Spatial Dimensions of Environmental RegulationsWhat happens to simple regulations when space matters? Hotspots?Locational differences?

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/2002Group_Projects/Newport/newport_final.pdf

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?

Carpinteria Salt Marsh

Salt Marsh

The Carpinteria Marsh problem

Marsho

Where we care about pollution: receptor (o)Where pollution originates: sources (x)

x

x

x

x

x x

x

x

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: pj=fj(e1,e2,…,eI) “Transfer function”—from Arturo

“Transfer coefficients”

Typically f is linear (makes life simple) pj = 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

Example: concrete-lined channelDoes this increase or decrease transfer coefficient?

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) = i + i(Ai) + i(Ai)2 Control costs (by industry) often available

from EPA, other sources (e.g. Midterm) What is marginal cost of abatement?

MCi(Ai) = βi +2 i Ai

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 i ci(Ei-ei) s.t. i aiei ≤ S In words: minimize abatement cost

such that total pollution at Carpinteria Salt Marsh ≤ S.

Solution (mathematical)

Set up Lagrangian L = Σi ci(Ei-ei) + µ ( 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

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 “a”’s controlled more tightly

Effect of higher “a”

Abatement

MCAMCBMCA(a high)

MCA(a low)

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

Spatial Version of Marketable Permits

Issue 10 permits to degrade Salt Marsh Allowed emissions for source i, holding x permits:

ei=xi/ai. What is total pollution at receptor?

aiei = ai(xi/ai) = xi = 10 Does the equimarginal principle hold?

Price of permit = π (cost for i: π xi) Price per unit emissions = π xi/ ei= π xi /(xi/ai) = π ai

For each source, marginal cost divided by ai = π Therefore, Equimarginal Principle Holds

Idea: Trade or value damages not emissions.

Constructing a Policy Analysis ModelCarpinteria Salt Marsh Example

Variables of interesti=1,…,I sourcesei, emissions by source iAi, pollution abatement by source i

Data neededCi(Ai), pollution control cost function for source

iEi, uncontrolled emissions by source iai, transfer coefficient for source iS, upper limit on pollution at single receptor

Model Construction

Goal is to minimize cost of meeting pollution concentration objective

Objective function (minimize): Σi ci(Ai) = Σi [i + i(Ai) + i(Ai)2] or Σi ci(Ei-ei) = Σi [i + i(Ei-ei) + i(Ei-ei)2]

Constraintsi aiei ≤ S ei ≥ 0 (non-negativity constraint)

Solve using Excel or other optimization software

Policy Experiments with Model

What is the least cost way of meeting S?Always start with this baselineCan be achieved through spatially differentiated

permits Consider a variety of different policies

RollbackSimple (non-spatially differentiated) emission

permits

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 emissionsCompute costs of this emission level

Policy Experiments with ModelEmission 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

i ei ≤ E+ where E+ is number of permits issued• This simulates how a market for E+ emission permits would

operate Calculate resulting pollution levels: i 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

What might the results look like?

Total PollutionControlCosts ($)

Pollution at Salt Marsh

Rollback Approach

Emission Permits

Least CostUncontrolled pollution levels at Marsh

0

Note: order of costs need not be as shown.