Reciprocal Dumping Model of
International Trade
Brader, James and Krugman, Paul (1983)
S. Bharathi
Rahul Singh
Ashish Bharadwaj
Arindam Jana
Introduction
What is “dumping”?
• If a profit maximizing firm believes it faces
a higher elasticity of demand abroad that
an home, and it is able to discriminate
between foreign and domestic markets,
then it will charge a lower price abroad
than at home. This is dumping.
• Such an explanation seems to rely on
“accidental” differences in country
demands.
Dumping contd…
• Under the assumptions of imperfectly
competitive segmented markets. (Helpman,
1982)
• Seen to be welfare improving.
• However it is still a controversial issue in trade
policy, where it is widely regarded as an “unfair”
practice subject to rules and penalties.
P, C
PDOM
MC
PFOR
DFOR = MRFOR
DDOM
MRDOM
O
QDOM
QMON
Domestic Output
Exports
Total Outputs
Q
“Reciprocal” Dumping
• Brander (1981) argues that oligopolistic
rivalry between firms would naturally give
rise to RD – Each firm dumps into other
firms’ home market.
• The model tries to show that free entry
gives rise to welfare improvement, ex post;
but it is possible that welfare may decline.
The Model
• Basic Cournot Duopoly Market.
• Positive transportation costs incurred in
exporting goods
• Identical countries
• Producing single identical (Brader,1981)
commodity, Z, with symmetric cost
structures
• Constant marginal costs, c
The profit functions of each firm is as below:
π = x. p( Z ) + x* . p* ( Z * ) − c( x + x* g ) − F
π * = y. p(Z ) + y . p (Z ) − c( y + y g ) − F *
*
*
*
*
By symmetry we need to only consider the domestic country
Best Reply Function (First Order Conditions)
π x = x. p '( Z ) + p − c = 0
π * = y. p '(Z ) + p − c g = 0
y
0 ≤ g ≤1
Their solution is the trade
equilibrium
•
•
Let σ = y/Z = y/x+y, the foreign share in
domestic market, and,
ε = -p/Z.p’, elasticity of domestic demand
Rewriting the implicit best-reply functions, we get,
p = cε ( ε + σ − 1)
and,
p = cε g ( ε −σ )
Solving for σ and p we get,
σ = (ε ( g −1) +1) (1+ g)
p = cε (1 + g ) g ( 2ε − 1)
Assuming that the second order
conditions are satisfying the maxima
(proof in Seade (1980) and Friedman
(1977); shown as in the case of noncooperative models),
•Own marginal revenue declines when
other firm increases output
•Equivalent to downward sloping best
response functions
•They imply stability, and if held
globally, an unique equilibrium
Best response functions
(using constant elasticity demand, p=A.Z-1/ε)
• Reciprocal dumping occurs when
monopoly mark-ups exceed transport
costs ex-ante
• RD is not Pareto Efficient since monopoly
distortions exists ex post
• The question, however, is whether in the
second best world free trade is superior to
autarky or not?
• Trade
Welfare loss/gain ?
Conflicting effects on welfare
Prohibitive level: p=c+t and y=0
Since dZ/dt = dx/dt + dy/dt
dW/dt > 0 since dx/dt > 0
A slight fall in transport cost tends to make
domestic output (x) fall as imports (y)
come in. Therefore, a slight fall in t from
the prohibitive level would reduce welfare.
Decline in costs
Rise in consumption
Loss due to replacement of domestic
production
Welfare Effects Under Free Entry
Rewriting the implicit best-reply functions under the n firms case and
solving for σ and p, we get
σ = ( nε ( g −1) +1) (1+ g)
p = cεn(1+ g) g ( 2nε −1)
FOC for each firm maximizing
profit is:
Also, each firm earns zero profit because
of free entry
•After trade, price movements explain changes in welfare
•Price falls
welfare rises
•This can be shown by the fall in price ex post
Proof:
(from FOC)
=>
>0
(from second order assumptions)
Therefore profits can now be given as:
•If Δp, Δx ≥ 0 => (p-c)xi – F > 0
•(p*-c/g) x*I > 0 since p*>c/g if trade takes place
Therefore, profits must be strictly positive which is a contradiction
Price falls => Welfare rises
Conclusion
• Oligopolistic interaction between firms can cause
trade in the absence of any usual motivation for
trade
• Neither cost differences nor economies of scale
are necessary
• Interesting welfare effects of RD
Low TC
High TC
positive profits welfare increase
loss welfare decline
Free entry Cournot model increases welfare
• If we move from Cournot model to Bertrand
model, RD does not arise in the homogenous
product case product differentiation
required
• Important element is just that firms have a
segmented markets perception
• Given this perception, this kind of trade is
relatively robust
• This model of RD can be extended to a twoway FDI model (Baldwin & Ottaviano, 2001)
Friberg (2005) has investigated whether
transport cost losses from trade can outweigh
the partial equilibrium gains from trade (stronger
competition and more brands to choose from).
He has evaluate the empirical relevance of the
proposition that trade can lower welfare through
wasteful transportation.
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