A Mathematical Version of Garrison's Model

We develop a simple mathematical version of Garrison's model. The purpose to develop a mathematical framework is to (1) show how such representation can be used and (2) layout a path for future work that requires a more flexible version of Garrison's treatment than the graphical exposition. While the graphical model is limited to three dimensions, a mathematical version can include more variables of interest. First, we develop the mathematical framework of Garrison's treatment. Then we apply it to the cases of increase in savings, secular growth, and the Austrian business cycle theory