As discussed at greater length in a companion paper (Casella and Rauch 1997), our model can be read as an assignment problem: different producers must meet and they are not equally well-suited to one another (Becker, 1973; Mortensen, 1988; Sattinger, 1993). In domestic partnerships, there is no information problem, and equilibrium matches will correspond to the complete information solution of the assignment model. In international partnerships, on the contrary, each other’s type cannot be observed before matching, a scenario equivalent to the incomplete information assignment problem without resampling.

Complete Information

Because the focus of this paper is on the impact of informational barriers on trade, it is important to establish as a benchmark how our world would fare in the absence of such barriers.

With a constant returns to scale production function, total profits from the match of types i and / can be written as:
where w is the wage paid to labor employed by the partnership, and the function тz(w) is decreasing and convex in w. For ease of later proofs, let us also assume that n(w) is a constant elasticity function (as would be the case, for example, if the technology were Cobb-Douglas).

Any individual partnership considers the wage constant, and thus joint profits are simply proportional to the distance between the two producers’ types. When choosing a partner, each type will want to match with someone on the opposite side of zero, and as close as possible to the outer edge of the distribution. But at the same time, competing for the more desirable partners requires renouncing a larger share of total profits. Proposition 1, established in a general setting, determines individual equilibrium returns in the complete information matching game:

Proposition 1. Consider a continuum of types distributed on a line. Call IzJI type i *s distance from the median and the distance between types i and j. If the matching of i and] results in total profit С Zjj, where С is a positive constant, and each type is free to choose and bidfor any matching partner, then in equilibrium type i ’s return r(i) will equal СЦг^]. (The proof is in the Appendix.)

Thus in equilibrium all matches will be formed by partners on the opposite side of the median, and each type can only guarantee for himself a return equal to his net contribution to total profits. Complete information leads to competition, and competition to the disappearance of all “extra” returns. Notice that the proposition cannot predict which matches will take place, but only that all matches must be between two types on opposite sides of the median (generating total returns equal to (||z,|| +||^||)). Because individual returns are determined uniquely, the indeterminacy of the matches is irrelevant.