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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