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									 EEP 101/ECON 125
     Lecture 15:
Natural Resources (NR)

      David Zilberman
       UC Berkeley
Review of Renewable Vs. Non Renewable
   Nonrenewable resources (mineral, fossil water,
    remnants of ancient civilizations, old growth
    forest, “dead things”).

   Renewable resources (fisheries, forests, grasslands,
    water systems, “living things”).

   Many renewable resources and most nonrenewable
    ones are exhaustible.
     Analysis of dynamic systems
   Natural resource management is control and direction of dynamic
    systems. Policies affect the evolution of populations and/or resource
    inventories

   The indicators of the situation of dynamic systems are state
    variables-
      Number of fish in a lake at a moment of time

      Volume of water in an aquifer



   Policy makers affect control variables
      Size of harvest
      Price of water


   Systems are affected by random shocks
      Weather

      Pest infestations
           Quantification of NR systems
   Measurement of dynamics systems is challenging
       counting fish is not easy

   NR resource systems may be heterogeneous
       trees and fish of different sizes, of different ages, and at different
        locations
       minerals of different qualities at varying locations

   The art of modeling identifies crucial features of the
    system and integrates simplicity with realism

   Models are approximations that are subject to error
                    Equations of motion
   Depict the evolution of state variables over time
       How the stock of oil or number of fish change

   Stock size today is
                         the resource stock of tomorrow is
                                     EQUAL TO
                                    today’s stock
                                       MINUS
                             today’s harvest (or mining)
                                       PLUS
                   resource stock growth (for renewable resource)
                                       PLUS
                                   new discoveries
                                       PLUS
      Applying Our Knowledge of
            Interest Rates
   Higher interest rates lead to increased mining or
    harvesting

   Resource owners that have to pay high interest for
    funds are more likely to mine resources & sell them
    than resource owners who face low interest rates

   Poor individuals with heavy credit constraints are more
    likely to mine their resources

   Income & credit support for the poor reduce NR mining
            Non renewable resources
   The actual stock of non renewable resources is declining over
    time, but known reserves may increase because of discoveries

   Perceived shortages and improved discovery technologies trigger
    searches and lead to discoveries

   Known oil reserves are estimated to last 40-80 years, the same
    estimate was given in the 1940s

   Still oil and natural gas reserves may run out

   Non renewable resources are rarely depleted, but may become
    too expensive to mine
    Factor determining extraction: demand
   Demand is reflecting marginal value of resource in applications (value
    of oil in transportation and heating)
   Higher incomes and lower prices increase demand
   Demand increases with increased population
   It may be reduced by introduction and adoption of resource
    conserving technologies (fuel efficient cars)
   It is reduced by back stop technologies (solar energy)
   Demand can be reduced by
      Taxes

      Population policies

      R&D
Other factors determining extraction
   Extraction cost- reduced mining or harvesting cost or improved
    infrastructure (roads) increase extraction

   Recycling- alternative supply sources reduce extraction

   Known Reserves (more reserves increase extraction)

   Market structure
     Cartels extract less than competitive producers

     Open access result in excessive mining



   Regulation and policies
      Technology control (restriction on use of explosives)

      Zoning ( do not drill in Alaska)
                       Generic Model
   Marginal Mining cost. MNC(x) .

   Marginal future cost (User costs). MFC(x). The future cost
    represents loss of future opportunities by present extraction.

   Externality cost. MEC
                                                    C =Optimal
                                                    allocation
                                                    A=Allocation
                                                    under open
                                                    access
                                                    B=Allocation
                                                    without
                                                    considering
                                                    externality costs
              Alternative Allocations
   Open access and no regulation will result in excessive
    resource use (A- Pollution & future ignored)

   Competitive supply by firms with well defined
    resources, ownership rights without pollution control
    still result in excessive mining (B)

   Competitive supply when ownership is well defined and
    pollution is taxed results in optimum (C)

   Cartel may under provide resources (if price under
    monopoly is greater than at C) or under provide if
    pollution cost great than the cartel’s price increase.
          Elements of a Resource Policy
   (1) Establishing private prosperity for the resource. This prevents the open
    access problem and moves from point A to point B in Figure 1.

   (2) Externality control. Including tax on the resource (leading to a transition
    from B to C). Gasoline tax in U.S. can
      affect Climate change dynamics

      reduce air pollution



   Resource taxes also lead to
      adoption of resource efficient technologies

      emergence of backstop technologies (recycling when appropriate)



   (3) Support to Backstop research

   (4) Subsidy for adoption of resource efficient technologies( fuel efficient
    cars,public transport)
              Renewable resources
   Growth provides a base for harvest without ultimate
    depletion.

   Change of stock = Growth minus harvest

   At a Steady state (sustainable solution)
    Growth = Harvest

   There are many sustainable solutions, the one that
    maximizes discounted net benefits is optimal
                   Resource dynamics
   St=resource stock time t
   Xt=extraction
   g(St)=growth. Growth formulas vary
       Proportional growth g(St)=St
       Fixed growth g(St)=Constant
       With non renewable resources g(St)=0 once all the stock has
        discovered.
   Equation of motion
Change in stock St+1-St =g(St) -Xt
Steady State         St+1-St=0 harvesting equals growth
        Not all steady states are alike
   Steady states outcomes are sustainable- but some
    sustain low stock levels and other largfe stocks
   Steady states analysis aims to stabilize outcomes
    providing the same levels of output or resoruces
    over long periods of time.But things change, evolve.
   It is useful to investigate when steady states will
    persist and study how chagens of conditions affect
    steady states.
   Fishery dynamics-fast growth=.1
                          Harvesting
growth          times     cost=n/S
=           0.1 stock     n=                5 price=
year    stock   growth    harvest     cost    profits
   1.00   40.00   -1.00          5.00    0.63    4.38
   2.00   39.00   -1.10          5.00    0.64    4.36
   3.00   37.90   -1.21          5.00    0.66    4.34
   4.00   36.69   -1.33          5.00    0.68    4.32
   5.00   35.36   -1.46          5.00    0.71    4.29
   6.00   33.89   -1.61          5.00    0.74    4.26
   7.00   32.28   -1.77          5.00    0.77    4.23
   8.00   30.51   -1.95          5.00    0.82    4.18
   9.00   28.56   -2.14          5.00    0.88    4.12
  10.00   26.42   -2.36          5.00    0.95    4.05
  11.00   24.06   -2.59          5.00    1.04    3.96
  12.00   21.47   -2.85          5.00    1.16    3.84
  13.00   18.62   -3.14          5.00    1.34    3.66
  14.00   15.48   -3.45          5.00    1.62    3.38
  15.00   12.03   -3.80          5.00    2.08    2.92
  16.00    8.23   -4.18          5.00    3.04    1.96
Fishery dynamics-slow growth=.05
                          Harvesting
growth          times     cost=n/S
=          0.05 stock     n=                5 price=
year    stock   growth    harvest     cost    profits
   1.00   40.00   -3.00          5.00    0.63    4.38
   2.00   37.00   -3.15          5.00    0.68    4.32
   3.00   33.85   -3.31          5.00    0.74    4.26
   4.00   30.54   -3.47          5.00    0.82    4.18
   5.00   27.07   -3.65          5.00    0.92    4.08
   6.00   23.42   -3.83          5.00    1.07    3.93
   7.00   19.59   -4.02          5.00    1.28    3.72
   8.00   15.57   -4.22          5.00    1.61    3.39
   9.00   11.35   -4.43          5.00    2.20    2.80
  10.00    6.92   -4.65          5.00    3.61    1.39
  11.00    2.27   -4.89          5.00   11.03   -6.03
  12.00    0.00       0          0.00    0.00    0.00
  13.00    0.00       0          0.00    0.00    0.00
  14.00    0.00       0          0.00    0.00    0.00
  15.00    0.00       0          0.00    0.00    0.00
  16.00    0.00       0          0.00    0.00    0.00
       Steady state-fast growth=.1
                          Harvesting
growth          times     cost=n/S
=           0.1 stock     n=                5 price=
year    stock   growth    harvest     cost    profits
   1.00   40.00    0.00          4.00    0.50    3.50
   2.00   40.00    0.00          4.00    0.50    3.50
   3.00   40.00    0.00          4.00    0.50    3.50
   4.00   40.00    0.00          4.00    0.50    3.50
   5.00   40.00    0.00          4.00    0.50    3.50
   6.00   40.00    0.00          4.00    0.50    3.50
   7.00   40.00    0.00          4.00    0.50    3.50
   8.00   40.00    0.00          4.00    0.50    3.50
   9.00   40.00    0.00          4.00    0.50    3.50
  10.00   40.00    0.00          4.00    0.50    3.50
  11.00   40.00    0.00          4.00    0.50    3.50
  12.00   40.00    0.00          4.00    0.50    3.50
  13.00   40.00    0.00          4.00    0.50    3.50
  14.00   40.00    0.00          4.00    0.50    3.50
  15.00   40.00    0.00          4.00    0.50    3.50
  16.00   40.00    0.00          4.00    0.50    3.50
              Wait and grow
                          Harvesting
growth          times     cost=n/S
=           0.1 stock     n=                5 price=
year    stock   growth    harvest     cost    profits
   1.00   40.00    4.00          0.00    0.00    0.00
   2.00   44.00    4.40          0.00    0.00    0.00
   3.00   48.40    4.84          0.00    0.00    0.00
   4.00   53.24    0.00          5.32    0.50    4.82
   5.00   53.24    0.00          5.32    0.50    4.82
   6.00   53.25    0.00          5.32    0.50    4.82
   7.00   53.25    0.01          5.32    0.50    4.82
   8.00   53.26    0.01          5.32    0.50    4.82
   9.00   53.26    0.01          5.32    0.50    4.82
  10.00   53.27    0.01          5.32    0.50    4.82
  11.00   53.28    0.01          5.32    0.50    4.82
  12.00   53.29    0.01          5.32    0.50    4.82
  13.00   53.29    0.01          5.32    0.50    4.82
  14.00   53.30    0.01          5.32    0.50    4.82
  15.00   53.31    0.01          5.32    0.50    4.82
  16.00   53.33    0.01          5.32    0.50    4.82
               Alternative strategies
   There are variable strategies of resource
    management-and many steady states
   Optimal one depends on
       objective function
       interest rate and outpur prices
        growth equation
       Extraction cost
   If Objective to maximize net present value higher
    interest rate lead to higher extraction
   In extraction cost decline with stock-optimal steady
    state has larger stock
          Growth as function of stock
   We have steady state (harvest =growth) at B,M,C,X
             B= low stock sustainable outcome
             C = High stock sustainable outcome
             M=Maximum Sustainable yield
             X=maximum Sustainable Stock
                G                      M
               g
               r             B                    C
               o
               w
               t
               h

                   O                                  X
                        Resource Stock
     Alternative Sustainable Outcomes
   Extinction- no stock on growth

   X=maximum Sustainable Stock (All food goes for consumption not
    growth)

   M=Maximum Sustainable yield (Between O and X)

   B= low stock sustainable outcome (Between O & M)

   C = High stock sustainable outcome (Between M &X)

   Maximum Sustainable yield is not necessarily optimal

   Higher stocks reduce harvesting costs

   Lower stocks allow more extraction
       Alternative extraction strategies
   Extract first sustain later
                                Extr
   The story U.S &Europe acti
                                on


                                         Time


   Conserve first sustain later
   Occurs in fisheries        Extrac
    which are near extinction tion
   Or in restoration efforts           Time
       Open access may lead to over
               extraction
   Competition and open access lead to over
    extraction- the tragedy of the commons
   Therefore extraction needs to be regulated
   Many polices are used to regualte harvesting
    some are better than others
   Optimal regulation is by incentive or tradable
    trading that leads to maximize net present value
    subject to constraint
Major Contributors to extraction:
Demand, Open access,Extraction technology
 Extraction is affected by policies

 Policies can reduce demand and thus extraction
       taxes, subsidies to resource use reducing technologies
   Policies to reduce extraction by control of access
       establishing property rights
       requiring licenses to extract
       limiting harvesting season
   Extraction control by regulating technology
       restricting size of equipment
       restricting total harvesting capacity
       regulating externality caused by harvesting (By catch)
        Multiple benefits of resources
   Resources (forests, wetlands, etc.) provide multiple services
    (recreation, bio-diversity, etc.)

   Harvesting reduces alternative environmental benefits

   One solution: taxation of harvested resources

   Alternatives: subsidies for conservation (not harvesting), debt
    for nature, payment for environmental services

   Marketing of environmental amenities (Ecotourism, bio-
    prospecting, tropical nuts )
      Intensification and conservation
   Agricultural intensifications (fertilizers,chemicals)-
    increases yield per acre and reduces utilized land and
    deforestation

   Aquaculture provides substitutes for fishing, but has its
    own environmental side effects (to be controlled)

   Forest plantation reduces pressure on natural forest

   Husbandry of animals (rhinos) would reduce pressure for
    tasks and other features of wild animals
                       Fishery Issues
   International water. There are international agreements and
    evolving “laws of the sea,” yet, open access problems continue
   Monitoring problems. Countries establish transferable fishing
    permits. Monitoring and enforcement may limit their effectiveness
   Regulation of timing. The size, number of boats and duration of
    fishing may be regulated. Limitations:
         (i) It leads to overinvestment in equipment.
         (ii) Frozen fish are inferior to fresh ones.
 Technology controls. Some techniques (use of explosive, fishing
    with fine mesh nets) have future and externality costs
 Aquaculture and marine culture. Provide alternative sources of
    fish, but have externality costs
P0




         Non renewable resource prices
    Prices are indicators of scarcity
    Prices of non renewable resources decline when known
     resources grow faster than use
    Prices of most non renewable resources has decline
    Higher interest rates lead to lower prices at present and
     higher future prices (they increase present mining)
    Higher mining cost increases prices but reduces price
     changes over time
Optimal price of resource over time
     with zero extraction cost

                         Higher interest rate
                         reduces initial price

                         BUT

                         Increased rate of
                         price changes when
                         stock is constant
More mining under higher interest rates in earlier periods and
                   less mining beyond t=t*
    Price Dynamics of Renewable Resources
   The rate of the price change is affected by:
       The discount rate tends to increase price over time.
       Rate of resource population growth tends to reduce price over time
        (as supply increases)
        Extraction cost factor dampens the other two


   Demand growth increases prices

   New resource sources tend to reduce prices

   Prices of most renewable resources have decline over time
                       Stock pollution
   Some pollution problems are dynamic in nature
       Climate change
       Ground water quality
   The stock may be provide negative value
   Without intervention competitive market leads to accumulation of
    pollution
   Polices can affect dynamics
       Reduce build up of stock of pollution
       Lead to more desirable steady state
   Policies may affect prices of outputs and inputs and distribution
    between groups and generations
   Market structure and interest rate will affect optimal policy

								
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