Simulating resource movements and markets: A continuous dynamical system with delays to model anthropogenic metal cycles

Abstract

A material flow analysis and mineral commodity model based on ordinary and delay differential equations is derived from first principles in physics and economics, namely conservation of mass and the cobweb theorem. The dynamical system models anthropogenic metal stocks, flows and markets, including prices. An application to copper is demonstrated. Numerical simulations show that the model is able to reproduce the dynamics of the anthropogenic stocks and flows as well as the broad, long-term trends or cycles in the market variables. In the model, longer mining lead times generate more volatile and more prolonged market cycles, while shorter ones have the opposite effect. The present approach is capable of quantitatively representing the relationship between material and price movements by considering the resource cycle as a system that is both physical and socio-economic in nature.