ROLE OF DIFFERENTIATING GOODS: Modeling Bilateral Trade 3


Exports Xy = NjXy from country i to country j are shown in the lower panel of Figure 1.

Within the interval (La,Lb) both countries are producing the Coumot-Nash good, and they will also both be exporting provided that the F.O.B. price received (which is net of transport costs) exceeds marginal cost. This will be true in Figure 1 provided that P/% > с , as we shall assume.4 When L]=La then exports of the Coumot-Nash are zero because production is also zero, but as country 1 grows then exports also rise, as illustrated by the curve Xn. When Li=Lb, country 2 ceases production of the Coumot-Nash good. Further re-allocations of labor towards country 1 reduce its exports, because demand falls in country 2.5 Thus, the general shape of exports from country 1 are as illustrated by X12, increasing from La and then decreasing after Lb. The corresponding export curve X21 from country 2 is also illustrated.

Reciprocal dumping occurs in the interval (La,Lb) in the sense that the F.O.B. price for exports pj/т, is below the price pi for both countries. As is clear from Figure 1, the reciprocal dumping interval depends on transport costs: as T—»l, the two export curves move apart and the interval (LA,LB) shrinks to the point Li=L2=1/2. Thus, to observe a significant range of reciprocal dumping transport costs cannot be too small. On the other hand, recall that Figure 1 is drawn under the assumption that that P!% > с, which requires that transport costs are not too large.6 Thus, the range of reciprocal dumping is greatest when transport costs are at some intermediate level.
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Despite the fact that the countries produce homogeneous goods, the reciprocal dumping model leads to a well-defined trade pattern. This pattern results not from comparative advantage, but from the desire of imperfectly competitive firms to enter each others’ markets. Figure 1 suggests that trade will be highest when countries similar in size. This is the most important implication of the “gravity” equation, and in the next section we relate the reciprocal dumping model to that equation.

The Home Market Effect and the Gravity Equation

One feature of the export flows in Figure 1 deserves special mention. As drawn, exports

X12 from country 1 to 2 reach a maximum when country 1 is somewhat larger than country 2.

This is a deliberate feature of the diagram which illustrates the home market effect: as country 1 becomes larger, the number of firms located there grows more rapidly than output, and country 1 becomes a net exporter of the good, despite the increase in domestic demand. To confirm this result, we consider a re-allocation of labor between the countries, keeping the world labor supply fixed. The following result is proved in Appendix 1:

Proposition 2

Assume Cobb-Douglas preferences and equal transport costs, so that Ti2=T2i=x. Then evaluated at L]=L2, a slight re-allocation of labor from country 2 to country 1 increases country 1 exports (X12), and reduces country 2 exports (X21).

Proposition 2 implies that net exports of the Coumot-Nash good from country 1 to 2 grow as country 1 grows, given global GDP.