L6: Pollution Control Policies: Targets

Question 1

Define stock and flow pollution and give 2 examples for each

Answer 1

Flow Damage: occurs when damage results only from the flow of residuals; that is,
the rate at which they are being discharged into the environmental system.
❖In pure cases, the damage instantaneously goes to zero if pollution flow ceases (e.g. noise and light pollution)
▪ Stock Damage: Refers to the case in which damages depend only on the stock of the
pollutant in the relevant environmental system at any point in time.
❖Residuals from pollution have positive lifespan and pollution is produced at a rate that exceeds assimilative
capacity (e.g. metals such as lead and mercury)

Question 2

What letter denotes flow and stock?

Answer 2

M = flow

A= stock

Question 3

What is the formula for net balance?

Answer 3

NB = B(M) - D(M)

Question 4

TD rises at increasing rate with the size of the ___ ___, and so MD will be increasing in M

▪ TB of emissions will rise at a decreasing rate as emissions increase because per-unit pollution
____ ____ will be more expensive at ____ levels of emissions reduction.

MB of pollution ___ as pollution flows increase

Answer 4

TD rises at increasing rate with the size of the pollution flow, and so MD will be increasing in M

▪ TB of emissions will rise at a decreasing rate as emissions increase because per-unit pollution
abatement costs will be more expensive at higher levels of emissions reduction.

MB of pollution falls as pollution flows increase

Question 5

Sometimes possible to achieve environmental objectives at no cost or, better still at ____ cost.

Ways of doing this are known as ___ ____ policies. Reasons why they arise:

x4

Answer 5

Sometimes possible to achieve environmental objectives at no cost or, better still at negative
cost. Ways of doing this are known as no regrets policies. Reasons why they arise:

(i) Double dividends
(ii) Elimination of technical and economic inefficiencies in energy using or energy producing sectors
(iii) Induced technical change
(iv) Achievement of additional ancillary benefits, such as improved health or visual amenity

Question 6

How is induced technological change a ‘no regrets’ policy?

Answer 6

▪ There are other reasons why an environmental programme can lead to double benefit
e.g. market imperfections can result in a firm producing away from the technically
and/or economically efficient frontier
▪ Firms may be unaware of new techniques, be poorly informed about waste recycling or
have old technology because of credit market imperfections. A programme that requires
firms to use new or less polluting techniques can also lead to productive efficiency gains
e.g. regulatory constraints may induce firms to be more innovative

Question 7

Explain the concept of Double Dividends as a ‘no regrets policy’?

Answer 7

Idea arises from the possibility that the revenues from an emissions tax could be
earmarked to reduce marginal rates of other taxes in the economy
▪ If those other taxes have distortionary effects i.e. inefficiency generating, then reducing
their rate will create efficiency gains for the economy as a whole
▪ Hence, an environmental tax with revenues that are ring-fenced for reducing
distortionary taxes has a double benefit (dividend); the environment is improved and
efficiency gains accrue to the economy as whole.
▪ If there is a double dividend then the marginal benefit function will overstate the true
value of emissions benefits

Question 8

In the Emission Efficiency function:

▪ The efficient level of pollution is M* (see figure in next slide).

The value of MD and MB at their intersection is m* which we can think of as the equilibrium price of ___.

However, because there is no market for pollution, we can think of m* as the ___ price of the pollution ___

Answer 8

▪ The efficient level of pollution is M* (see figure in next slide).

The value of MD and MB
at their intersection is m* which we can think of as the equilibrium price of pollution.

However, because there is no market for pollution, we can think of m* as the shadow
price of the pollution externality

Question 9

▪ The flow pollution model provides the correct answers in the special but highly unlikely
case where the pollutant stock degrades into a harmless form instantaneously. In all
other cases the flow model is ____. Majority of major pollution problems are
due to ____ pollutants. EPA may seek to control the ___ even where the ___ is the problem. This is because they cannot regulate stocks

Answer 9

▪ The flow pollution model provides the correct answers in the special but highly unlikely
case where the pollutant stock degrades into a harmless form instantaneously. In all
other cases the flow model is inappropriate. Majority of major pollution problems are
due to stock pollutants. EPA may seek to control the flow even where the stock is the
problem. This is because they cannot regulate stocks

Question 10

What is uniform mixing? example 1

Answer 10

Uniform mixing: Spatial dispersion is uniform i.e. the measured concentration rate does not vary from place to place (e.g. greenhouse gases).

All that matters is the total amount of those emissions

Question 11

What is non-uniform mixing?

Answer 11

▪ Non-uniform mixing: Spatial dispersion is non-uniform. Very important as many types of pollution fall into this category

e.g. ozone accumulation in the lower atmosphere, particulate pollutants from diesel engines

Question 12

How may the EPA control spatial issues and stock pollutants?

Answer 12

▪ An EPA may attempt to control spatial issues ex ante by placing restrictions on the
location of pollution creators and victims through zoning and other forms of planning
control (e.g. admissible location of activities or heavy industry zoning regulations).

Question 13

What does Dij represent in the ambient pollution model?

What does it imply if this is constant over time?

What cause these to change?

Answer 13

transfer coefficients

Transfer coefficients dij describe the impact on pollutant concentration at receptor j attributable to source i.

Constant transfer coefficients imply linearity over time

Coeffs will vary according to wind and climate over time. Reasonable assumption for
most pollutants when we consider average values over some period of time.

Question 14

Ambient Pollution Standards:

Benefits consist of the sum over all N ___ of each firm’s ____ ____:

Damages consist of the sum over all J ____ areas of the ____ incurred in that area:

The emissions target should be set so that ____=___

▪ Since the ith firm’s emissions are transferred to some or all of the receptors the ___ ____ caused by the ith firm is obtained by summing its contributions over the J receptors

▪ Not only will the level of ___ emissions differ from firm to firm but also the level of pollution across ____

▪ Should the sources with the highest impact emit the least? Doesn’t work like that as the objective is max ___ ___

Answer 14

Ambient Pollution Standards:

Benefits consist of the sum over all N sources of each firm’s pollution benefits:

Damages consist of the sum over all J receptor areas of the damage incurred in that area:

The emissions target should be set so that MPB=MD

▪ Since the ith firm’s emissions are transferred to some or all of the receptors the marginal damage caused by the ith firm is obtained by summing its contributions over the J receptors

▪ Not only will the level of efficient emissions differ from firm to firm but also the level of pollution across receptors

▪ Should the sources with the highest impact emit the least? Doesn’t work like that as the objective is max NB

Question 15

Intertemporal Analysis of stock pollution:

Let’s now take account of time. Consider pollutants that have a long damaging ____ and are
___ mixing. No ____ dimension

____ is determined by the stock size/concentration rate. _____ depend on the flow

▪ Stock (A) and flow (M) are not ____ of each other. With long-lived pollutants, emissions add to existing stocks and those stocks accumulate over time

▪ However, likely part of the existing stock will decay into a ____ form, with negative impact on ___ accumulation. The stock–flow relationship has a rate of change in ___ over time

What does alpha represent?

Answer 15

Let’s now take account of time. Consider pollutants that have a long damaging lifespan and are uniformly mixing. No spatial dimension

Damage is determined by the stock size/concentration rate. Benefits depend on the flow

▪ Stock (A) and flow (M) are not independent of each other. With long-lived pollutants, emissions add to existing stocks and those stocks accumulate over time

▪ However, likely part of the existing stock will decay into a harmless form, with negative impact on stock accumulation. The stock–flow relationship has a rate of change in stock over time

▪ The last term is the per period decay

Question 16

stock-flow relationship:

0< Alpha < 1 in (18). When alpha=0 we have a ____ pollutant. Integration of (18) shows that
the stock is the sum of all ____ emissions i.e. damages last ____.

Pollution stock will increase without bounds as long as M is ____

▪ ______ persistent pollutant so the pollutant stock decays gradually over time

▪ When alpha=1, we have ____ decay so we have a ___ pollutant.

Linearity results in a ___ decay

Answer 16

0< Alpha < 1 in (18). When alpha=0 we have a persistent pollutant. Integration of (18) shows that
the stock is the sum of all previous emissions i.e. damages last indefinitely.

Pollution stock will increase without bounds as long as M is +ve

▪ Imperfectly persistent pollutant so the pollutant stock decays gradually over time

▪ When =1, we have instantaneous decay so we have a flow pollutant.

Linearity results in a constant decay

Question 17

Relationship between A and M is not independent of ____ because even if emissions had been at a constant level in the past and this was to continue, _ would not be constant over time

Answer 17

Relationship between A and M is not independent of time because even if emissions had been at a constant level in the past and this was to continue, A (TOTAL LEVEL OF POLUTION OR Concentration rate) would not be constant over time

Question 18

For a steady-state, emission ____, M, must be equal to the amount of ____ which ____, alphaA (αA)

Answer 18

For a steady-state, emission inflows, M, must be equal to the amount of stock which decays, alphaA

M = αA

Question 19

The efficient steady-state level of emissions requires the following condition:

Answer 19

The efficient steady-state level of emissions requires the following condition:

dB/dM = dD/dM (1 / r + α)

Question 20

Conditions the efficient steady-state level of emissions requires the following condition: dB/dM = dD/dM (1 / r + α)

(i) Other things being equal, the faster the ___ rate, the higher will be the efficient level of steady state
emissions. For any 𝑑𝐷/ 𝑑𝐴, a rise in 𝛼 means that 𝑑B/ 𝑑M has to ____ to ensure marginal equality. Lower 𝑑B/ 𝑑M implies higher ____. Hence higher ___ rate means larger ‘effective’ discount rate (attach less weight to future, so raise emissions today)

(ii) Other things being equal, the larger the consumption discount rate, the ___ will be the efficient level of steady-state emissions

Answer 20

Conditions the efficient steady-state level of emissions requires the following condition: dB/dM = dD/dM (1 / r + α)

(i) Other things being equal, the faster the decay rate, the higher will be the efficient level of steady state
emissions. For any 𝑑𝐷/ 𝑑𝐴, a rise in 𝛼 means that 𝑑B/ 𝑑M has to fall to ensure marginal equality. Lower 𝑑B/ 𝑑M implies higher emissions. Hence higher decay rate means larger ‘effective’ discount rate (attach less weight to future, so raise emissions today

(ii) Other things being equal, the larger the consumption discount rate, the higher will be the efficient level of steady-state emissions

Question 21

when α>0 and r = 0

An efficient steady-state of emissions requires that the contribution to ___ from a marginal unit of ___ ___ be equal to the contribution to damage of a marginal unit of pollution ____

The pollutant eventually ___ to harmless form:

=

Answer 21

What happens when α>0 and r = 0

An efficient steady-state of emissions requires that the contribution to benefits from a marginal unit of pollution flow be equal to the contribution to damage of a marginal unit of pollution flow

The pollutant eventually decays to harmless form:

dD/dM = dB/dM

Question 22

When α>0 and r>0

With r and α being +ve the equilibrium condition is given by (24).

◼M** is the equilibrium level of ___ in the figure in previous slide
◼As r increases above zero the MB function ___ . Discounting ____ the steady-state level of emissions
◼A larger value of r ___ the PV of future damages associated with the pollutant stock.
◼A bigger weight is attached to present benefits relative to the ___ ___

Answer 22

When α>0 and r>0

With r and α being +ve the equilibrium condition is given by (24).

◼M** is the equilibrium level of e mission in the figure in previous slide
◼As r increases above zero the MB function pivots about . Discounting increases the
steady-state level of emissions
◼A larger value of r reduces the PV of future damages associated with the pollutant stock.
A bigger weight is attached to present benefits relative to the future costs.

Question 23

When α=0 and r=0, α=0 and r>0:

In both cases the pollutant is ____ ___. (24) is undefined when α=0 so no steady-state exists except when __=0. A steady-state cannot exist for any _____ value of M as A would ___ without bound.

▪ EPA will at some point in time require emissions to be permanently ___ to avoid intolerable ____. Pollution stock would remain at whatever level A had risen to.

Pollution damage would therefore continue at some ____ level. What date should emissions be permanently set to zero?

▪ Zero natural decay rate but policy makers could make this negative through ____-___ _____

Answer 23

When α=0 and r=0, α=0 and r>0:

In both cases the pollutant is perfectly persistent.
(24) is undefined when α=0 so no steady-state exists except when M=0. A steady-state cannot exist for any +ve value of M as A would rise without bound.

▪ EPA will at some point in time require emissions to be permanently zero to avoid intolerable damage. Pollution stock would remain at whatever level A had risen to.

Pollution damage would therefore continue at some constant level. What date should emissions be permanently set to zero?

▪ Zero natural decay rate but policy makers could make this –ve through clean-up expenditure