Intuitive mathematical economics series: General equilibrium models and the Gradient Field Method

General equilibrium models are typically presented with mathematical methods, such as the Edgeworth Box, that do not easily generalize to more than two goods and more than two agents. This is fine as a conceptual introduction, but it may be insufficient in the "Big Data-Machine-Learning-Era", with gigantic databases filled with data of extremely high dimensionality that are already changing the practice, and perhaps even the conceptual basis, of economics and other social sciences. In this paper present what we call the "Gradient Field Method" to solve these problems. It has the advantage of being, 1) as intuitive as the Edgeworth Box, 2) easily generalizes to far more complex situations, and 3) nicely mesh with the data friendly techniques of the new Era. In addition, it provides a unified framework to present both, partial equilibrium, and general equilibrium problems.