Lecture #6 - Nonrenewable Resources


Hotelling's Rule


1. Non Renewable Resource - once the resource is used, it cannot be replenished; its gone forever.

  • Three classifications of exhaustible resources:
    1. Current reserves - known reserves that can be profitably extracted at current prices.
    2. Potential reserves - reserves that could be recovered at higher prices.
    3. Resource endowment - the entire geological supply of resources (including those not yet discovered).
  • The problem is scientists and companies are not 100% certain how much reserves are in the ground
  • Engineers define the following:
    1. Proven reserves - have at least 90% or 95% certainty of containing the amount specified.
    2. Probable reserves have an intended probability of 50%
    3. Possible reserves have an intended probability of 5% or 10%
  • Current technology is capable of extracting about 40% of the oil from most wells.
    • Some say future technology will make higher extraction possible, but this is already included Proven and Probable reserve numbers.
  • Companies have incentives to overstate their proven reserves
    • Oil companies want to improve their financial statements and their potential net worth
    • Producing countries gain a stronger international stature.
      • Other countries will be nicer to them.
    • Governments of consumer countries give false security and stability to their citizens.
    • In 2004 Shell Corporation had a scandal, where 20% of its reserves evaporated
  • BP's estimate of a country's Proved Petroleum Reserves as of 2009


2009 Country Non-OPEC
(Billions of barrels)
(Billions of barrels)
1. Saudi Arabia   264.209
2. Iran   138.400
3. Iraq   115.000
4. Kuwait   101.500
5. United Arab Emirates   97.800
6. Venezuela   87.035
7. Russia 79.432  
8. Libya   41.464
9. Kazakhstan 39.828  
10. Nigeria   36.220
11. United States 30.460  
12. Canada 27.664  
13. Qatar   27.436
14. China 15.493  
15. Brazil 12.624  
16. Algeria   12.270
17. Mexico 12.187  
  • Resource depletion
    • Mathematical analysis is much more complicated
    • Extraction involves dynamic decisions
    • As resource is extract, then less can be extracted in the future
      • The present and future are tied together
  • Costs of Extraction
    • Extraction cost - the cost to remove resource out of ground, process it, and transport it to the market
      • Producers extract when P >= Marginal Extraction Cost (MEC)
      • Example - if MEC = $60 to extract oil out of Alaska
        • Producers shut down production when petroleum price drops below $60
        • Producers extract oil when price equals or exceeds $60
    • User cost - the opportunity cost of not having the resource to sell in the future
      • The owner of a resource has two sources of money for next year:
        • Sell all the oil now, and invest the profits at interest rate, i.
        • Wait and sell the oil next year.
      • Thus, the price of the resource has to be greater than the MEC, because of user cost
    • Proof
      • Called intertemporal arbitrage
      • Case A: Expected price next year rises less than the rate of interest:
        • The owner of the resource is better off selling the oil now and investing it.
        • Leads to lower prices now (greater supply) and higher prices next year (lower supply).
      • Case B: Expected price next year rises faster than the rate of interest:
        • The owner of the oil is better off waiting to sell the oil next year.
        • Leads to higher prices now (lower supply) and lower prices next year (higher supply)
    • By using this arbitrage, the petroleum companies cause petroleum prices to increase at the rate of interest
  • Profit maximization
    • Farmer: Choose output where p = MR = MC
    • Miner: Choose output where p = MEC + user costs (i.e. rent)
      • Miner: rent = P - MEC
      • Still assuming it is a competitive industry
    • Similar to a monopoly
      • Market price is higher, and thus, market quantity is lower
      • Miners could earn long run profits, called rent
        • Hotelling rent - profit created by a resource scarcity in a competitive market, because the resource is fixed in nature
        • Also called Ricardian rent, resource rent, and user costs

2. Hotelling's Rule

  • In Year 0, the firm starts extracting a depletable resource
    • The market price and quantity are P* and Q*
  • In Year 1, the firm extracts less resources, because some of it has been used up
    • The supply function decreases
    • The market price is higher and market quantity is lower
  • In Year 2, the firm again extracts less resources
    • Supply function decreases
    • The market price becomes higher and market quantity is lower
  • Thus, market prices should continuously increase for a depletable resource
    • The higher prices are not evidence of abuse of market power.
    • The higher prices represent economic rent due to scarcity.

Using Supply and Demand to show Hotelling's Prices

3. Marginal Extraction Costs (MEC) should increase over time as petroleum and ores are depleted

  • Producers will extract the highest-quality ores first.
  • As the high quality ores are depleted, then producers start to mine the less pure ores
  • The MEC should increase over time
    • Energy cost to extract may increase
    • Higher cost to process the metal
    • May create more toxic waste
    • Example 1 - Petroleum
      • Heavy crude oil, oil sands, and oil shale are not included in oil reserves
      • Producers can uses these petroleum sources
        • They contain more sulfur and heavy metals
        • Higher costs to extract this crap out
        • Produces more greenhouse gas emissions
          • Processing this stuff may create three times more as regular petroleum 
    • Example 2- Gold mining in Nevada
      • Produces 6 million ounces per year (82% of the supply within the United States)
      • Uses open pit mining and cyanide heap leaching recovery
        • Producers dig out large pits
        • Then they form large mounds
        • They spray it with cyanide that dissolves the gold
        • Collect the leeched residue and recover the gold
  • Our present mining operations have left a legacy of scarred earth and polluted water— how will we deal with future higher-impact requirements?
  • Thus, market price for minerals have to increase for companies to extract lower quality ores.

4. Problems with Hotelling's Rule

  • The empirical evidence is mixed for Hotelling's Rule
  • Hotelling's Rule ignores three factors
    1. Technological improvements cause marginal extraction costs to fall over time
      • A competitive industry passes the lower costs to the consumers as a lower price
    2. Hotelling’s prices depend on the petroleum reserves being known and fixed
      • Then petroleum extraction is based on intertemporal arbitrage.
      • Petroleum companies do not know the location of all reserves.
        • Petroleum companies have a strong incentive to explore and drill for new petroleum reserves, when petroleum prices are high
        • High petroleum prices
          • Companies are exploring where extraction is much more expensive
          • Extremely deep wells
          • Extreme downhole temperatures
          • Environmentally sensitive areas
          • Allow extraction from the deep waters of the Gulf of Mexico or the cold Alaskan climate.
    3. Demand for petroleum can change
      • As petroleum price increases, consumers reduce quantity demanded for petroleum products
        • High fuel prices cause consumers to reduce their demand
          • Conserve
          • Law of Demand
        • Consumers buy more fuel efficient cars
        • Consumers move closer to work
      • Consumers can greatly decrease their consumption of fossil fuels when market prices are high in the long run

Hubbert's Life Cycle Hypothesis or Peak Oil


M. King Hubbert - a petroleum engineer

  • Petroleum prices, petroleum extraction, and well productivity should be parabola shaped
    • Violates Hotelling’s rule.
  • When the petroleum industry was young and expanding its infrastructure, petroleum companies discovered and developed new large petroleum reserves
    • Market price is initially high but falls once companies get the infrastructure in.
  • As discoveries become rarer and smaller, and petroleum depletion caused marginal extraction costs to increase, then petroleum prices exhibit scarcity and begin to increase over time.
  • Below is U.S. Petroleum Production.

U.S. Petroleum Production

  • Oil depletion - when production of petroleum begins to decline
    • The declining portion of the u-shaped production curve
  • U.S. peaked in 1969
    • Hubbert underestimated the U.S. oil production peak by 10 years.
    • Why?
      • Technology - companies became better at extracting oil
        • Companies also become better at locating new reserves
        • Companies can drill deeper, etc.
  • Many believe the world's petroleum production peaked in 2005 / 2006
    • Out of the largest 21 petroleum fields, at least 9 are in decline
    • Saudi Arabia admitted its mature fields are now declining at a rate of 8% per year
    • Kuwait - the Burgan field, second largest in the world, is in decline since November 2005
    • Be careful
      • Many countries nationalize their petroleum production industries
      • All OPEC members - government owns the petroleum resources
      • Incentive to keep production low and market prices high
      • Firms maximize profits
      • Political organizations do crazy things which may not maximize profits


U.S. First Purchase Price for Petroleum

  • I think this is the refinery's acquisition of oil
    • The dollars have been converted to real
      • Nominal - measured in U.S. dollars
      • Real - remove the effect of inflation
        • A price increase may be from stronger demand or smaller supply
  • In 2005, petroleum prices dramatically shot up
    • China and India are developing
    • China has some petroleum resources
    • India has to import most of its petroleum needs
    • As these two economies develop, they can put upward pressure on demand for petroleum
  • U.S. dollar was depreciating against the Euro and other strong currencies
    • Petroleum producing nations want to be paid in non-U.S. dollars
      • Higher petroleum price incorporates the dollar’s weaker value.
    • Euro plunged in value during the 2008 Financial Crisis
    • Some countries are worried about the U.S. to pay its $10 trillion debt
    • Some countries are trying to move away from the U.S. dollar to another currency or commodity

Cost Per Well - Both Petroleum and Natural Gas

  • Many of the large and easy fields have been exploited
    • Petroleum companies have to drill deeper and develop drills from smaller reserves
    • Some claim that the U.S. outer continental shelf holds an estimated 100 billion barrels of oil and natural gas
      • Located in the deep waters of the Gulf of Mexico
  • As the petroleum reserves are depleted, wellhead pressure decreases and crude oil viscosity increases, increasing marginal extraction costs
  • Gold is another depletable resource
    • More is said about gold in Lecture 9
      • Gold can be recycled
    • The monthly gold price is below
    • This is nominal and has not been adjusted for inflation
    • Again, not obeying Hotelling's Rule

Monthly Gold Price since 1968

  • Silver is another depletable resource
    • More is said about silver in Lecture # 9
      • Silver can be recycled too
    • The nominal monthly sliver price is below
    • Again, price of silver is not obeying Hotelling's Rule

Monthly Silver Price since 1968



1. Pure monopoly - a firm is sole producer / supplier of a product in the market

  • Usually mineral and petroleum extraction and energy generation are dominated by very large corporations
  • Characteristics
    1. Single seller of a product
      • The demand for the monopolist's product is the market demand curve
      • A one firm industry
    2. No close substitutes for the product
      • You either buy the product from him or you don't
    3. A monopolist can exert control over the price
      • He decreases production level and market price increases
    4. Other firms are prevented from entering the market, because of high barriers
      • No competition
  • Market Entry Barriers - Prevent entry of competitors into the market
    1. Economies of scale - also called a natural monopoly - monopoly has to be large to obtain low per-unit cost.
      • Firm has very large fixed costs
        • Requires large amount of equipment & infrastructure
      • A new firm entering this market would need substantial amounts of capital to reach this low-cost production level
      • Monopoly usually supplies the whole market.
      • Examples: Local phone service, electricity, natural gas, petroleum, and mining companies
    2. Legal Barriers - government's rules or regulations create an entry barrier
      • Government usually nationalize the important minerals and petroleum industries
      • Government owns the companies directly or indirectly
    3. A firm controls an essential resource
      • Example: Before World War II
        • Aluminum Company of America (Alcoa) controlled the supply of bauxite
        • Other firms could not produce aluminum cheaply without bauxite.
      • Example: DeBeers Corporation of South Africa.
        • Controlled 80 to 85% of the world's supply of diamonds
        • Currently controls approximately 55% of market
        • "Diamond is forever."
    4. Unfair competition:
      • Example: Standard Oil - John Rockefeller.
        • Came into a small town and charge a price below cost.
        • Drove competitors out of business.
        • Standard Oil would buy these businesses for cents on the dollar and consolidate them into Standard Oil.
        • With no competition, Standard Oil charged monopoly prices.
        • Controlled 90% of U.S. oil market.

2. Price and output under monopoly

  • Profits are maximized at MR = MC
    • Monopolists expand output when MR > MC
    • Monopolists contract output when MC > MR
  • Unregulated monopolist: Market price, P* and production level, Q*
    • P* > C*, therefore monopolist earns economic profits
    • High entry barriers prevent competition
    • Monopolist earns long-run profits
    • Market barriers prevents competition
  • Monopolist does not have a supply function
    • Monopolist produces at MC =MR, which is one point
      • P* > MR
    • Monopolist has lower social welfare than a competitive market
      • Monopolistic market has higher price and lower quantity
      • Consumers' surplus is transferred from consumers to monopolist as profits
A Monopolist
Price, Per-unit costs
An unregulated monopoly earning profits
  • If the market was competitive, then the market price would be lower and the market quantity would be higher
    • Shown by the bars
    • Remember - purely competitive firms set the P = MR = MC
  • A monopolist conserves depletable natural resources
    • He extracts less over time than the pure competitive market
    • Higher market prices force consumers to conserve more of the resource too.
  • Shown below:

A Monopolist
Price, Per-unit costs
Comparing a monopoly to a competitive market

3. Why are monopolies bad?

Not only does this list apply to monopolies in the private market, but also includes government that has monopolies over certain services.

  1. Little competition limits the options to consumers
    • You either buy the product from the monopolist or you go without
  2. Reduced competition results in allocative inefficiency
    • Allocative efficiency is when P = MC
      • Only purely competitive markets are allocative efficient
    • Markets with monopolies
      • Consumers value the products more highly than what it costs to produce them
        • P* > MC
        • Firms are earning economic profits
  3. Consumers are not able to direct monopolies to serve their interests
    • Bad service
    • No incentive to improve products, etc.
  4. X-Inefficiency - firms or agencies may not produce at low cost
    • Lack of competition
    • No incentive to minimize costs or mismanagement
    • Poorly motivated workers
    • X-Inefficiency - may be worse with government organizations because they can be much larger
  5. Monopoly power may encourage rent seeking behavior
    • Rent seeking behavior - government officials take cash & assets from private companies & people
    • Russia:
      • Companies bribe public officials, then officials grant licenses to those businesses, restricting competition.
    • U.S.
      • Corporations funnel campaign money to Congressmen
      • Congress passes laws favorable to corporations

Backstop Technology


Backstop technology - resource is a perfect substitute for another natural resource, but has a higher cost.

  • Price may have to increase to a high enough level
  • Makes the alternative resource feasible.
    • The alternative resource may have higher extraction costs or requires expensive technology.
    • Example 1: Oil from shale rock
      • If petroleum price becomes too high, then someone invents new technology that allows petroleum to be extracted from shale rock.
    • Example 2: Solar panels
      • If the price of electricity becomes high enough, then people supplement their electricity demand with solar panels.
    • Example 3: Cracking and liquefaction
      • Use heat and pressure to convert organic substances like vegetable oils and crop residues into petroleum products.
  • Supply and demand are shown for a depletable resource
    • If the market price equals or exceed PB, then everyone switches to the backstop technology
      • Market demand would go to zero for this resource

Using a Demand Function to show Backstop Technology

  • This analysis has one flaw
  • At the backstop technology price, PB, enough of the backstop technology has to be supplied in sufficient quantities to the market
    • The supply function for the backstop technology has to be perfectly elastic supply, i.e. flat
  • Hotelling model
    • Resource price grows at the constant interest rate as supply function decreases each year.
    • If there is no backstop technology, then the resource extraction is driven to zero.
    • With backstop technology, at the switching point, the backstop technology replaces the depletable resource.
      • The resource may not be exhausted.