An interesting equation to explain the implicit function theorem and an example of application in macroeconomics using Python

We begin by explaining the origin of the application of equation models in economics. We emphasize that many of these models are implicit and not linear. From there, we look for a way to deal with these models to extract the desired information, that is, understand how slight variations in independent variables (government spending, taxation, etc.) can affect the dependent variables (product, interest rate, etc.). The way found for this was the use of the implicit function theorem. We explain the intuition of the theorem, and then we formalize it to an equation and a system of equations. Finally, we present a generic example of applying the theorem using Python.