# Electrical circuit model of spatiotemporal trade dynamics: Foundations and derivation of the gravity model

## TL;DR

This paper introduces a new model of trade dynamics using an electrical circuit analogy, showing how it can explain real-world trade patterns and derive the gravity model of trade.

## Contribution

The paper introduces a novel electrical circuit-based model for trade dynamics and derives the gravity model from first principles.

## Key findings

- The model explains price setting, price fluctuations, and trade network structure through emergent balances of supply and demand.
- The model reproduces the gravity model of trade with exponents matching empirical data and predicts core-periphery trade structures.
- Trade flows self-organize to minimize overall trade friction, emerging from local producer-consumer interactions.

## Abstract

A model of time-dependent trade of goods between spatial locations is formulated via an electric circuit analogy, in which goods are analogous to charge and price to voltage, while producers and consumers are represented by sources and sinks of goods flow, which is represented by current, located at the nodes of a trade network. The core ansatz is that the flow of goods along each network link is driven by the voltage difference across that link, opposed by resistance that represents trade friction. Market prices are then determined indirectly by internal balances of flows, subject to external constraints on supply and demand. The model yields multiple outcomes that support its validity and applicability, including price setting via emergent balance of supply and demand, price fluctuations, traditional and generalized elasticities, network structure-flow relations, competition between producers, and substitution between suppliers, between consumers, and/or between trade links. All these results prove to be consistent with observed features of trade dynamics, thereby supporting the validity of the model. The new model is then used to derive the widely used gravity model of international trade from a mechanistic basis, yielding exponents consistent with published data and leading naturally to core-periphery structure, as observed in real trade networks. The analysis also implies that trade flows self-organize to minimize trade friction in the system as a whole, an emergent global outcome from the purely local dynamics of the populations of producers, consumers, and traders. Possible generalizations and further applications are outlined, including incorporation of asymmetry and capacity limits of trade links, constraints on supply and demand, behavioral responses, and coupling to models of investment strategies.