Topics Today 111108

1
Topics Today (11/11/08)

• Resources and Energy.
• Hotellings Rule of Resource Extraction.
• Read chapter 14 in your book for next time.

2
Major questions addressed so far

• 1 Why do environmental problems occur and how
  can we do better?
• Property rights and market failure.
• Policies for market failure.
• 2 How much environmental damage should be
  allowed?
• Non-market valuation.
• Cost-benefit analysis.

3
Major questions remaining

• 3 Are we running out of natural resources?
• Oil and coal make up most of our current energy
  production.
• Oil and coal have no natural growth rate.
• 4 How can countries cooperate to improve the
  global environment?
• Climate change.
• Problems driven largely by energy production
  (e.g. burning fossil fuels).

4
Natural Resources

• Material resources are used as part of
  commodities (e.g. iron ore converted into steel).
  
• Energy resources are converted into heat and
  other forms of energy (e.g. natural gas converted
  to heat homes).
• Some resources are used as both materials and
  energy resources (e.g. oil is used to power cars
  and make plastic)

5
Natural Resources

• Renewable resources exhibit a natural rate of
  growth (e.g. fisheries and forests).
• Non-renewable resources do not exhibit a natural
  rate of growth (e.g. petroleum and zinc).

6
Hotellings Rule of Resource Extraction

• Suppose we have a firm trying to decide how much
  oil to extract this year and how much to extract
  next year.
• Assumptions
• Profit-maximizing firm.
• Competitive industry with constant demand.
• Costless extraction.
• Perfect information on future prices.
• Fixed reserve size.

7
Hotellings Rule of Resource Extraction

• Consider the situation where the producer is
  indifferent between selling the last unit of oil
  this year or next year.
• The present value of a barrel of oil would have
  to be the same in both periods.
• gt p1p2 / (1r)
• gt (1r)p1p2
• gt (p2 p1)/p1r Hotellings Rule

8
Hotellings Rule of Resource Extraction

• Hotellings rule (p2 p1) / p1 r
• The proportional increase in the price of oil
  equals the discount rate.
• Oil prices will rise through time.
• Market demand combined with firms reducing their
  output through time drives the price rise.

9
Hotellings Rule of Resource Extraction

• If we introduce costs, then the marginal profit
  becomes Mp p MC, where MC is the marginal
  cost of extraction.
• The term marginal profit is also called economic
  rent.
• A modified Hotellings rule follows
• (Mp2 Mp1) / Mp1 r
• The proportional increase in the marginal profit
  of oil equals the discount rate.

10
Hotellings Rule of Resource Extraction

• Ex/ Suppose there are 100 tons of Billite, a
  newly discovered non-renewable mineral. Assume
  the following
• Two-period model.
• Discount rate 10.
• The Billite industry is competitive (100 small
  producers, each with 1 ton of Billite).
• The marginal cost of producing Billite is 10.
• Inverse demand curve for Billite p 80 q,
  where p is price and q is quantity.
• Initially, there is 50 tons produced in the first
  year and 50 tons produced in the second year.

11
Hotellings Rule of Resource Extraction
12
Hotellings Rule of Resource Extraction
13
Hotellings Rule of Resource Extraction

• Is this equal division of Billite a market
  equilibrium?
• Suppose one of the producers decided to shift
  their production from period 2 to period 1.
• p1 falls to 29 and p2 increases to 31.
• The producer would be able to invest her 19 in
  profits at 10 discount and earn 20.90 in period
  2.
• So, her choice is between having 20 in the
  second period or having 20.90 gt incentive to
  switch production to period 1.

14
Hotellings Rule of Resource Extraction

• Is this 51/49 division of Billite an equilibrium?
• If one more producer shifts to period 1, p1 falls
  to 28 and p2 increases to 32.
• If that producer invested his 18 in profits at
  10 discount, then he would earn 19.80 in the
  second period.
• He would be better off not switching to period 1.
• The equilibrium outcome is p129 q151 tons
  p231 q249 tons.

15
Hotellings Rule of Resource Extraction

• Graphically

Note marginal profit marginal net benefit.
16
Hotellings Rule of Resource Extraction

• Graphically with two periods

17
Hotellings Rule of Resource Extraction

• Does this market equilibrium satisfy Hotellings
  Rule?
• (Mp2 Mp1) / Mp1 (21-19)/19 0.1.
• So, Hotellings rule describes a market
  equilibrium.
• Adding additional periods to the two-period
  model
• Some resource stock will be saved for future
  periods.
• Given a positive discount rate, the stock will
  eventually all be sold.

18
Hotellings Rule of Resource Extraction

• Two observations of the model
• First, notice that we dont extract all of the
  resource today. Why?
• Because there is an opportunity cost of consuming
  resources today, namely the value of consuming
  those resources in the future.
• This is called the marginal user cost.
• Second, notice that we consume more this year
  than we do next year.
• This reflects the opportunity cost of holding
  Billite in the ground.
• Opportunity cost of foregone investment.

19
Hotellings Rule of Resource Extraction

• What happens to the two-period model with higher
  discount rates?
• Suppose the discount rate were 20 rather than
  10.
• Would there be incentive to produce more than 51
  tons in period 1?
• If one more producer shifts to period 1, p1 to
  28 and p2 increases to 32.
• If that producer invested her 18 in profits at
  20 discount, then she would earn 21.60 in the
  second period.
• So, she would be better off by producing in
  period 1.
• The equilibrium outcome would be p128 q152
  tons p232 q248 tons.
• Higher discount rates imply faster extraction.

20
Hotellings Rule of Resource Extraction

• What happens to the two-period model with higher
  discount rates? Graphically

21
Hotellings Rule of Resource Extraction

• Resource price over a 50-year horizon with
  costless extraction, p010, and r0.05

22
Hotellings Rule of Resource Extraction

• Lifecycle of a non-renewable resource.
• Back-stop price
• The price at which demand is driven to zero.
• The price of a substitute for the non-renewable
  resource.
• Ex/ Back-stop price of oil is the price at which
  demand switches to a renewable alternative such
  as petrol or hydrogen.
• If we know the backstop price and the stock of
  the resource, the price and quantity of a
  non-renewable resource can be examined through
  time.

23
Hotellings Rule of Resource Extraction
Note this is figure 14.1 in your book.
24
Hotellings Rule of Resource Extraction

• Emprical test of Hotellings Rule (Krautkremer
  1998)
• Tracked prices for 9 non-renewable resources from
  1967 to 1994.
• There was no upward trend in prices. Why?
• Firms dont have perfect information on prices.
• Demand for the resource may change.
• Marginal costs may not be constant over time gt
  increases in technology may reduce the costs.
• Reserve size changes gt exploration expands
  reserves.

25
Hotellings Rule of Resource Extraction

• Emprical test of Hotellings Rule (Berck and
  Bentley 1997)
• Tracked the price of old-growth redwoods in CA
  after the government created Redwood National
  Park.
• Creation of Redwood National Park reduced the
  remaining stock of old-growth redwood.
• The price of remaining redwoods on private lands
  increased substantially.
• Hotellings rule supported.