o¤shoring costs borne by producers of either nationality. Also, with w = w<sup>�</sup> and nx = n<sup>�</sup> x<sup>�</sup> , the incentives for a deviant supplier to upset an equilibrium with concentrated task performance are the same for both countries. Therefore, I = I<sup>�</sup> and this common value represents the boundary between traded and non-traded tasks. The ...gure shows M (E) and M (W) for the equal-wage equilibrium, as well as I = I<sup>�</sup> .

Although the equal-wage equilibrium has an indeterminate pattern of specialization, there are two constraints on the allocation of the traded tasks. First, an equilibrium allocation must satisfy T (E) � T ([0; M (E)]), because the total o¤shoring costs for tasks concentrated in East must be at least the cost of o¤shoring the measure M (E) of tasks that are least costly to o¤shore. Second, the allocation of tasks must obey T (E) � T ([0; I]) � T ([0; M (W)]), because the o¤shoring costs for tasks concentrated in East can be at most the cost of o¤shoring the measure M (E) of traded tasks that are most costly to o¤shore; i.e., it is maximized when the measure M (W) of tasks with the lowest o¤shoring costs locate in West. An equilibrium with equal wages in which the measure M (E) of tasks that are least costly to o¤shore is concentrated in East is identical to the limiting equilibrium with w < 1 as w ! 1. And the equilibrium with equal wages in which the measure M (E) of tasks that are most costly to o¤shore is concentrated in East is identical to the limiting equilibrium with w > 1 as w ! 1. This explains the convergence of the various thin and thicker curves in Figure 4. When the gap between L and L<sup>�</sup> grows too large, one of the constraints must be violated, and so the equal-wage equilibrium ceases to exist. The ...gure shows that when this equilibrium fails to exist, neither does an equilibrium exist in which the smaller country has the greater wage.<sup>23</sup> Let us recapitulate. Proposition 4 characterizes the general equilibrium when o¤shoring costs are high even for the tasks that are easiest to perform at a distance. The country with more resources has higher wages, has more ...rms, and produces more output per ...rm. If the size asymmetry is su¢ ciently great, there is task trade in equilibrium, possibly in both directions. In the example we showed, the smaller country performs the tasks that are easiest to o¤shore whereas the larger country performs tasks with intermediate costs of o¤shoring. Proposition 5 characterizes outcomes when the schedule of o¤shoring costs is lower. Then, if the countries are close in size, there are multiple equilibria. In one set of equilibria, the countries have equal wages and equal aggregate outputs. Generically, there also exist an equilibrium in which the larger country (in terms of resources) has the greater volume of ...nal output and the higher wage and an equilibrium in which the smaller country has the greater volume of ...nal output and the higher wage.

The equilibria with unequal wages that we have seen in our numerical examples share a common

> 23 We o¤er one further observation about the equal-wage equilibrium. Although our model lacks explicit dynamics, the equal-wage equilibrium has a knife-edge property that suggests instability under plausible adjustment mechanisms. Suppose we perturb such an equilibrium by misallocating a few tasks in such a way that total production costs in the two countries remain unchanged. Then the labor markets will fail to clear, which will exert pressure on the relative wage. As soon as the wage equality is broken, the remaining traded tasks will relocate so that those with low o¤shoring costs are concentrated in the low-wage country and those with intermediate o¤shoring costs are concentrated in the high-wage country. In other words, a small perturbation creates incentives for a large reallocation of resources and moves the economy into the neighborhood of one of the two equilibria with unequal wages.

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