Unemployment in an Interdependent World



Appendix

A1 Relationship between φ*i and ^*j

Using the demand equations (3) and the fact that pij[^] = τijpii[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:

Rij И = τι-σ (P V-1 ( j ʌ (MMi.V-ν
Rii [φ]    ij  к Pi       Yi    M J


(A1)


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] = σfiiPi and Rij*j] = σfijPi,
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:

λ*

^ij

Λij


Λij <⅛


Pi


τ ij Pj


with


f YifijA σ-1 f⅛ ʌ σ-1
к Yj fii       MJ   ’


(A2)

(A3)


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 Λij1. In the symmetric case, this requirement boils
down to
fij τ σ-1 > fii .

46



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