Unemployment in an Interdependent World

Appendix

A1 Relationship between φ*_i and ^*_j∙

Using the demand equations (3) and the fact that pi_j∙[^] = τi_j∙pii[φ], we can express relative
revenues at home and in the foreign country j from a firm with productivity φ based in
country i as:

The zero-productivity cut-off above which firms produce for the domestic market, φ*_ii,
and the exporting productivity cut-off, above which firms produce for both the domestic
and the export market j, φ*j, are determined by Rii[φ*i] = σf_iiP_i and Ri_j∙[φ*j] = σfi_j∙Pi,
respectively.

Combining these two equations leads to an equation that links the revenues of a firm
at the zero-profit productivity cut-off to those of a firm at the exporting productivity cut-
off. Further, the relationship between revenues of two firms with different productivities
′′ ^σ-1

^4 Rii[φ'ii]. These two
relationships together yield and equilibrium relationship between the two productivity
cut-offs:

The profits from serving the foreign market have to be large enough to justify the extra
fixed costs fij, where Λij would collapse to τij (fij /fii)^1σ-11 in the case of complete
symmetry. For φ*j > φ*i, we need Λi_j∙ > 1. In the symmetric case, this requirement boils
down to fij τ ^σ-1 > fii .

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