The welfare effect of international cost harmonization*
Anthony Creanea and Kaz Miyagiwab
Abstract
Cost harmonization is said to occur when foreign firms’ marginal costs are brought closer or
equalized to domestic firms’ costs. It can occur for various reasons, ranging from foreign direct
investment to falling transport cost and policy changes in the foreign country. In this paper we
derive general welfare effects of cost harmonization that can be induced by any of these changes.
Assuming Cournot oligopoly, we identify a number of situations in which cost harmonization,
whether induced by rising or falling marginal costs for foreign firms, can reduce domestic
welfare. We then apply the results to various cases and evaluate policy implications.
Key words: cost harmonization, FDI, Cournot oligopoly, export subsidy
a
Department of Economics, Michigan State University, East Lansing, MI 48824-1038 USA;
creane@msu.edu
b
Department of Economics, Emory University, Atlanta GA 30322-2240 USA;
kmiyagiwa@gmail.com
*
We benefited from comments by C. Davidson, S. Matusz, C.-H. Miao, J. Tirole, and seminar
participants at the Michigan State University, University of South Carolina and at the 2009 EEA
and the 2010 COE Hitotsubashi University Trade meetings. All errors are our own.
1
1. Introduction
Cost harmonization is said to occur when foreign firms’ (marginal) costs are brought
closer or equalized to those facing domestic rivals. Cost harmonization can occur for various
reasons; for example, by falling transport costs, which brings the foreign firms’ cost down to the
level facing the domes. As another example, suppose that the foreign government dismantles its
export subsidy programs. Then, the loss of subsidies raises the foreign firms’ costs, thereby
closing the cost gap between the foreign and the home firms. In this case, the cost is closed by a
rise in the foreign firms’ cost.
Cost harmonization can arise in other circumstances, i.e., as a result of tax laws changes
in foreign countries or adoption of cost-saving technology by foreign firms. The costharmonizing phenomenon most analyzed in the literature perhaps concerns foreign direct
investment (FDI). It is standard in the literature to assume that FDI lowers foreign firms’
marginal cost relative to exporting. However, cost-raising FDI is not too uncommon to observe
in the real world, as firms often choose to locate to higher-marginal cost countries for various
reasons; e.g., to escape from high home country corporate taxes, to avoid future trade conflicts
with host countries, to take advantage of FDI inducement measures, which often decrease
overhead costs, or simply because FDI results in a sufficient decrease in fixed costs of operation.
A well-known example of cost-raising FDI is demonstrated by the case of Japanese automakers,
which initially exported all of their cars to the United States from Japan, where production costs
were lower, but which soon moved production in the U.S. to avoid trade barriers present and
potential, even though relocation raised their production costs. As these examples show, cost
harmonization can occur both when foreign firms’ costs rise and when they fall, depending on
their initial level relative to that of home firms.
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The objective of the present study is to examine the welfare effect of cost harmonization
when firms engage in oligopolistic competition in the domestic market. To motivate our analysis,
suppose that harmonization arises from foreign cost falling to the domestic level. Evidently, this
intensifies competition, decreasing profit to the domestic firms. However, stiffer competition
benefits domestic consumers, so the welfare effect hangs in the balance of these two opposing
changes. Suppose that the loss outweighs the benefit, so domestic welfare is decreased. Given
this result, then one is tempted to conclude that rising foreign costs in the identical circumstance
must increase domestic welfare. However, such a conclusion is erroneous, since domestic
welfare can decrease when foreign firms’ costs rise. Our objective is therefore not to examine
various instances of cost harmonization separately, which has been done in the literature. Rather,
our goal is to present the general welfare implications of cost harmonization in a common
framework. In particular, we want to identify the conditions under which cost harmonization,
whether induced by rising or falling foreign cost, is harmful to domestic welfare.
The remainder of the analysis is organized in four sections. The next section presents the
basic model. Section 3 is the main section. Among several results we obtain here, we find that if
domestic output share exceeds 40 per cent of industry output, cost harmonization, whether
induced by rising or falling foreign cost, can reduce domestic welfare. Section 4 applies the main
results of section 3 to various cases and derives policy implications for the domestic country.
Section 5 concludes.
2. Model
Suppose n firms compete in the domestic country, of which nd are domestic and nf are
foreign. Let n denote the total number of active firms; i. e., n = nd + nf. All domestic firms face
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(constant) marginal costs cd. All foreign firms initially have marginal costs cf, but some or all of
them may face cd as a result of cost harmonization, where cd can be higher or lower than cf. Let x
denote the number of foreign firms whose cost has changed from cf to cd, with 0 ≤ x ≤ nf. That is,
cost harmonization will have nd + x (domestic and foreign) firms produce at marginal cost cd and
nf – x foreign firms produce at cf.
Turning to the domestic market demand, we consider a representative consumer model
with quadratic preferences given by U(Q) = Q – Q2/2, where Q is industry output. This
preference specification yields the inverse domestic market demand given by P = 1 – Q.
Firms are assumed to play a quantity-setting (Cournot) game, with a representative firm i
choosing output qi to maximize profit πi = (1– Q – ci)qi. From the first-order conditions of all
firms we obtain the Cournot-Nash equilibrium. We assume that the values of cd and cf are such
that all firms produce positive output in equilibrium at all times. It is straightforward to show
that a firm facing marginal cost cd, be it foreign or domestic, has equilibrium output
qd(x) = [1 – (nf + 1)cd + nf⋅cf + x⋅(cd – cf)]/(n + 1),
while a foreign firm facing marginal cost cf has equilibrium output
qf (x) = [1 – (nd + 1)cf + nd⋅cd + x⋅(cd – cf)]/(n + 1).
With nd + x firms producing at the cost cd and nf – x foreign firms producing at the cost cf,
aggregate output is
Q(x) = [n – nd⋅cd – nf⋅cf – x⋅(cd – cf)]/(n + 1).
From these expressions the profits to the representative domestic firm is
πd(x) = qd(x)2.
Given the preferences on our representative consumer, consumer surplus is
CS(x) = Q(x)2/2.
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Therefore, domestic welfare, comprising domestic consumer surplus and total profits to domestic
firms, is given by:
W(x) = nd⋅πd(x) + Q(x)2/2.
This completes the description of the model.
3. Welfare effects of cost harmonization
Our strategy is to examine the welfare effect of a change in the number of foreign firms
whose costs have changed. Although x is discrete, we find it more convenient to treat x as
continuous. This has no serious consequences for our analysis, as we show shortly. Then, W(x),
given at the end of section 2, is differentiable. Therefore, the welfare change from x foreign
firms adopting cost cd is given by
W(x) – W(0) =
where
W’(x) = (cd – cf)(2ndqd(x) – Q(x))/(n + 1) .
(1)
In (1) W’(x) measures the marginal welfare impact of cost harmonization, i. e., a welfare change
as a small fraction of foreign firm undergoes cost change from cf to cd.
Equation (1) shows that a welfare change hinges on the product of two terms. One is the
cost differential, cd – cf. This term determines the direction of cost harmonization, and is positive
if and only if the foreign cost is initially lower than the domestic cost. The other term on the
right-hand side of (1), 2ndqd(x) – Q(x), pertains to the output share of the domestic firms. This
term is positive if and only if domestic output exceeds half the industry output Q(x); i. e., ndqd(x)
> Q(x)/2.
Differentiating (1) yields the second derivative:
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W′′(x) = (1 + 2nd)(cd – cf)2/(n + 1)2 > 0.
(2)
This implies that W(x) is convex in x. Now, the next result is immediate from equations (1) and
(2).
Lemma 1:
(A) if W ′(0) > 0, FDI is welfare-improving.
(B) if W ′(0) < 0 and W ′(x) < 0, FDI is welfare-decreasing.
(C) If W ′(0) < 0 and W ′(x) > 0, then max {W(0), W(x)} ≥ W(y) where 0 < y < x.
The first part of the lemma says that, if W’(0) is positive, domestic welfare is maximized at x =
nf. On the other hand, if W’(0) is negative, then lemma 1B and 1C imply that domestic welfare is
at its maximum either at x = 0 or x = nf. These observations immediately yield the next result.
Corollary 1: Domestic welfare is maximized when either cost harmonization affects all the
foreign firms or none at all.
The exclusion of the middle implies that the welfare impact of cost harmonization is fully
examined by comparing welfare at x = 0 and x = nf.
When there are no domestic firms, domestic output is clearly less than half the industry
output. Therefore, by (1) the welfare effect of cost harmonization depends on the initial cost gap.
Corollary 2: When there are no domestic firms, cost harmonization improves domestic
welfare if and only if cost harmonization decreases foreign firms’ cost.
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We now turn to more general cases.
Case nd = n/2 (half the firms are domestic)
This case includes the standard Cournot duopoly case of one domestic and one foreign firm. If
half the firms are domestic, the domestic firms can have more than half the market if and only if
domestic cost is lower, that is, ndqd(x) > Q(x)/2. if and only if cd < cf. Thus, the domestic output
share term and the cost differential term in (1) are always in opposite signs, meaning that W′ (x)
< 0 for all relevant x. Then by lemma 1.B, and continuity we obtain this surprising result.
Proposition 1: When sufficiently close to half of all producers are domestic, cost
harmonization reduces domestic welfare, whether cost harmonization decreases or
increases the foreign firms’ costs.
This result is related to the finding by Ono (1990), who analyzes the welfare effect of foreign
sales in the oligopolistic domestic market. Treating foreign output as a parameter and assuming
that domestic firms play a Cournot game under the residual demand, Ono (1990) shows that
domestic welfare reaches its minimum when foreign sales capture exactly 50 percent of total
sales in the domestic market. His analysis abstracts from competition between domestic and
foreign firms, and hence the effect of foreign cost relative to domestic cost, let alone the
implications of cost harmonization, is left unexamined.
We turn to another case often analyzed in the literature (e.g., Qiu and Zhou 2006).
Case: nd = n - 1 > 1 (all firms but one are domestic).
If nd = 1, this case is reduced to the standard duopoly case, which has already been examined, so
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assume nd ≥ 2. Straightforward computation yields
W′ (0) = [(n – 1)qd(0) – qf(0)](cd – cf)/(n + 1)
W′ (1) = (nd – 1)qd(1)(cd – cf)/(n + 1).
Suppose that cd < cf. Then, cost harmonization lowers the foreign firm’s cost. The cost inequality
also implies that qd(0) > qf(0), so W′ (0) < 0. We also have that W′ (1) < 0. Then, lemma 1.B
implies that cost harmonization decreases domestic welfare. This has the following intuitive
explanation. Cost harmonization makes the lone foreign firm (whose cost was higher) more
efficient. As the foreign firm expands output as a result, all domestic firms contract output. Since
domestic firms are more efficient than the foreign firm, their output contraction results in a
decrease in domestic welfare. This is similar to the result obtained by Lahiri and Ono (1988),
who have shown that in autarky a slight cost reduction by the most inefficient firms can reduce
domestic welfare by causing output contractions of more efficient firms.
We have just shown that cost harmonization induced by falling foreign costs reduces
domestic welfare. Then it is tempting to conclude that cost harmonization induced by rising
foreign costs must increase domestic welfare. Surprisingly, however, this symmetry in results
does not always hold. To see this, note that cd > cf implies that W′ (1) > 0, as can easily be
checked. However, it is possible that W′ (0) < 0, that is,
(n – 1)qd(0) – qf(0) < 0.
(3)
If that is the case, lemma 1.C implies that domestic welfare can still fall. Condition (3) is likely
to be satisfied if qd(0) is sufficiently small relative to qf(0), that is, cd is sufficiently higher than
cf.1 Of course, a symmetry in results can occur too. If cd is sufficiently close to cf, condition (3) is
reversed so W′ (0) > 0. Therefore, by the lemma domestic welfare increases. The next proposition
summarizes the key findings of the present case.
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Proposition 2: Suppose there is only one foreign firm (nf = 1). Then:
(A) if cd < cf, cost harmonization is welfare-decreasing;
(B) if cd > cf, cost harmonization is welfare-decreasing (welfare-increasing) if the domestic
cost is sufficiently higher than (close to) the foreign cost
The above cases illustrate the importance of the distribution of firm ownership. For cost
harmonization triggered by rising foreign cost, welfare decreases if there are no domestic firms
but may increase welfare if there are a sufficient number of domestic firm. However, if the cost
gap is sufficiently high, cost harmonization always decreases welfare, no matter what the
proportion of domestic firm ownership (the proof is in the appendix).
Proposition 3. If the domestic cost is sufficiently high relative to the foreign cost, cost
harmonization induced by rising foreign cost can be welfare decreasing, no matter how
large the share of domestic production.
Cost harmonization induced by falling foreign cost is welfare-increasing if there is no
domestic ownership (corollary 2), but it is welfare-decreasing when domestic ownership exceeds
50 percent (proposition 1). In fact, this percentage can be pushed down to 40 percent for a
sufficiently large cost gap (see the proof in the appendix). This, together with Proposition 3,
leads to the following general result.
Proposition 4: When at least 40% of the firms are domestic, cost harmonization is welfare-
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decreasing when marginal cost differentials are sufficiently large, whether cost
harmonization results in a decrease or an increase in the foreign cost.
4. Applications
In this section we apply the main findings from section 3 to several cases of cost
harmonization that are examined in the recent literature. We begin with cost harmonization that
occurs when foreign firms change access modes from exporting to FDI.
4.A. Exporting versus FDI
There is a vast and growing literature comparing exporting and FDI; see, e.g., Markusen
(2002). Although most of this literature focuses on FDI that reduces foreign firms’ marginal cost,
FDI can result in increases in their marginal cost, as we noted in the introduction. In this
subsection we examine both cases of cost harmonization in the common framework by explicitly
considering the role fixed and variable cost can play in the foreign firm’s decision to choose FDI
over exporting. We then examine how home country government policy tools can be used to
raise domestic welfare. We conclude this subsection by considering world welfare in this
environment. Surprisingly, we are able to show that profitable FDI can make the whole world
worse off.
To focus on the issue at hand, consider the duopoly model, with one foreign firm and one
domestic firm, which is standard in this literature. As before, the domestic firm’s marginal cost
of production is cd. In contrast, the foreign firm faces marginal cost cf and fixed cost Ff if it
chooses to export, and marginal cost cd and fixed cost Fd if it chooses FDI. It is assumed that the
values of cd, cf, Fd and Ff are such that the both firms produce positive quantities in equilibrium.
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The foreign firm’s profit from exporting is
(1 – 2 cf + cd)2/9 − Ff
while its profit from FDI is
(1 – cd)2/9 − Fd.
The foreign firm then prefers FDI over exporting whenever
(4/9)(1 – cf)(cf – cd) – (Fd – Ff) > 0.
(4)
As is clear from (4), the foreign firm can prefer FDI even if domestic marginal cost is greater
than foreign marginal cost because of the fixed cost difference.
Many governments provide subsidies in order to attract FDI. Such inducements are
necessary if foreign firms do not find it profitable to choose FDI over exporting, given cost
conditions. In a recent article, Chor (2009) has shown that a fixed subsidy for FDI can raise
domestic welfare under monopolistic competition. Using our previous derivations, however, we
can immediately obtain the opposite result for oligopolistic industry. First, we have already
established that in a duopolistic environment cost harmonizing reduces domestic welfare
(proposition 1). Second, any subsidy to the foreign firm is a transfer to the foreign firm, which
further reduces domestic welfare. Hence, a fixed subsidy for FDI can reduce domestic welfare
under international oligopoly.
Chor (2009) also shows that a per-unit subsidy could raise domestic welfare. However, in
the presence of strategic interaction, a per-unit subsidy for the foreign firm choosing FDI always
reduces welfare under international duopoly. To show this, note that domestic welfare in this
case comprises consumer surplus, the domestic firms profit, and the cost of the subsidy, i.e.,
(2 – 2cd + s)2/18 + (1 – cd – s)2/9 – s(1 – cd + 2s)/3
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The derivative at is negative:
(– 1 + cd)/3 < 0.
(5)
Intuitively, domestic welfare falls because (i) a production subsidy results in the cost
harmonization when it induces the foreign firm to choose FDI over exporting and (ii) a
production subsidy is a drain on national income. Thus, our results contrasts sharply with those
from the Dixit-Stiglitz framework (Chor 2009).
Proposition 5: Either a fixed or a per-unit subsidy for the foreign duopolist, when it
chooses FDI, reduces domestic welfare.
A direct corollary of the above analysis is that a per-unit tax on FDI raises domestic
welfare, even if we ignore the tax revenue, because the tax causes dis-harmonization of costs.
From (5), the optimal per-unit tax on FDI production, ignoring the possibility of the foreign firm
choosing to export, is computed to be
(6)
However, this tax rate may be untenable because at this rate the foreign firm prefers exporting to
FDI. In that case, the optimal tax requires that the government lower the tax until the foreign
firm is indifferent between exporting and FDI. Denote this tax t′, which is defined by
For the case when there are no fixed cost (Fd = Ff = 0) so that it must be that domestic marginal
cost are lower (cf > cd) for (4) to hold, this tax is simply the marginal cost difference: t′ = (cf −
cd). In this case from (6), t’ is the optimal tax whenever cf ≤ (2 + cd)/3. We summarize the case
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with no fixed costs with
Proposition 6: When there are no fixed costs by location and the foreign firm prefers FDI,
the optimal per-unit tax is (cf − cd) when cf ≤ (2 + cd)/3 and (1 − cd)/3 otherwise.
If there are fixed costs, the analysis becomes subtler. First, consider the case in which
domestic fixed costs are greater than foreign fixed costs (Fd > Ff). Since (4) holds, it must be
that domestic marginal cost is lower (cf > cd), but also that t′ < (cf − cd) to compensate for the
increase in fixed cost. As a result there is partial harmonization, which still harms domestic
welfare. In this case, if the harm from the (diminished) cost harmonization is greater than the tax
revenue, a tax greater than t′ is optimal so as to prevent FDI; it is optimal for the government to
forgo the possible tax revenue.
Consider next the case in which foreign fixed costs are greater than domestic fixed costs
(Fd < Ff). In this case t′ > | cf − cd |, as the domestic government can capture the foreign firm’s
fixed cost gain. This case needs to be further broken down into two cases, depending on the level
of foreign marginal cost relative to domestic marginal cost. If foreign marginal cost is greater (cf
> cd), then t′ > 0 and as a result this tax causes cost dis-harmonization relative to the exporting
state: FDI increases domestic welfare because of the greater cost dis-harmonization and the tax
revenue. Indeed, the domestic government could induce this outcome by setting a fixed import
fee (thereby raising Ff) and correspondingly increasing the per-unit fee for when the foreign firm
chooses FDI.
On the other hand, if foreign marginal cost is less than domestic marginal cost (cf < cd),
then there still is cost harmonization with FDI if t′ < 2(cd − cf) as in the case when foreign fixed
13
cost is less than domestic fixed cost, in which case the optimal policy is to prevent FDI by setting
the tax greater than t′.
We close this subsection by considering the implications of cost harmonizing FDI on
world welfare. A standard presumption is that even if domestic welfare is harmed by costharmonizing FDI, the benefit to the foreign firm from choosing FDI should offset the domestic
harm, that is, world welfare should increase if FDI is profitable to the foreign firm. Here we
show that this presumption can be incorrect, that is, world welfare can be reduced by profitable
FDI.
World welfare is defined as the sum of the foreign firm’s profit and domestic welfare.
Domestic welfare is harmed when the foreign firm chooses FDI:
W FDI – W X = −(cf – cd)2/6.
The change in world welfare when the foreign firm chooses FDI is
.
(7)
The first two terms measure the profit gain to the foreign firm when it switches from exporting to
FDI; cf (4). If this gain is sufficiently small, (7) is positive since the last term is always positive
for all cd ≠ cf. We can now state our result.
Proposition 7: Assume both firms are active. Suppose that the profit gain to the foreign
firm from choosing FDI over exporting is sufficiently small. Then, profitable FDI that
(strictly) harmonizes marginal costs and raises either the foreign firm’s marginal cost or
fixed cost reduces welfare.
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4.B. Other applications
Our results also shed light on the welfare impact of falling transport costs, a quintessence
of globalization. To see this, assume there is no FDI and foreign firms export their products
initially at cost cf > cd, where the cost difference is due to transport costs. Then ρ is the inverse of
transport costs – a measure of globalization, with ρ = 1 indicating the case of complete cost
harmonization. Then, W(nf) – W(0) measures a welfare change caused by lower transport costs.
The implications are straightforward: for example, the domestic country is harmed when the
domestic firms have the majority of the market and when transport costs fall (proposition 1).
Our results also have some implications for the strategic trade policy literature. To see
this, consider the standard setting, in which one home and one foreign firm compete Cournot
fashion in the domestic market. In this setting, the optimal tariff is positive,2 which implies that
trade liberalization or removal of the (optimal) tariffs decreases domestic welfare. While this
welfare loss is often attributed to the lost tariff revenues, our analysis shows that domestic
welfare falls without the loss of tariff revenues. Since trade liberalization induces cost
harmonization, like cost-reducing FDI, all the results from the previous sections apply. If the
revenue losses are taken into account, domestic welfare can decrease even if domestic firms are
less than 40 percent.
As another application of our results, consider the case in which the domestic country
practices “free trade” but the foreign government either taxes or subsidies its firms’ exports to
the domestic market. Then, our analysis implies that the domestic country is made worse off if
the foreign government moves to freer trade by reducing its tax (or subsidy) on its exporters
because of the cost harmonization effect such policy changes can bring about.
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5. Concluding remarks
We live in a globalized world. Globalization takes many forms: falling transport cost,
limiting export subsidies, switching from exporting to FDI, and coordinating corporate income
taxes across countries, to name a few. Many of these changes bring foreign firms’ (marginal)
costs closer to those faced by their domestic rivals, a phenomenon which we call cost
harmonization. In this paper we consider the welfare implications of cost harmonization between
domestic and foreign firms when they compete strategically in the domestic market.
As we emphasized in the text, cost harmonization arises when foreign firms’ marginal
costs fall, as well as rise, to those facing domestic rivals. The diametrically opposite movements
of foreign costs may at first appear to yield the diametrically opposite effect on domestic welfare.
However, our analysis shows that is not always the case. In fact, assuming Cournot oligopoly
with linear demand and constant marginal costs, we can identify a number of situations in which
cost harmonization can reduce or increase domestic welfare, whether induced by rising or falling
foreign costs. Of particular interest is the finding that, when domestic firms produce 40% or
more of total industry output, cost harmonization can reduce domestic welfare, regardless of the
direction of foreign cost change. We then apply the main results to various cases that have
received closer attention in the recent literature, especially, the foreign firms’ FDI decisions, and
derive policy implications.
16
Appendix: Proof of Proposition 3 and 4
Let s = nd/n denote the proportion of firms that are domestic. Substituting, we obtain
W(0) = s⋅n{1 – (1 + n(1 – s))cd + n(1 – s)cf}2/(n + 1)2
+ n2[1 – scd – (1 – s)cf]2/[2(n + 1)2].
W(nf) = s⋅n(1 – cd)2/(n + 1)2 + n2(1 – cd)2/[2(n + 1)2].
Hence, after manipulation we obtain
W(nf) – W(0) = -A⋅n2(1 – s)(cd – cf)/[2(n + 1)2]
where
A = (1 – s)(1 + 2s⋅n)(cd – cf) + 2(1 – 2s)(1 – cd)
Suppose that cd > cf. Then W(nf) < W(0) if and only if A > 0. We compute for given cf the largest
cd such that qd(0) = 0. We then substitute that value, cd = [1 – (1–s)n⋅cf]/[1 + (1 – s)n], into A,
finding after collecting terms that A > 0 if and only if
(1 + 2s⋅n) + 2n(1 – 2s)= 1 + 2n(1 – s) > 0.
Since the last inequality holds for any n and s, we have proved Proposition 3. Suppose next that cd < cf. Then, W(nf) < W(0) if and only if A < 0. We then compute for
given cd the largest cf such that there are interior solutions: cf = (1 + s⋅n⋅cd)/(1 + s⋅n). Substituting
this, A < 0 if and only if 2(1 – 2s) – (1 – s)(1 + 2s⋅n) < 0. This is satisfied only if
.
The right hand side is decreasing in n, so evaluating it at n = 2 we find that A < 0 if s > (7 –
351/2)/8 ≈ 0.39. This result combines with Proposition 3 to prove Proposition 4. 
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Endnotes
1. The maximum cd that results in an interior solution (all firms produce) is cd = (1 + cf)/2,
obtained by solving qd(0) = 0. At that value of cd, qf(0) > 0 and hence (3) holds.
2. Unless demand is highly convex; see Brander and Spencer (1984).
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