Spatial Dimensions of Environmental Regulations

1
Spatial Dimensions of Environmental Regulations

• What happens to simple regulations when space
  matters?
• Hotspots?
• Locational differences?

2
Motivation

• Group Project on Newport Bay TMDL
• What rules on maximum emissions from different
  industries will assure acceptable level of water
  quality in Newport Bay?
• Reference http//www.bren.ucsb.edu/research/2002G
  roup_Projects/Newport/newport_final.pdf

3
Example Carpinteria marsh problem

• Many creeks flow into Carpinteria salt marsh
  pollution sources throughout.
• Pollution mostly in form of excess nutrients
  (e.g. Nitrogen Phosphorous)
• How should pollution be controlled at each
  upstream source to achieve an ambient standard
  downstream?

4
Carpinteria Salt Marsh
5
Salt Marsh
6
The Carpinteria Marsh problem
x
x
x
x
x
x
x
x
Marsh o
Where we care about pollution receptor (o) Where
pollution originates sources (x)
7
Sources and Receptors

• Sources are where the pollutants are generated
  index by i. emissions
• Receptors are where the pollution ends up and
  where we care about pollution levels index by
  j. pollution
• Emissions e1, e2, , eI (for I sources)
• Pollution concentrations p1, p2,,pJ
• Connection pjfj(e1,e2,,eI)
• Transfer functionfrom Arturo

8
Transfer coefficients

• Typically f is linear (makes life simple)
• pj S aijei Bj
• Where B is the background level of pollution
• aij is transfer coefficient
• dfj/dei aij transfer coefficient (if linear)
• Interpretation of aij if emissions increase in a
  greenhouse on Franklin Creek, how much does
  concentration change in salt marsh?
• What causes the aij to vary?
• Distance, natural attenuation and dispersion
• Higher transfer coefficient higher impact of
  source on receptor

9
Example concrete-lined channelDoes this
increase or decrease transfer coefficient?
10
Add some economics Simple case of one receptor

• Emission control costs depend on abatement
• Ai Ei ei where
• Ei uncontrolled emissions level (given)
• ei controlled level of emissions (a variable)
• E.g. ci(Ai) ai bi(Ai) gi(Ai)2
• Control costs (by industry) often available from
  EPA, other sources (e.g. Midterm)
• What is marginal cost of abatement?
• MCi(Ai) ßi 2 gi Ai

11
How much abatement?

• To achieve ambient standard, S, which sources
  should abate and how much?
• Problem of finding least cost way of achieving S
• Mine Si ci(Ei-ei) s.t. Si aiei S
• In words minimize abatement cost such that total
  pollution at Carpinteria Salt Marsh S.

12
Solution (mathematical)

• Set up Lagrangian
• L Si ci(Ei-ei) µ (S aiei - S)
• Differentiate with respect to ei, µ
• ?L/?ei -MCi(Ei-ei) µ ai 0 for all i
• ? equalize MCi/ai µ for all i
• Solution find ei such that
• Marginal abatement cost normalized by transfer
  coefficient is equal for all sources
  (interpretation?)
• Resulting pollution level is just equal to
  standard

13
Spatial equi-marginal principle

• Instead of equating marginal costs of all
  polluters, need to adjust for different
  contributions to the receptor.
• All sources are controlled so that marginal cost
  of emissions control, adjusted for impact on the
  ambient, is equalized across all sources.
• MCi / ai equal for all sources.
• Sources with big as controlled more tightly

14
Effect of higher a
MCA(a low)
MCB
MCA(a high)
MCA
Abatement
15
What kind of regulations would achieve desired
level of pollution?

• Rollback
• Standard engineering solution.
• Desired pollution level x of current level ?
  reduce all sources by x
• Marketable permits no spatial differentiation
• Polluters with big transfer coefficients would
  not control enough
• Polluters with small transfer coefficients would
  control too much.
• Constant fee to all polluters
• Same problem as permits

16
Spatial Version of Marketable Permits

• Issue 10 permits to degrade Salt Marsh
• Allowed emissions for source i, holding x
  permits eixi/ai.
• What is total pollution at receptor?
• S aiei S ai(xi/ai) S xi 10
• Does the equimarginal principle hold?
• Price of permit p (cost for i p xi)
• Price per unit emissions p xi/ ei p xi
  /(xi/ai) p ai
• For each source, marginal cost divided by ai p
• Therefore, Equimarginal Principle Holds
• Idea Trade or value damages not emissions.

17
Constructing a Policy Analysis Model Carpinteria
Salt Marsh Example

• Variables of interest
• i1,,I sources
• ei, emissions by source i
• Ai, pollution abatement by source i
• Data needed
• Ci(Ai), pollution control cost function for
  source i
• Ei, uncontrolled emissions by source i
• ai, transfer coefficient for source i
• S, upper limit on pollution at single receptor

18
Model Construction

• Goal is to minimize cost of meeting pollution
  concentration objective
• Objective function (minimize)
• Si ci(Ai) Si ai bi(Ai) gi(Ai)2 or
• Si ci(Ei-ei) Si ai bi(Ei-ei) gi(Ei-ei)2
• Constraints
• Si aiei S
• ei 0 (non-negativity constraint)
• Solve using Excel or other optimization software

19
Policy Experiments with Model

• What is the least cost way of meeting S?
• Always start with this baseline
• Can be achieved through spatially differentiated
  permits
• Consider a variety of different policies
• Rollback
• Simple (non-spatially differentiated) emission
  permits

20
Policy Experiments with Model Rollback

• How much would it cost to achieve S using
  rollback?
• Calculate pollution from current emissions, Ei
• Calculate percent rollback and then emissions
• Compute costs of this emission level

21
Policy Experiments with Model Emission permits

• Why?
• Simpler than spatially differentiated emission
  permits
• How much would it cost to use emission permits
  (non-spatially differentiated)?
• Eliminate constraint on pollution and substitute
• Si ei E where E is number of permits issued
• This simulates how a market for E emission
  permits would operate
• Calculate resulting pollution levels Si aiei
  S
• How do you think the cost of achieving S with
  emission permits will compare to the least cost
  way of achieving S?
• Vary E, until S exactly equals S.
• Bingo! You know the amount of emission permits
  to issue

22
What might the results look like?
Rollback Approach Emission Permits Least Cost
Total Pollution Control Costs ()
Uncontrolled pollution levels at Marsh
0
Pollution at Salt Marsh
Note order of costs need not be as shown.