Economic Circuit Theory: Electrical Network Theory for Dynamical Economic Systems

In this paper, we develop what we refer to as economic circuit theory. Our purpose is to exploit the proven effectiveness of electrical circuit theory for the design, modeling, and analysis of complex electrical networks to economic systems; in particular, it permits us to incorporate the dynamics of price into those of the flow of physical commodities, analogous to how this is done for magnetic flux and electrical charge. The theory is agent-based, wherein agents are conceptualized as electrical components, and the dynamics are determined by matching the agents' behavioral laws with the constitutive equations of the analogous components. We take a modern graph-theoretic approach, identifying the conditions for stock-flow consistency (Kirchhoff's current law) and price clearing (Kirchhoff's voltage law). With this, we develop the theory to model representative agents (equivalent networks), single-good markets (circuits), and general competitive markets (magnetically coupled circuits). We show how to apply the theory by designing and analyzing an economic circuit model for a two-good market in detail. To prove the effectiveness of the theory, we fit and validate a circuit for the global market in crude oil to the historical data, and we examine a relatively complex circuit for a hypothesized market in hydrogen.