An economic model of long-term phosphorus extraction and recycling

Phosphorus (P) is a macronutrient necessary for life. In the form of phosphates it presents a mineral resource that we depend on, having no substitute for its fertilizer use. These limited reserves of P are depleting globally, and maintaining or improving food security will require careful long-term use of the resource. We study here the extraction and recycling of P with an optimal control framework, and develop a resource-specific model. We determine time-paths for extraction and recycling when both technological progress and a geological stock effect drive the supply of P. Demand is described by a hyperbolic function with a strictly positive lower bound reflecting the key properties of the resource, its non-substitutability and its essentiality. We obtain three insights: (i) Although essential and non-substitutable, P resources will be depleted due to a strict minimum consumption level. Recycling could postpone depletion costs and maintain a minimum consumption forever but at rising marginal costs. (ii) Although extraction depletes the resource and increases its scarcity over time, we observe that on an optimal path the price can fall, which will increase extraction. This underlines that market prices cannot serve as reliable scarcity indicator and fail to support resource augmenting technologies. (iii) If the shadow price is used as scarcity indicator, it would provide incentives for recycling even under declining primary resource prices. --------------------------------------------------------------------------------