APPENDIX

Derivation of equation [12]

From the ratio of imports to exports in [11]:

Differentiating this equation:

Since: g_Y = (1/γ)dY/dt and g_y* is (1/T)(dY*/dt), [A.2] becomes:

Substituting γ_t^β from [A.1] and rearranging:

Which is equation [12] in the text.