when e (nominal exchange rate) goes up, and p goes up, the dollar depreciates. More domestic currency is needed per the same amount of foreign currency as before the depreciation.
BoP Schedule:
\(BoP = CA + KA = X(\rho, Y, Y^*) + \sigma (i - i^*) + k\)
Totally differentiating, rewriting the system in matrix form and using Cramer's rule we can find the government multiplier (impact of government expenditure on output):
\(\frac{dy}{d \bar G} = (\frac{L_i}{(1 - c_y - nx_y)L_i + (c_r + I_r)L_y - (L_y \sigma - nx_y L_i)}) > 0\)