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We develop a small open economy general equilibrium model with sticky prices and partial dollarization -- a situation where both domestic and foreign currencies coexist. We derive a tractable representation of the model in terms of domestic inflation and the output gap in which a trade-off, which depends on the degree of dollarization, arises endogenously due to the presence of foreign interest rate shocks. We use this framework to show analytically how higher degrees of dollarization induce larger volatilities of the output gap and inflation, thus hampering a central bank's effectiveness to stabilize the economy. Our impulse response functions show that the transmission of such shocks has a positive (negative) effect on inflation and negative (positive) effect on the output gap when money aggregates and consumption are complements (substitutes).