Differential Forms: A New Tool in Economics

Investors would like to calculate profits in advance, “ex ante”, like the path of a flying ball. But income can only be given “ex post”, after the money is earned. The properties “ex ante” and “ex post” have never been investigated in economic theory by a mathematical tool. According to this paper the tool is given by exact and not exact differential forms. Integrals of inexact forms depend on the path of integration and may only be given “ex post”, when the path of integration is known. The equivalence of monetary and production cycles leads to closed integrals of differential forms and a first and second law of economics, that deviates in many aspects from neoclassical theory. The most important result is entropy as the new production function, which enters production, trade, growth, optimization. Differential forms move economics close to thermodynamics and statistics. This new approach is called econophysics.

• Type: Conference
• Year: 2009
• Where: COMPLEX
• Authors: Jürgen Mimkes
• Keywords: COMPLEX 2009, Ex Ante, Ex Post, Inexact Forms, Theoretical Computer Science