The Social Cost of Sub-Soil Resource Use
Abstract
:1. Introduction
2. Materials and Methods
2.1. Hotelling’s Model and the Determinants of the Market Price
2.1.1. Time Path of the Resource Price According to Hotelling’s Model
2.1.2. Causes of Market Price Differing from Socially Optimal Price
2.2. Correcting the Market Price
2.2.1. Model 1: Principle of the Method
2.2.2. Model 2: Integrating Extraction Cost
2.2.3. Model 3: Integrating Elastic Demand
2.2.4. Applied Method in Practice
3. Data and Assumptions
3.1. Market Price Including Extraction Costs
3.2. Extraction Cost
3.3. Time before Depletion
- (1)
- t = time of convergence of the market and the social discount rates (our base case)
- (2)
- t = resource-specific estimate of time before depletion (sensitivity analysis)
- (3)
- t = resource-specific estimate of time before depletion, but not >50 years (sensitivity analysis)
3.4. Social and Market Discount Rates
3.4.1. The Social Discount Rate
3.4.2. The Market Discount Rate
3.4.3. Evolution of the Discount Factors and Derivation of the Socially Optimal Price
4. Results
4.1. Externality Cost of Depletion of Sub-Soil Resources
4.2. Limitations
4.2.1. Modelling Assumptions Limits
4.2.2. Data Limitations
5. Comparison to Other Methods
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Resources | 5-Year | Extraction | Estimated Time | Upper Bound Externality Cost of Depletion Relative to the Resource Prices | |||||
---|---|---|---|---|---|---|---|---|---|
Trend Price (€ 2017/kg) | Cost/Price | Before Depletion (Years) | Using Constant Market Discount Rate | Using Declining Market Discount Rate | |||||
t = 300 (Base Case) | t = specific | t = specific; max. 50 | t = 300 | t = specific | t = specific; max. 50 | ||||
Abrasives (natural) | 0.15 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Aluminium | 1.39 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Antimony | 6.29 | 75% | 13 | 0.60 | 0.29 | 0.29 | 0.39 | 0.28 | 0.28 |
Arsenic | 0.77 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Asbestos | 1.66 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Barite | 0.12 | 75% | 51 | 0.60 | 0.40 | 0.40 | 0.39 | 0.34 | 0.34 |
Bauxite | 0.02 | 75% | 71 | 0.60 | 0.45 | 0.40 | 0.39 | 0.36 | 0.34 |
Beryllium | 419 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Bismuth | 16.2 | 75% | 27 | 0.60 | 0.33 | 0.33 | 0.39 | 0.31 | 0.31 |
Boron | 0.43 | 75% | 64 | 0.60 | 0.43 | 0.40 | 0.39 | 0.35 | 0.34 |
Bromine | 1.13 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Cadmium | 1.29 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Cement | 0.09 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Caesium | 66,000 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Chromium | 1.95 | 75% | 18 | 0.60 | 0.30 | 0.30 | 0.39 | 0.29 | 0.29 |
Clay | 0.05 | 85% | 100 | 0.36 | 0.30 | 0.24 | 0.23 | 0.22 | 0.20 |
Coal | 0.05 | 82% | 113 | 0.43 | 0.37 | 0.29 | 0.28 | 0.27 | 0.25 |
Cobalt | 24.4 | 75% | 57 | 0.60 | 0.42 | 0.40 | 0.39 | 0.35 | 0.34 |
Copper | 3.92 | 54% | 39 | 1.11 | 0.67 | 0.67 | 0.71 | 0.60 | 0.60 |
Crude petroleum | 0.22 | 57% | 49 | 1.04 | 0.68 | 0.68 | 0.66 | 0.58 | 0.58 |
Diamond (industrial) | 959 | 75% | 13 | 0.60 | 0.29 | 0.29 | 0.39 | 0.28 | 0.28 |
Diatomite | 0.26 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Feldspar | 0.09 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Fluorspar | 0.21 | 75% | 40 | 0.60 | 0.37 | 0.37 | 0.39 | 0.33 | 0.33 |
Gallium | 259 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Garnet (industrial) | 0.25 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Gemstones | 35,900 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Germanium | 1390 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Gold | 30,000 | 75% | 19 | 0.60 | 0.31 | 0.31 | 0.39 | 0.30 | 0.30 |
Graphite (natural) | 1.01 | 75% | 193 | 0.60 | 0.58 | 0.40 | 0.39 | 0.38 | 0.34 |
Gypsum | 0.01 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Hafnium | 516 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Helium | 18.9 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Indium | 495 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Iodine | 28 | 75% | 248 | 0.60 | 0.59 | 0.40 | 0.39 | 0.38 | 0.34 |
Iron ore | 0.04 | 70% | 26 | 0.72 | 0.39 | 0.39 | 0.46 | 0.37 | 0.37 |
Iron oxide pigments | 1.09 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Kyanite | 0.31 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Lead | 1.61 | 75% | 19 | 0.60 | 0.31 | 0.31 | 0.39 | 0.30 | 0.30 |
Lime | 0.11 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Lithium | 4.02 | 75% | 431 | 0.60 | 0.61 | 0.40 | 0.39 | 0.39 | 0.34 |
Magnesium metal | 4.11 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Manganese | 1.13 | 75% | 34 | 0.60 | 0.35 | 0.35 | 0.39 | 0.32 | 0.32 |
Mercury | 46.6 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Mica (scrap and flake) | 2.82 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Molybdenum | 14.5 | 75% | 41 | 0.60 | 0.37 | 0.37 | 0.39 | 0.33 | 0.33 |
Natural gas, LNG | 5.02 | 85% | 57 | 0.36 | 0.25 | 0.24 | 0.23 | 0.21 | 0.20 |
Natural gas, US | 2.16 | 85% | 57 | 0.36 | 0.25 | 0.24 | 0.23 | 0.21 | 0.20 |
Natural gas, Europe | 3.24 | 85% | 57 | 0.36 | 0.25 | 0.24 | 0.23 | 0.21 | 0.20 |
Nickel | 7.44 | 75% | 31 | 0.60 | 0.35 | 0.35 | 0.39 | 0.32 | 0.32 |
Nitrogen | 0.48 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Palladium | 20,800 | 75% | 171 | 0.60 | 0.56 | 0.40 | 0.39 | 0.38 | 0.34 |
Peat | 0.02 | 84% | 435 | 0.39 | 0.39 | 0.26 | 0.25 | 0.25 | 0.22 |
Perlite | 0.05 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Phosphate | 0.07 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Phosphate rocks | 0.07 | 75% | 309 | 0.60 | 0.61 | 0.40 | 0.39 | 0.39 | 0.34 |
Platinum | 22,100 | 75% | 171 | 0.60 | 0.56 | 0.40 | 0.39 | 0.38 | 0.34 |
Potash | 0.48 | 75% | 95 | 0.60 | 0.49 | 0.40 | 0.39 | 0.37 | 0.34 |
Potassium chloride | 0.17 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Propane | 0.10 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Pumice | 0.03 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Rare earth | 5.43 | 75% | 1048 | 0.60 | 0.62 | 0.40 | 0.39 | 0.39 | 0.34 |
Rhenium | 2180 | 75% | 54 | 0.60 | 0.41 | 0.40 | 0.39 | 0.34 | 0.34 |
Salt | 0.04 | 83% | 100 | 0.41 | 0.34 | 0.27 | 0.26 | 0.25 | 0.23 |
Sand/gravel (industrial) | 0.05 | 85% | 100 | 0.36 | 0.30 | 0.24 | 0.23 | 0.22 | 0.20 |
Selenium | 34.3 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Silicon | 2.14 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Silver | 360 | 75% | 21 | 0.60 | 0.31 | 0.31 | 0.39 | 0.30 | 0.30 |
Sodium carbonate | 0.13 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Sodium sulfate | 0.14 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Stone (crushed) | 0.01 | 85% | 100 | 0.36 | 0.30 | 0.24 | 0.23 | 0.22 | 0.20 |
Stone (dimension) | 0.15 | 85% | 100 | 0.36 | 0.30 | 0.24 | 0.23 | 0.22 | 0.20 |
Strontium | 0.32 | 75% | 21 | 0.60 | 0.32 | 0.32 | 0.39 | 0.30 | 0.30 |
Sulfur | 0.06 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Talc and Pyrophyllite | 0.19 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Tantalum | 213 | 75% | 83 | 0.60 | 0.47 | 0.40 | 0.39 | 0.36 | 0.34 |
Tellurium | 40.2 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Thallium | 6520 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Thorium | 249 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Tin | 14.6 | 75% | 16 | 0.60 | 0.3 | 0.30 | 0.39 | 0.29 | 0.29 |
Titanium dioxide | 2.1 | 75% | 42 | 0.60 | 0.38 | 0.38 | 0.39 | 0.33 | 0.33 |
Titanium metal | 9.12 | 75% | 130 | 0.60 | 0.53 | 0.40 | 0.39 | 0.37 | 0.34 |
Tungsten | 35.3 | 75% | 38 | 0.60 | 0.36 | 0.36 | 0.39 | 0.34 | 0.33 |
Uranium | 43 | 75% | 100 | 0.60 | 0.50 | 0.40 | 0.39 | 0.37 | 0.34 |
Vanadium | 15.7 | 75% | 189 | 0.60 | 0.57 | 0.40 | 0.39 | 0.34 | 0.34 |
Wollastonite | 0.19 | 75% | 164 | 0.60 | 0.56 | 0.40 | 0.39 | 0.34 | 0.34 |
Zinc | 1.96 | 75% | 15 | 0.60 | 0.29 | 0.29 | 0.39 | 0.34 | 0.29 |
Zirconium | 0.59 | 75% | 55 | 0.60 | 0.41 | 0.40 | 0.39 | 0.34 | 0.34 |
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Using Constant Market Discount Rate | Using Declining Market Discount Rates | ||
---|---|---|---|
t = 300 (Base Case) | t = 50 | t = 300 | t = 50 |
2.42 | 1.60 | 1.54 | 1.36 |
Resources | 5-Year | Extraction | Estimated Time | Upper Bound Externality Cost of Depletion Relative to the Resource Prices | |||||
---|---|---|---|---|---|---|---|---|---|
Trend Price (€ 2017/kg) | Cost/Price | Before Depletion (Years) | Using Constant Market Discount Rate | Using Declining Market Discount Rate | |||||
t = 300 (base case) | t = specific | t = specific; max. 50 | t = 300 | t = specific | t = specific; max. 50 | ||||
Antimony | 6.29 | 75% | 13 | 0.60 | 0.29 | 0.29 | 0.39 | 0.28 | 0.28 |
Bauxite | 0.02 | 75% | 71 | 0.60 | 0.45 | 0.40 | 0.39 | 0.36 | 0.34 |
Bismuth | 16.2 | 75% | 27 | 0.60 | 0.33 | 0.33 | 0.39 | 0.31 | 0.31 |
Boron | 0.43 | 75% | 64 | 0.60 | 0.43 | 0.40 | 0.39 | 0.35 | 0.34 |
Chromium | 1.95 | 75% | 18 | 0.60 | 0.30 | 0.30 | 0.39 | 0.29 | 0.29 |
Coal | 0.05 | 82% | 113 | 0.43 | 0.37 | 0.29 | 0.28 | 0.27 | 0.25 |
Cobalt | 24.4 | 75% | 57 | 0.60 | 0.42 | 0.40 | 0.39 | 0.35 | 0.34 |
Copper | 3.92 | 54% | 39 | 1.11 | 0.67 | 0.67 | 0.71 | 0.60 | 0.60 |
Crude petroleum | 0.22 | 57% | 49 | 1.04 | 0.68 | 0.68 | 0.66 | 0.58 | 0.58 |
Fluorspar | 0.21 | 75% | 40 | 0.60 | 0.37 | 0.37 | 0.39 | 0.33 | 0.33 |
Gold | 30,000 | 75% | 19 | 0.60 | 0.31 | 0.31 | 0.39 | 0.30 | 0.30 |
Graphite (natural) | 1.01 | 75% | 193 | 0.60 | 0.58 | 0.40 | 0.39 | 0.38 | 0.34 |
Iodine | 28 | 75% | 248 | 0.60 | 0.59 | 0.40 | 0.39 | 0.38 | 0.34 |
Iron ore | 0.04 | 70% | 26 | 0.72 | 0.39 | 0.39 | 0.46 | 0.37 | 0.37 |
Lead | 1.61 | 75% | 19 | 0.60 | 0.31 | 0.31 | 0.39 | 0.30 | 0.30 |
Lithium | 4.02 | 75% | 431 | 0.60 | 0.61 | 0.40 | 0.39 | 0.39 | 0.34 |
Manganese | 1.13 | 75% | 34 | 0.60 | 0.35 | 0.35 | 0.39 | 0.32 | 0.32 |
Molybdenum | 14.5 | 75% | 41 | 0.60 | 0.37 | 0.37 | 0.39 | 0.33 | 0.33 |
Nickel | 7.44 | 75% | 31 | 0.60 | 0.35 | 0.35 | 0.39 | 0.32 | 0.32 |
Palladium | 20,800 | 75% | 171 | 0.60 | 0.56 | 0.40 | 0.39 | 0.38 | 0.34 |
Peat | 0.02 | 84% | 435 | 0.39 | 0.39 | 0.26 | 0.25 | 0.25 | 0.22 |
Phosphate rocks | 0.07 | 75% | 309 | 0.60 | 0.61 | 0.40 | 0.39 | 0.39 | 0.34 |
Platinum | 22,100 | 75% | 171 | 0.60 | 0.56 | 0.40 | 0.39 | 0.38 | 0.34 |
Rhenium | 2180 | 75% | 54 | 0.60 | 0.41 | 0.40 | 0.39 | 0.34 | 0.34 |
Silver | 360 | 75% | 21 | 0.60 | 0.31 | 0.31 | 0.39 | 0.30 | 0.30 |
Strontium | 0.32 | 75% | 21 | 0.60 | 0.32 | 0.32 | 0.39 | 0.30 | 0.30 |
Tantalum | 213 | 75% | 83 | 0.60 | 0.47 | 0.40 | 0.39 | 0.36 | 0.34 |
Tin | 14.6 | 75% | 16 | 0.60 | 0.3 | 0.30 | 0.39 | 0.29 | 0.29 |
Titanium dioxide | 2.1 | 75% | 42 | 0.60 | 0.38 | 0.38 | 0.39 | 0.33 | 0.33 |
Titanium metal | 9.12 | 75% | 130 | 0.60 | 0.53 | 0.40 | 0.39 | 0.37 | 0.34 |
Tungsten | 35.3 | 75% | 38 | 0.60 | 0.36 | 0.36 | 0.39 | 0.34 | 0.33 |
Vanadium | 15.7 | 75% | 189 | 0.60 | 0.57 | 0.40 | 0.39 | 0.34 | 0.34 |
Zinc | 1.96 | 75% | 15 | 0.60 | 0.29 | 0.29 | 0.39 | 0.34 | 0.29 |
Zirconium | 0.59 | 75% | 55 | 0.60 | 0.41 | 0.40 | 0.39 | 0.34 | 0.34 |
Resource | Externality Cost of Depletion | ||
---|---|---|---|
Results from This Study (Computed from Table A1) (EUR2017/kg) | EPS 2015 (Steen, 2015 [24,25]) (EUR2015/kg) | Surplus Cost Potential Method (Vieira et al., 2016 [26]) (USD2013/kg) | |
Chromium | 1.2 | 59.5 | |
Coal | 0.023 | 0.16 | |
Cobalt | 15 | 179 | |
Copper | 4.4 | 90.9 | 0.74 |
Gold | 18 150 | 2 020 000 | |
Iron Ore | 0.027 | 0.85 | 0.022 |
Manganese | 0.7 | 4.92 | 4.42 |
Molybdenum | 8.8 | 2 430 | 3.97 |
Nickel | 4.5 | 107 | 5.62 |
Palladium | 12 585 | 6 860 000 | 2480 |
Silver | 217 | 72 800 | 114 |
Tin | 8.8 | 482 | |
Titanium | 5.8 | 0.89 | |
Tungsten | 21.3 | 3 350 | |
Uranium | 26.0 | 340 | 29 |
Vanadium | 9.5 | 34 | |
Crude petroleum | 0.23 | 0.47 | |
Zinc | 1.19 | 32 | 6.69 |
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Huppertz, T.; Weidema, B.P.; Standaert, S.; De Caevel, B.; van Overbeke, E. The Social Cost of Sub-Soil Resource Use. Resources 2019, 8, 19. https://doi.org/10.3390/resources8010019
Huppertz T, Weidema BP, Standaert S, De Caevel B, van Overbeke E. The Social Cost of Sub-Soil Resource Use. Resources. 2019; 8(1):19. https://doi.org/10.3390/resources8010019
Chicago/Turabian StyleHuppertz, Tom, Bo P. Weidema, Simon Standaert, Bernard De Caevel, and Elisabeth van Overbeke. 2019. "The Social Cost of Sub-Soil Resource Use" Resources 8, no. 1: 19. https://doi.org/10.3390/resources8010019