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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 Extraction costs**

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) 5.537 687 1.507 3.343 Öl Gas Kohle Bis Ende 2000 gefördert Verbleibendes Potenzial 125 552 316 236 57 1.450 287 1.163 100 3.243 Reserven Ressourcen 219 152/66 334 84/250 123 122/1 1.327 165/1.162 469 2.774 Source: RWE Weltenergiereport 2004

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**Resources and Reserves**

Increasing degree of economic feasibility McKelvey classification Increasing degree of geological assurance

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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 Mineral Prod. Cons. Econ. Res. Exp. Res. Tech. Res.**

Life Aluminium 112 19 23000 28000 222 Iron 930 960 150000 230000 161 Manganese 25 22 800 5000 42000 32 Chromium 13 419 1950 3260 Zinc 7.1 7.0 140 330 3400 20 Nickel .92 .88 47 111 2590 51 Copper 9.3 10.2 310 590 2120 33 Lead 3.4 5.3 63 130 550 18 Tin .18 .22 8 10 68 45 Tungsten .041 .044 3.5 ? 80 Mercury .003 .005 0.13 0.24 43 Million metric tons

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**Social optimum: Two-periods**

Demand function: Net social benefits: Welfare function: Constraint: Langrange: Necessary conditions:

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**Social Optimum: Multi-periods**

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

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**Graphical solution Net price Pt PT =K P0 Pt 45° T R R0 Time t Rt**

Demand P0 Pt 45° T R R0 Time t Rt Area = = total resource stock T Time t

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**Perfect Competition Perfect competition: Identical firms:**

Firms objective function: Equations of motion: Hamiltonian: Necessary conditions: Intertemporal efficiency:

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**Increase in demand Net price Pt K P0/ P0 R R0/ R0 T/ T Time t T/ T 45°**

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**Increase in interest rate**

P A C B K P0 Time T

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**Increase in interest rate (2)**

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

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**Increase in stock size Net price Pt K P0 P0/ R R0/ R0 T T/ Time t T T/**

Demand P0 P0/ R R0/ R0 T T/ Time t T T/ 45° Time t

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**Frequent new discoveries**

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

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**Backstop technology becomes cheaper**

Net price Pt K Backstop price fall PB P0 P0/ D R* R R0/ R0 T/ T Time t T/ T 45° Time t

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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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**Extraction costs Gross price: Hoteling rule required: Resource price**

Original gross price New gross price Original net price New net price cL cH Time T

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**Extraction costs (2) K T T/ Resource price Original gross price**

Original net price New gross price New net price T T/ Time

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**A rise in extraction costs**

Gross price Pt Original gross price path K New gross price path P0/ P0 R R0 R0/ T T/ Time t T T/ 45° Time t

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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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**Monopoly and perfect competition**

Net price Pt Monopoly and perfect competition Perfect competition PT = PTM = K Demand P0M Monopoly P0 R R0 R0M T TM Time t T Area = TM 45° Time t

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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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