 9 if the R-D activity is
not successful and a marginal cost cl = 3 if it is successful. The probability of a successful
R-D activity is equal to
√
r where r ∈ [0,1] is the amount of R-D investment. We assume
that ﬁrms compete in prices.
In order to study the R-D investment decision, we solve ﬁrst the two possible price
subgames: the ”unsuccessful R-D game” (denoted UG) and the”successful R-D game”
(denoted SG), and then we go backward to address the R-D decision.
• In UG, the foreign ﬁrm beneﬁts from an absolute cost advantage. Under Bertrand
competition, the Nash equilibrium sees the low cost ﬁrm either playing its monopoly
strategy or naming a price that just undercuts the high cost ﬁrm. Under our par-
ticular parametrization, the monopoly solution is not feasible: the foreign ﬁrm thus
names pS =9 −  while the domestic ﬁrm names pN = 9. The domestic ﬁrm therefore
nets zero proﬁts in UG.
• In the SG, the two ﬁrms enjoy identical constant marginal costs. The unique Nash
equilibrium in this case is (3,3). The two ﬁrms share the market evenly and both
make zero proﬁts.
• Having solved the two possible price subgames, we note that the domestic ﬁrm nets
zero proﬁts in both cases. R-D investment is therefore purposeless and the optimal
decision is r = 0 under free trade.
2Consider now the introduction of a VER, that is set exactly at the level of demand
faced by the foreign ﬁrm in UG, i.e. VER=15+ , as proposed in Bou¨ et (2001, section 7).
• Even though this VER is apparently not binding in the SG, it alters the whole game,
so that a new equilibrium emerges. Under Bertrand competition with homogeneous
goods, a quantity restriction, imposed on one ﬁrm only, and set below the compet-
itive aggregate demand level ensures positive equilibrium payoﬀs to both ﬁrms (see
Levitan and Shubik (1972) for a theoretical treatment particularily well-suited for
the present analysis). By way of consequence, the introduction of the VER at a
level of 15+  will for sure yield positive payoﬀs for the domestic ﬁrm in SG. The
particular form of the (mixed strategy) equilibrium and the level of the payoﬀs will
depend on the exact speciﬁcation of the rationing rule at work in the market. Note
that a closed-form solution of such games is not necessary for our present purpose
(see Levitan and Shubik (1972)). We only need to know that πSG
N > 0.
• UG is formally equivalent to a pricing game where one ﬁrm faces a capacity con-
straint and where unit costs diﬀer. Again, obtaining closed-form solutions for such
games is far from being trivial (see Deneckere and Kovenock (1996) for a detailed
analysis of such pricing games). However, it the present case, the cost diﬀerential
is so large that as long as we consider VER at or suﬃciently close to 15, the free
trade equilibrium remains feasible. The intuition for this runs as follows: supppose
ﬁrm S is a monopolist facing a capacity constraint k, its monopoly payoﬀ is deﬁned
by πm = p.min{k,24 − p}. The maximum of this function is obviously pm =9−  .
Since this price is below ﬁrm N’s marginal cost, it cannot be undercut by ﬁrm N,
and therefore deﬁnes the optimal strategy of ﬁrm S Accordingly, the domestic ﬁrm’s
payoﬀs in UG is not aﬀected by the presence of the VER.
• Having solved the two subgames we can now go backward in the game tree. Since
the domestic ﬁrm’s payoﬀ in SG has increased, relative to free trade, whereas it is
unaﬀected in UG, ﬁrm N is more prone to invest in R-D than under free trade.
It is not necessary to compute the optimal R-D investment level to see that the presence
of the VER alters the domestic ﬁrm’s incentives in a direction that is exactly opposite to
what happens under Cournot competition: In this example, the introduction of the VER
tends to increase R-D expenses!
4 Example 2
The previous example looks rather extreme because under free trade the domestic ﬁrm
never ﬁnds it optimal to invest in R-D. Note however that it should not be viewed as
”pathological”: after all, it is an exact counterpart to the example considered in Bou¨ et
(2001) to illustrate his result under Cournot competition. Notice however that, when deal-
ing with price competition, Bou¨ et’s switches from an homogeneous example to markets
for diﬀerentiated products. Could it be then that our previous example owes too much
to the presence of homogeneous goods? The following example shows that the conclusion
of example 1 carries over to diﬀerentiated industries.
3Let us consider a textbook version of the Hotelling model with linear transportation
costs.1 We assume that ﬁrms are located at both ends of the unit line. The utility
derived by a consumer located at a distance d of ﬁrm i is deﬁned as S−d−pi. Refraining
from consuming yields a utility of zero. In the pricing games, ﬁrm S produce at zero
marginal cost while ﬁrm N produces at marginal cost a>0i nUG pricing games and at
zero marginal cost otherwise. The R-D investment stage is modelled as in the previous
example.
It is a straighforward exercice to obtain the following equilibrium characterization
under free trade.
• The price equilibrium in SG is given by pSG
N = pSG
S = 1, with DSG
N = DSG
S = 1
2 and
πSG
N = πSG
S = 1
2
• The price equilibrium in UGis given by pUG
N =1 + 2a
3 , pUG
S =1 + a
3, with DUG
N = 1
2−a
6,
DUG
S = 1
2 + a
6 and πUG
N = 1
2(1 − a
3)2.
Suppose now that we impose a quota on ﬁrm S at the level DUG
S = 1
2+ a
6 = q. Applying
the method laid out in Krishna (1989) it is relatively straighforward to show that no pure
strategy equilibrium will exist, neither in subgames UG, nor in SG. Instead a mixed
strategy equilibrium exists, in which ﬁrm N randomizes between a high price S − 1
2 + a
6
at which it sells 1
2 − a
6 and some lower price, while ﬁrm S plays a pure strategy.2 Since
ﬁrm N faces a pure strategy, its equilibrium payoﬀs can be computed at one of its atom.
Accordingly, we may state the following:
• In the presence of a quota q, ﬁrm N’s equilibrium payoﬀs in subgames UG is given
by πUG
S (q)=( S − 1
2 − 5a
6 )(1
2 − a
6).
• In the presence of a quota q, ﬁrm N’s equilibrium payoﬀs in subgames SG is given
by πSG
S (q)=( S − 1
2 + a
6)(1
2 − a
6).
It is then straightforward to show that ﬁrm N’s payoﬀs increase in UGand SGbecause
of the quota. Moreover, it turns out that the increase in payoﬀs tends to be sytematically
larger in SG than in UG. Therefore, in relative terms, the presence of the quota makes
the R-D investment more attractive. As in the previous example, we are thus lead to
conclude that the presence of the VER increases the marginal beneﬁt of R-D investment,
instead of decreasing it.
5 Comments
The reason why our two examples yield to a conclusion that runs against Bou¨ et’s one is
that the domestic ﬁrm payoﬀs increases due to the presence of the quota, whatever the
outcome of the R-D program. Whenever this is the case, the argument used in Bou¨ et for
establishing his main result (the fact that a marginal value of R-D investment decreases
because domestic payoﬀ in SG is not aﬀected by the VER) cannot be invoked. Obviously,
1The reader is referred to Tirole (1988) for the exposition of the model
2Boccard and Wauthy (1997) provide a detailed analysis for such pricing subgames.The present
characterization can be directly inferred from their model.
4we cannot claim either that a VER will never lead to a decrease in R-D eﬀort under price
competition. In order to apply the argument of Bou¨ et, one basically needs the quota to
be ”suﬃciently” above the free trade equilibrium level of the SG pricing game in order
to preserve the corresponding prices as a pure strategy equilibrium. What ”suﬃcently”
means exactly will essentially depend on the degree of product diﬀerentiation and the
costs diﬀerential. Given some cost diﬀerential, the larger the degree of diﬀerentiation, the
more likely it is that the R-D will decrease because of the quota. However, no general
conclusion should be expected to hold here.
Because we are considering a VER, the case of price competition is intrinsically dif-
ferent from the case of quantity competition: the basic feature of the VER in a Cournot
game is that it is not eﬀective if set above the Free Trade equilibrium level whereas the
basic feature of a VER under Bertrand competition is that it is eﬀective even if set above
the Free Trade equilibrium level. Accordingly, if some result obtained under Cournot
competition crucially depends on whether the VER is binding or not relative to the Free
Trade benchmark, we should not expect that it naturally extends to Bertrand competi-
tion. Stated diﬀerently, what makes Bou¨ et’s argument fully compelling under Cournot
competition is also what makes it not under Bertrand.
This conclusion is not too surprising since it captures in fact the essence of Krishna
(1989)’s paper: in oligopolistic markets, a quota has very diﬀerent implications depending
on the mode of competition. Fairly enough however, very few papers elaborated on
Krishna’s original idea by dealing explicitely with price competition in the presence of
export restrictions. In particular, almost all papers dealing with the possible impact of
quotas in early stages of oligopoly games (where ﬁrms commit to strategic variables such
as products’ characteristics, or R-D) retained a Cournot framework for the analysis of
the market competition stage. Accordingly, the key issue raised by Krishna has been
progressively overlooked. New material aimed at improving our understanding of price
competition in the presence of quantitative restrictions and product diﬀerentiation seems
to be called for.
References
[1] Boccard, N. and X. Wauthy (1997) ”Export restraints and horizontal diﬀerentiation”
CORE DP 9782; Universit´ e catholique de Louvain
[2] Bou¨ et, A. (2001) ”Research and development, voluntary export restriction and Tar-
iﬀs” European Economic Review 45, 323-336
[3] Deneckere, R., and D. Kovenock (1996) ”Bertrand-Edgeworth duopoly with unit cost
asymmetry”Economic Theory 8, 1-25
[4] Krishna, K. (1989) ”Trade restrictions as facilitating practices” Journal of Interna-
tional Economics, 251-270
[5] Levitan, R., and M. Shubik (1972) ”Price duopoly and capacity constraints” Inter-
national Economic Review 13, 111-122
[6] Tirole J. (1988) The Theory of Industrial Organization MIT Press, Cambridge Mas-
sachussets
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A note on Research and Development and Voluntary Export Restrictions".

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