# Nonlinear Economic State Equilibria via van der Waals Modeling

## TL;DR

This paper applies the van der Waals equation from physics to economics to model how prices, demand, and income interact in equilibrium.

## Contribution

It introduces a novel economic framework using van der Waals modeling to explain nonlinear equilibria and substitution mechanisms.

## Key findings

- Price and income elasticity of demand can exhibit cusp-catastrophe singularities.
- The model illustrates substitution mechanisms in contexts like carpooling and medication.
- Empirical validation is shown using Germany's electricity market data.

## Abstract

The renowned van der Waals (VDW) state equation quantifies the equilibrium relationship between the pressure P, volume V, and temperature kBT of a real gas. We assign new variable interpretations adapted to the economic context: P→Y, representing price; V→X, representing demand; and kBT→κ, representing income, to describe an economic state equilibrium. With this reinterpretation, the price elasticity of demand (PED) and the income elasticity of demand (YED) are non-constant factors and may exhibit a singularity of the cusp-catastrophe type. Within this economic framework, the counterpart of VDW liquid–gas phase transition illustrates a substitution mechanism where one product or service is replaced by an alternative substitute. The conceptual relevance of this reinterpretation is discussed qualitatively and quantitatively via several illustrations ranging from transport (carpooling), medical context (generic versus original medication), and empirical data drawn from the electricity market in Germany.