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<p>Taylor’s Rule is a widely used mining heuristic that links installed capacity to reserve tonnage through a power law, with the canonical exponent near 3/4. Yet the rule has remained largely empirical. This paper derives a Taylor-type capacity–reserve relationship from a Hotelling model with an ex ante capacity investment decision. A mine chooses installed throughput to maximize discounted net present value from a finite reserve base, trading off earlier revenues against convex capacity costs. To motivate the cost function, the paper uses a first-order geometric/engineering approximation in which some development and material-handling requirements scale with orebody volume, while access, utilities, tailings, and supporting infrastructure scale with the serviced mine interface or footprint. Under approximately self-similar large mine layouts, a Cobb–Douglas aggregation of these components implies an effective capacity-cost curvature consistent with Taylor’s 3/4 benchmark. Empirically, the paper re-estimates the rule for copper heap-leach projects and for a broader cross-section of copper concentrator projects compiled from public technical reports. The heap-leach subset reproduces the classical exponent, while the concentrator sample yields a lower elasticity, consistent with more convex effective capacity costs in processing-intensive mine-plant systems.</p>

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Deriving taylor’s mine capacity rule from a hotelling model with capacity investment

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • Juan Ignacio Guzman

摘要

Taylor’s Rule is a widely used mining heuristic that links installed capacity to reserve tonnage through a power law, with the canonical exponent near 3/4. Yet the rule has remained largely empirical. This paper derives a Taylor-type capacity–reserve relationship from a Hotelling model with an ex ante capacity investment decision. A mine chooses installed throughput to maximize discounted net present value from a finite reserve base, trading off earlier revenues against convex capacity costs. To motivate the cost function, the paper uses a first-order geometric/engineering approximation in which some development and material-handling requirements scale with orebody volume, while access, utilities, tailings, and supporting infrastructure scale with the serviced mine interface or footprint. Under approximately self-similar large mine layouts, a Cobb–Douglas aggregation of these components implies an effective capacity-cost curvature consistent with Taylor’s 3/4 benchmark. Empirically, the paper re-estimates the rule for copper heap-leach projects and for a broader cross-section of copper concentrator projects compiled from public technical reports. The heap-leach subset reproduces the classical exponent, while the concentrator sample yields a lower elasticity, consistent with more convex effective capacity costs in processing-intensive mine-plant systems.