Exploring mining extraction dynamics in Africa: A Hotelling model perspective with non-linear costs

Abstract

This paper assesses the applicability of the Hotelling model to non-renewable resource extraction in Africa by examining seven key minerals (bauxite, copper, gold, iron, nickel, phosphate, and tin) across 18 major producing countries. Our findings systematically reject the Hotelling model’s predictions: estimated discount rates are significantly negative across most countries and commodities, contradicting the theoretical assumption of intertemporal profit maximization. Furthermore, observed depletion times (averaging 105 years) fall markedly short of theoretical optima (240–256 years), suggesting systemic over-extraction. Results vary substantially by mineral and country, with phosphate reserves (e.g., Morocco) showing slower depletion, while copper and gold sectors (e.g., DRC, Ghana) exhibit faster extraction. These deviations suggest that the Hotelling model may be inadequate for capturing the complex realities of resource extraction in developing economies, where factors such as widespread illegal mining, institutional rigidities, political instability, and regulatory weaknesses that facilitate resource predation create different optimization conditions than those assumed by the classical model.