RDP 2007-06: The Butterfly Effect of Small Open Economies Equation

\begin{array}{l} σ_{α} \equiv \frac{σ}{(1 - α) + α ω} \\ ω \equiv σ τ + (1 - α) (σ ι - 1) \\ ϕ_{2} \equiv \frac{σ_{α} - σ}{σ_{α} + φ} \\ ϕ_{3} \equiv α (ω - 1) + ϕ_{2} \\ ϕ_{4} \equiv \frac{1 + φ}{σ_{α} + φ} \end{array}