international trade fall 2007 problem set 6 · international trade-fall 2007 problem set 6 1....
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International Trade-Fall 2007Problem Set 6
1. Import tari¤s
Determine welfare implications of imposing an import tari¤a) in a small country - perfect competitionb) in a large country - perfect competition
2. Reciprocal dumpingDe�ne reciprocal dumping. Discuss under what conditions reciprocal dumping is welfareimproving (globally).
1. Import tari¤sa) Consider the following partial equilibrium analysis from Feenstra ch7.
The supply of import goods to the small home market is unlimited at the current worldmarket price p�, therefore the supply curve X is horizontal.
Imposing a tari¤ t > 0 :
� The pass-through from tari¤s to home price will be 100%. p = p� + t and @p=@t = 1because p� is �xed. Hence, terms of trade is unchanged.
� Imports will decline, home production increases, consumption declines.
� Welfare: Change in consumer surplus: �(a + b + c + d), change in producer surplus:+a, tari¤ revenue: +c. Net e¤ect: �(b+ d).
� Thus, the e¤ect on a small country is always negative.
b)The supply of import goods to the large home market is now upward sloping. Initial equi-librium: Imports m0, price p0:
Imposing a tari¤ t > 0 :
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� The pass-through from tari¤s to home price will less than 100%. @p=@t < 1 because@p�=@t < 0. Hence, terms of trade improves.
� Imports will decline, home production increases, consumption declines.
� Welfare: Change in consumer surplus: �(a + b + c + d), change in producer surplus:+a, tari¤ revenue: +(c+ e). Net e¤ect: e� (b+ d).
� In general, the welfare e¤ect is ambigous. However, we see that the net e¤ect willdepend on the slopes of the demand/supply curves. If the pass-through is small (ToTimprovement large), imposing a tari¤ may be welfare improving. The pass-throughwill be small if the elasticity of import supply (wrt price) is small (i.e. steep supplycurve). Intuition: If foreign supply is relatively insensitive to price, the fall in worldmarket prices will be larger.
� It can be shown that the optimal tari¤ is
t�
p�=1
�(1)
where � is the elasticity of foreign export supply.
2. Reciprocal dumping (RD)Reciprocal dumping is
� Rivalry of oligopolistic �rms gives rise to "dumping" of output in foreign markets,
� Such dumping can be "reciprocal" �that is, there may be two-way trade in the sameproduct.
Hence, RD models is an independent cause of intra-industry trade in homogeneous goods.Note: In the monopolistic competition models, trade is a result of di¤erentiated goods. In theR D model, goods are homogeneous - Hence, RD is a competing explanation of intra-industrytrade.
Main results:
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� In equilibrium, p=T < p�. LHS is the price an F-producer receives from selling in H(fob), RHS is the price an F-producer gets from selling in F. Thus, the F-�rm "dumps"products in H.
� Symmetrically, p�=T < p: LHS is the price a H-producer receives from selling in F, etc.
Welfare e¤ects:
� (-) Pointless trade - resources are wasted in the cross-handling of goods;
� (+) Increased competition reduces monopoly distortions.
Model setup:
� Oligopoly, competing Cournot
� Iceberg trade costs T > 1
� Two countries with identical demand elasticity � and marginal costs c:
Home �rms maximize
maxyi;y�i
f(p(z)� c) yi + (p�(z�)� cT ) y�i � �g (2)
where total amount consumed is
z =NXyi +
N�Xxj (3)
yi is home goods, xj is foreign. There are N and N� �rms operating in home and foreignrespectively. FOCs:p(z)� c+ yip0(z) = 0 and p�(z�)� cT + y�i p�0(z�) = 0: Symmetry yi = y and use demand el.� = @z=@p � p=z to write FOCs
p(z)
�1� y=z
�
�= c (4)
p�(z�)
�1� y
�=z�
�
�= cT (5)
We can write �hh = y=z and �hf = y�=z� (�ij = market share of i-�rm in mkt j): Then,
�hh = (1� c
p)� (6)
�hf = (1� cTp�)� (7)
Symmetrical FOCs for the F-�rm.
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Equilibrium: Market shares in the two countries sum to 1,
N�hh +N��fh = 1 (8)
N�hf +N��ff = 1 (9)
In matrix terms, A2x2N2x1= 12x1. Solving for N yields N2x1= A�12x212x1, where
A�12x2 =
1
det(A)
��ff ��fh��hf �hh
�(10)
In scalar notation,
N =1
det(A)(�ff � �fh) (11)
N� =1
det(A)(�hh � �hf ) (12)
Inserting the �0s;
N =1
det(A)� [1� c=p� � (1� cT=p)] = 1
det(A)�c [T=p� 1=p�] (13)
N� =1
det(A)� [1� c=p� (1� cT=p�)] = 1
det(A)�c [T=p� � 1=p] (14)
Hence, if N > 0 and N� > 0, the equilibrium must satisfy T=p� 1=p� > 0 and T=p� � 1=p(given det(A) > 0): Rearranging,
p
T< p� (15)
p�
T< p (16)
which shows that the foreign and home �rm will dump products in the export markets,respectively.
Welfare implications:
� Consumers will gain because prices decline compared to no trade (less monopolypower).
� Social welfare loss because homogeneous goods are transported around the world, whenproduction technologies and factor endowments are identical.
� Ambiguous e¤ect with a �xed number of �rms. However, trade is more likely to bewelfare improving if transport costs are small.
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