Dynamical systems applied to economic science. A Sraffian supermultiplier model with the addition of inventory dynamics

The dynamic study of economic systems is an area of Economics that is now a century old, starting with the first economic growth models of Harrod-Domar. Through thework of economist Nicholas Kaldor and the eclectic Richard M. Goodwin, non-linear relationships have made their appearance in endogenous growth models, which are, we might say, the gateway to complex systems. In this work, we will study a series of models that deal with the mathematisation of the business cycle and the study of its fluctuations. In particular, the absolute protagonist will be the dynamic model of the Sraffian Supermultiplier, belonging precisely to the school of economic thought initiated by the work of Italian economist Piero Sraffa. Although the author will attempt to explain the differences between the various schools of thought and introduce notions of economics, the central theme of the work will be the addition of inventory fluctuations to the Sraffian Supermultiplier model developed by Freitas and Serrano (2015). We firmly believe that this topic deserves detailed investigation within the Sraffian School, not only for its mathematical content, but, above all, for the addition of an element of realism to the study of economic fluctuations and endogenous growth.