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ERE6: Non-Renewable Resources Resources and Reserves Social optimum and a model for a perfectly competitive market Sensitivity analysis –Increase in interest rate and resource stock –Change in demand and extraction costs Market failure –Monopoly Taxes and subsidies Reality

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Last week A simple optimal depletion model –Resource substitutability –Static and dynamic efficiency –Hotelling‘s rule –Optimality Extraction costs Renewable resources Complications

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Potential, Resources and Reserves Gesamtpotential (Mrd. toe) 125 Bis Ende 2000 gefördert Verbleibendes Potenzial ReservenRessourcen ÖlGasKohle / /250 Source: RWE Weltenergiereport /66 122/1

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Resources and Reserves Increasing degree of geological assurance Increasing degree of economic feasibility McKelvey classification

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Potential for oil Source: Bundesamt für Geowissenschaften und Rohstoffe (BGR)

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Oil production Source: BGR

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Availability Source: BGR

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Mineral Reserves MineralProd.Cons.Econ. Res.Exp. Res.Tech. Res.Life Aluminium Iron Manganese Chromium Zinc Nickel Copper Lead Tin Tungsten ?5180 Mercury Million metric tons

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Social optimum: Two-periods Demand function: Welfare function: Constraint: Langrange: Necessary conditions: Net social benefits:

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Social Optimum: Multi-periods Social welfare function: Equations of motion: Hamiltonian: Optimality has that the stock is zero too: Necessary conditions: Demand goes to zero if price exceeds the choke price (K): Demand function:

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Net price P t Time t P0P0 PtPt T T R R0R0 Area = = total resource stock RtRt Demand P T =K 45° Graphical solution

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Perfect Competition Firms objective function: Hamiltonian: Equations of motion: Necessary conditions: Identical firms: Perfect competition: Intertemporal efficiency:

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Net price P t Time t P0P0 T T R R0R0 R0/R0/ T/T/ P0/P0/ K T/T/ D 45° D/D/ Increase in demand

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K P Time T CAB P0P0 Increase in interest rate

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Net price P t Time t P0P0 T T R R0R0 R0/R0/ T/T/ P0/P0/ K T/T/ Demand Increase in interest rate (2) 45°

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Net price P t Time t P0P0 T T R R0R0 R0/R0/ T/T/ P0/P0/ K T/T/ Demand Increase in stock size 45°

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PtPt Net price path with no change in stocks Net price path with frequent new discoveries t Frequent new discoveries

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Net price P t Time t P0P0 T T R R0R0 R0/R0/ T/T/ P0/P0/ K T/T/ D Backstop technology becomes cheaper 45° Backstop price fall PBPB R*R*

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Results of the sensitivity analysis so far Higher demand: Higher initial price, higher initial extraction; price increase unaffected, so choke price reached earlier Higher interest rate: Initial price will be lower, but price increase faster, and choke price reached earlier; overall higher extraction Greater resource stock: Initial price goes down, initial extraction goes up; growth unaffected; exhaustion postponed Lower choke price: Final price lower, but price increase unaffected, so initial price must be lower; overall higher extraction

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Resource price Time T New gross price New net price Original net price Original gross price cLcL cHcH Hoteling rule required: Gross price: Extraction costs

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Resource price Time T T/T/ New gross price New net price Original net price Original gross price K Extraction costs (2)

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Gross price P t Time t P0P0 T T R R0R0 R0/R0/ T/T/ P0/P0/ K T/T/ Original gross price path 45° New gross price path A rise in extraction costs

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Sum up: Extraction costs Gross price increases slower Final gross price is choke price If the new gross price starts lower, it never picks up with the old; resource extraction must be greater during the entire period; this cannot be optimal Therefore, new gross price starts higher, extraction is lower, and exhaustion is reached later

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Monopoly Firms objective function: Equations of motion: Hamiltonian: Necessary conditions: Marginal profit function:

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Net price P t Time t P0MP0M Perfect competition TMTM TMTM R R 0M Area = R0R0 T Monopoly P0P0 P T = P T M = K T Demand 45° Monopoly and perfect competition

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Royalty and Revenue Taxes A royalty tax does not change extraction A royalty tax does redistribute revenue from firms to the government Subsidies are negative taxes A revenue tax is equivalent to increasing the extraction cost, that is, higher initial gross price, slower growth, exhaustion postponed

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Further issues Private and social extraction costs might differ Private and social discount rates might differ Absence of forward markets and expectations Differences in risk perception Uncertainty

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How Real is Hotelling? Hotelling‘s rule has been derived for very simple economies So, either the analysis has to be made more complicated, or the data have to be manipulated before we can subject Hotelling to an empirical test Studies that have done either or both are inconclusive; some say, Hotelling is real, others say not so It may be that markets assume that resource stocks are infinite, until they are almost depleted

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