Spatial Dimensions of Environmental Regulations

How can economics help us better regulate when the damages occur over space?

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 source to achieve an ambient standard?

The Carpinteria problem

Marsho

1 Receptor (o)Many sources (x)

x

x

x

x

x x

x

x

“Transfer coefficients”

If emissions increase in a greenhouse on Franklin Creek, how much does N concentration change in salt marsh?Index sources with i ; receptors with j.Pollution at receptor j is fn of emissions:

pj = fj(e1, e2, …, eI)

dfj/dei = aij = transfer coefficient

Natural attenuation, concrete channels?

A concrete-lined channel

Pollution if no interaction effects

pj = aijei + Bj

Where Bj is background level of Nitrogen.

Now aij = dpij/dei

The cost of emissions control

Cost is a function; depends on how much emission the source has to control:

ci(Ei – ei), where Ei = uncontrolled emissions level.E.g. ci(Ei – ei) = i + i(Ei-ei) + i(Ei-ei)2

Then MC is linear.Control costs (by industry) often available from EPA, other sources.

How much abatement?

To achieve ambient standard, A, which sources should abate and how much?

Mine ci(Ei-ei) s.t. aiei A

In words: minimize abatement cost such that total pollution at Carpinteria Salt Marsh A.

Possible regulations to consider

RollbackStandard engineering solution.

Marketable permitsNot efficient because ai’s different.

Constant fee to all pollutersSame effect as permits

Spatial version of Equi-marginal Principle

Current pollution level

PaiEi > A

“Rollback”

Standard engineering solution.Everyone “rolls back” pollution by the same percentage:

x = A/P0

ei = Eix

E.g. A=100 ppm, P0=1000 ppm.Everyone rolls back by 10%If I started at 40, new level is 36.

Effects of the rollback

Structured to exactly hit target (A).Ignores cost of abatement!Ignores different contribution of each source to receptor (Carpinteria Marsh)

Can we do any better with an economic approach?

Marketable permits / Emission fees

Permits: Fix total amount of pollution that is allowed (A).Distribute A permits, where permit required for polluting, let firms trade.

But this ignores the different contribution of each source to MarshSame for uniform Emission fees.

Treat firms differently

Since each polluter has a different contribution to overall pollution, they need to be treated differently.If we’re only worried about N in ocean, then likely to be worse the closer you are to ocean!Need a mechanism that captures this effect…need an adjusted version of equi-marginal principle.

Adjusted equi-marginal principle

Instead of equating marginal costs of all polluters, need to adjust for different contributions to the receptor.Strong contribution, cheaper to abate per effective unit of pollution:

MCk/ak = MCj/aj

Set these = to marginal damage for efficiency