Nonlinear Economic State Equilibria via van der Waals Modeling

Abstract

The renowned van der Waals (VDW) state equation quantifies the equilibrium relationship between pressure $P$, volume $V$ and temperature $k_{B}T$ of a real gas. We assign new variable interpretations adapted to the economic context: $P \rightarrow Y$, representing price; $V \rightarrow X$, representing demand; and $k_{B}T \rightarrow \kappa$, 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.