In undergraduate international economics coursework students are often exposed to the IS-LM-BP model via diagrammatic analysis. The model itself presents the intuitive mechanics behind how an open economy functions and is generally regarded as useful to policy makers. The goal of this paper is to present an in-depth investigation of the IS-LM-BP model through algebraically representing its components. Our model features a two-country framework with sticky prices and flexible exchange rates. We display some interesting relations between factors that must hold in order for monetary and fiscal policy to be effective. Additionally, a peak at a possible extension to the model is presented in the last section.