NONRENEWABLE RESOURCES 1. Introduction. 2. Measures of abundance 3. Hotelling s model of nonrenewable resources: production known reserve a. Hotelling s rule for price b. Comparative dynamics of price paths c. Monopoly vs. competition d. What drives oil prices? 4. Applications and policy issues a. Effects of a backstop technology b. Extraction from a common pool 4/11/2011 NRResources 1
Measures of Abundance, 1: Current (Proved) Reserves: Deposits that have been discovered, are known to exist, and can be extracted profitably; current price exceeds development and extraction cost. 4/11/2011 NRResources 2
Measures of Abundance, 2: Potential Reserves: (Ultimately Recoverable Resources) Deposits for which technical feasibility of extraction has been demonstrated or seems likely; price may or may not cover development and extraction cost. 4/11/2011 NRResources 3
Measures of Abundance, 3: Resource Endowment (Resource Base or Crustal Abundance): Natural abundance of a mineral in the earth's crust (to depth of 1 km., concentration > 1 pp mill), oceans, atmosphere, regardless of whether or not extraction and use is technically or economically feasible. 4/11/2011 NRResources 4
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Hotelling Rule for Competitive Market 1. Notation P t price of extracted mineral in year t. C r A T unit extraction cost (assumed constant). interest rate (assumed constant). choke price; price at which quantity demanded goes to zero. date when exhaustion occurs, i.e., year last unit is consumed. P t C value of a unit of the mineral in the ground. R Size of initial reserve. 4/11/2011 NRResources 6
A $/unit A: choke price C: unit cost of extraction P: price P 2 P 1 C D Quantity per unit time Q 2 Demand curve for nonrenewable resource Q 1 4/11/2011 NRResources 7
2. Conditions for Equilibrium ( Pt C) (i) is equal in all periods. t (1 + r) (Production in any period yields same present value profit per unit.) This implies P C = ( P C) ( 1+ r) t t 0 (ii) P T = A. (Last unit sold sells at choke price.) 4/11/2011 NRResources 8
3. Explanation of conditions Condition (i): Consider one unit of the mineral in the ground. ( P ) PV profit from selling is P0 C in year 0, 1 (1 + rc ) ( P2 C) in year 1, 2 (1 + r) in year 2, etc. If positive amounts are sold for consumption in all periods, PV profit must be the same in all periods. Therefore: ( Pt C) = t (1 + r) P 0 C for t = 1,2,3,..., or t ( P C) ( r) t P C = 1+ 0 In words, price minus marginal cost increases over time at the rate of interest. 4/11/2011 NRResources 9
3. Explanation of conditions (cont.) Condition (ii): If the last unit sold at a price below A, any mineral owner who anticipated this would have earned a capital gain exceeding r% per year by withholding a unit of the resource until all others had exhausted their deposits, and then selling it at price A in the next instant. This cannot occur in equilibrium. If the price rose to A before all deposits were exhausted, then those holding deposits at that point would earn a zero rate of return on them. This cannot occur in equilibrium. 4/11/2011 NRResources 10
$/unit A A: choke price C: unit cost of extraction P: price r: interest rate T: date of exhaustion Price P 2 P 1 r% growth per year C 1 2 time Competitive equilibrium: time path for price T 4/11/2011 NRResources 11
Nonrenewable Resources Sample Problem Demand: Qt = 100 - Pt (Q is in tons, P is in $/ton). Cost: C = 10 Interest rate: r =.10 Reserve: R = 153 tons. Questions: During how many periods does extraction take place? What is price in initial period? (Assume exactly 1 unit is sold in period T.) 4/11/2011 NRResources 12
Solution: year P t P t - C Q t Sum(Q t ) T 99 89 1 1 T-1 91 81 9 10 T-2 84 74 16 26 T-3 77 67 23 49 T-4 71 61 29 78 T-5 65 55 35 113 T-6 60 50 40 153 T-6 is initial year of extraction; price is $60. Extraction occurs over 7 years. Note: (P T-1 - C) = (P T - C)/(1 + r); (P T-2 - C) = (P T - C)/(1 + r) 2 ; etc. 4/11/2011 NRResources 13
Real World Oil Prices, 1970-2005 (Prices adjusted by CPI for all Urban Consumers, 2005) $90 $80 $70 Saudi Light Refiner Acquisition Cost Constant $2005 per barrel $60 $50 $40 $30 $20 $10 $- 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 Source: EIA 4/11/2011 NRResources 14
$/unit A A: choke price C: unit cost of extraction r: interest rate T: date of exhaustion Price (no constraint) C Price (with capacity constraint) Date of shift time T (no cons.) T (with cons.) Effect of temporary extraction capacity constraint on time path for price 4/11/2011 NRResources 15
$/unit A A: choke price C: unit cost of extraction T: date of exhaustion R: size of reserve Price (smaller R) Price (larger R) C Date of shift time T (smaller R) Effect of increase in size of reserve on time path for price T (larger R) 4/11/2011 NRResources 16
A $/unit A: choke price C: unit cost of extraction r: interest rate T: date of exhaustion Price (high r) Price (low r) C Date of shift time T (high r) Effect of increased interest rate on time path for price T (low r) 4/11/2011 NRResources 17
Hotelling Rule for a Monopoly 1. New Notation MR t marginal revenue from sales in t. T M year when last unit is consumed with monopoly. 2. Conditions for Equilibrium (i) MR t C ( 1+ r) t is equal in all periods. (Production in any period yields the same present value marginal profit.) This implies ( MR C) = ( MR C) ( 1+ r) t t 0 (ii) P M T = A. 4/11/2011 NRResources 18
3. Explanation of Conditions Condition (i): MR1 C PV profit from selling one unit of the mineral is MR 0 C in year 0, 1 + r year 1, MR 2 ( 1 + r ) 2 ( ) C in year 2, etc. In equilibrium the monopolist is indifferent between selling that unit in the present or in any future period, so the PV profit must be the same in all periods. This implies in ( MR C ) ( r ) t MR t C = 0 1 + for t = 1,2,3,... Condition (ii): Same rationale as for competitive case. 4/11/2011 NRResources 19
A $/unit A: choke price C: unit cost of extraction T: date of exhaustion Price (monopoly) r% growth per year Price (competition) MR monopoly C Date of shift time T (competition) T (monopoly) Effect of monopolization (vs. competition) on time path for price 4/11/2011 NRResources 20
Major Events and Real World Oil Prices, 1970-2005 (Prices adjusted by CPI for all Urban Consumers, 2005) $90 $80 $70 Iran-Iraq War Begins; oil prices peak Refiner Acquisition Cost Constant $2005 per barrel $60 $50 $40 $30 Saudis abandon "swing producer" role; oil prices collapse Gulf War Ends Prices spike on Iraq war, rapid demand increases, constrained OPEC capacity, low inventories, etc. Prices rise sharply on OPEC cutbacks, increased demand $20 Saudi Light Iranian Revolution; Shah Deposed $10 $- 1973 Arab Oil Embargo Iraq Invades Kuwait Asian economic crisis; oil oversupply; prices fall sharply Prices fall sharply on 9/11 attacks; economic weakness 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 Source: EIA 4/11/2011 NRResources 21
$/unit A A: original choke price B: unit cost of backstop supply source DDD: effective demand curve C: unit cost of extraction P: price B D D C D Quantity per unit time Effect of backstop supply source on demand for resource 4/11/2011 NRResources 22
$/unit A B A: choke price B: Backstop supply source unit cost C: unit cost of extraction T: date of exhaustion Price (no backstop) C Price (backstop available) Date of shift time T (backstop T (no backstop) available) Effect of introducing backstop supply source on time path for price 4/11/2011 NRResources 23
Common pool oil resources Normal opportunity cost of leaving oil in the ground 1 year is foregone interest on profit, r times value in ground Suppose any barrel left unextracted for 1 year has a 20% chance of being extracted by your neighbor. Then you will discount future profits from it at r+20%. Predict more rapid extraction; also physical waste due to less oil recovered. 4/11/2011 NRResources 24
Oil reservoir Owner A Owner B Owner C Oil well. Owner D Unrecovered oil Property boundary Question: Which property owner is being most aggressive? 4/11/2011 NRResources 25
Owner C Photos 4/11/2011 NRResources 26