Tropical Geometry for Economic Analysis and Demand Modeling

Traditional calculus often struggles with the discrete, non-smooth decisions found in modern multi-product markets. Tropical geometry offers a revolutionary mathematical framework that translates complex economic optimization into intuitive piecewise-linear geometry. In this course, you will transition from the absolute basics of tropical algebra to modeling real-world consumer preferences and demand systems. You will learn how to represent discrete utility functions geometrically and analyze market equilibrium with precision. What you'll learn: 1. Understand the core principles of tropical arithmetic, including max-plus algebra and tropical polynomials. 2. Map consumer preferences and utility functions to tropical hypersurfaces and subdivisions. 3. Analyze multi-product demand systems and identify equilibrium states using geometric boundaries. 4. Apply tropical geometry to model substitute and complement goods in complex markets. 5. Practice solving discrete optimization and resource allocation problems using tropical methods. The course begins with foundational definitions and algebraic concepts, ensuring you build a strong mathematical base. From there, you will progress through structured lessons that connect these geometric structures directly to microeconomic demand theory and market design. This course is designed for beginners in tropical mathematics, including economics students, data analysts, and researchers looking for a modern analytical toolkit. A basic understanding of microeconomics and linear algebra is recommended but not required. Begin reading today to master a powerful geometric approach to economic modeling.