INTERNATIONAL RESOURCE ALLOCATION: Trade with Incomplete Information

This last qualification is necessary because equilibrium returns are defined with respect to distance from the median: if the distribution of types has a gap in the immediate neighborhood of the median, any point in that gap can be interpreted as a median itself, and can provide the anchor against which equilibrium returns are measured. A simple symmetry requirement turns out to be sufficient to rule out this possibility:

Corollary 1. In any equilibrium in which the distribution of types in the markets is symmetrical around zero, if any domestic trade takes place type i *s return in the domestic market must equal IzJt^w), where |z;| is his distance from zero. (The proof is in the Appendix.)

In all that follows we concentrate on equilibria where the distribution of types in the markets is symmetrical around zero.
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Having characterized equilibrium returns in the last stage of the game—when and if a producer goes back to the domestic market—we can now evaluate under what conditions a producer can be expected to do better internationally. We begin by finding the set of acceptable foreign partners for each home producer and vice-versa. We label the former set S(i) and the latter set S*(i*), Consider a home country producer of type zt ^ 0 (the opposite case is just a mirror image). An international match yields [\zr z^Tifw) – (z/n(w) + \zf*\Tz(w*))]/2 + z/iz(w), where we have used the fact that internationally matched producers will employ labor in the country where it is cheaper (it is not difficult to see that this can never be the foreign country). The term in square brackets equals the gains from trade, hence the international match is acceptable when: