Pollution control: Target(II)

Question 1

What are the majority of important pollution problems associated with? And why can policy makers not do anything about it?

Answer 1

Stock pollutants

While the damage is associated with the pollution stock, that stock is
outside the direct control of policy makers. At best environmental protection agencies are able to control the rate of emission flows.

Question 2

Why should we think about stock pollutants intertemporal (across time)

Answer 2

Spoiler alert: An efficient pollution control program will need to take
account of the trajectory of emissions over time, rather than just at a
single point in time.

Because:

We now consider the case of stock pollutants that have a relatively
long active (i.e. damaging) lifespan but which are uniformly mixing.

Doing so has two implications.
– The uniformly mixing assumption implies that pollutant
concentrations will not differ from place to place, and so the spatial
dimension of emissions control is no longer of direct relevance.
– Persistence of pollution stocks over time means that the
temporal dimension is of central importance.

Question 3

Outline the modelling of stock pollutants

Answer 3

Pollution targets model:

In this case the simplest possible model which deals with intertemporal choices

Damage at time t is determined by the contemporaneous stock size
or concentration of the pollutant in a relevant environmental
medium.

Gross benefits depend on the flow of emissions.

Hence our damage and (gross) benefit functions have the general
forms

Dt = D(At)
Bt = B(Mt)

Question 4

Outline the stock-flow relationship, now with a decay coefficient

Answer 4

A_t+1 - A_t = M_t - alpha*A_t,

where alpha = 1 - a

The parameter alpha is a decay coefficient, and is a proportion that must lie in the interval zero to one.

Question 5

What is a perfectly persistant pollutant?

Answer 5

A pollutant for which alpha = 0 exhibits no decay, and so the second
term on the right-hand side of the stock-flow relationship is zero. This is known as a perfectly persistant pollutant.

Question 6

How can we represent the flow problem from last time?

Answer 6

Fully so for: alpha = 1 , equivalently a = 0 .

Question 7

How can we represent the approximated stock problem from last time?

Answer 7

Approximately so for: Fixed M and low a.

Question 8

What are the key differences between the flow and stock problems?

Answer 8

Whether damages come from M or A.

Question 9

What is an imperfectly persistent pollutant?

Answer 9

More generally, we expect to find 0 < alpha < 1, and denote this as an
imperfectly persistent pollutant.

Here, the pollutant stock decays gradually over time, being converted into
relatively harmless elements or compounds.
– Greenhouse gases provide one example, but with slow or very slow
rates of decay.

Question 10

What level of alpha, would make the pollutant a flow pollutant?

Answer 10

The second limiting case, where alpha = 1, implies instantaneous decay, and so the pollutant can be regarded as a flow rather than a stock pollutant.

Question 11

Outline the stock pollutant with a constant rate of decay

Answer 11

Assume parameter alpha is constant; a constant proportion of the pollution stock decays over any given interval of time. (This may be invalid in practice!)

A_t = Sum a^(i)M_(t-1-i)
= Sum (1-alpha)^(i)M_(t-1-i)

The reason we use a sum, is because we are looking at the level of A_t in different time periods, intertemporal.

Thus, for a stock pollutant with a constant rate of decay,
the current pollution stock is af function of all past emissions,
with exponentially declining weights to emissions that
occurred further back in time.

Question 12

Assume that policy maker aims to maximise discounted net benefits
over some suitable time horizon. What would they look to maximise?

Answer 12

See slide 16 for equation.

Using t = 0 to denote the current period of time, and defining the net
benefits of pollution as gross benefits minus damages (specified
respectively by equations 5.15 and 5.16) the policy maker’s objective is to
select Mt for t = 0 to t = ∞ to maximise.

They want to maximise the amount of flow pollution, the maximizes the benefits.

Question 13

Which kind of analysis are we gonna use for finding efficient pollution targets and policies?

Answer 13

As time periods are linked together through a stock–flow relationship,
efficient pollution targets and policies must be derived from an intertemporal analysis.

A complete description of efficient stock pollution will, therefore,
consist not of a single number for, but a trajectory (or time path) of,
emission levels through time.

In general, this optimal trajectory will be one in which emission levels
vary throughout time.

Question 14

The trajectory will often consist of two phases, before we get to an optimal level.

Answer 14

1. One of these phases is a steady state in which emissions (and
   concentration levels) remain constant indefinitely at some level.
2. The other is an adjustment phase; the trajectory describes a path by
   which emissions (and concentrations) move from current levels to
   their steady-state levels. This adjustment process may be quick, or it may take place over a long period of time.

Question 15

How is the steady-state pollution level defined in chapter 5?

Answer 15

The pollution flow and the pollution stock are each at a constant level.

With an unchanging stock equation 5.17 simplifies to M = alphaA.
– Intuition: For a pollutant that accumulates over time, the pollution stock can only be constant if emission inflows to the stock (M) are equal to the amount of stock which decays each period (alphaA).

A = M / alpha

It then follows that in a steady state, the stock–flow relationship between A and M can be written as A = M/ alpha (5.19)
* In a steady state, if the level of alpha falls, the lager will the pollution stock become for any given level of emissions.

Question 15

In theory what is the optimal pollution in the long run?

Answer 15

Suppose we are in steady state in period 0, but then we temporarily allow the emission of one more unit in period 0 (but only in that period).

The present value of the benefit from doing so will simply be

PVB = dB / dM

The present value of the damage cost of allowing the emission of an extra
unit in period 0 will be

PVD = (dD / dA) * 1 / (r+A)

Thus, in the steady state, the optimal level of pollution must satisfy

   PVD = PVB  => dB / dM = (dD / dA) * 1 / (r+A)   5.20

This is a variant of the familiar marginal condition for efficiency: The
marginal benefit and the marginal cost of the chosen emissions level should be equal.

It can be read as an equality between the immediate or short-term benefit gained from releasing an additional unit of pollution into the environment (benefit of a marginal unit of pollution (the LHS of 5.20)) and the present value of the damage that arises from the marginal unit of pollution (the RHS of 5.20). “Present value” means we’re considering the future damages but expressing them in today’s dollars. This includes impacts like climate change, health problems, loss of biodiversity, and many others, discounted back to their value in the present moment.

• The discount factor 1/(r + ) has the effect of transforming the single period
  damage into its present-value equivalent.

Question 16

What is a shadow price?

Answer 16

At the level of M that satisfies equation 5.20, the value taken by
the expression on each side of the equation is known as the
shadow price of a unit of emission.

Question 17

Rephrase this

“Note that while the damage arising from the marginal emission
takes place today and in future periods, a marginal emission
today has benefits only today, and so the instantaneous value
of the marginal benefit is identical to its present value.”

Also make and intuitive example (party)

Answer 17

So, when we say the “instantaneous value of the marginal benefit is identical to its present value,” we mean that the benefit derived from pollution happens now and doesn’t change or accumulate over time. E.g. the company uses the energy (pollution) to produce electricity today, not tomorrow. It’s a one-time gain. In contrast, the damages from that same pollution spread out over time, requiring us to calculate their total cost in today’s terms to understand the full extent of the impact. E.g. pollution has longterm consequences on climate, biodiversity, health and so on. That’s why we need to discount the damage.

In simpler terms: If you decide to have a party today, the fun you have is immediate and doesn’t increase or change tomorrow or the day after; it’s a one-time benefit. However, if the party causes noise and litter, the annoyance and cleanup might affect you and your neighbors today and could have lingering effects (like upset neighbors or a damaged lawn) that last much longer. To decide if the party is worth it, you’d weigh the immediate fun against not just today’s cleanup but also any longer-term consequences, all considered in today’s terms.

Question 18

Insights from optimum condition 5.20

Other things being equal, the faster is the decay rate, the higher will
be the efficient level of steady-state emissions?

Answer 18

Yes. The greater is the rate of decay, the faster is the decline in the future
damage resulting from an extra unit of emissions today, so the smaller
is the present value of the damage. Hence we can tolerate a higher
level of emissions.

Question 19

Insights from optimum condition 5.20

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

Answer 19

Yes. The greater is the consumption discount rate r, the larger is the discount rate applied to the stock damage term and so the smaller is its present value. A higher discount rate means we attach less weight to damages in the future, and so the emission level can be raised accordingly.

Remember the mathmathical logic behind discount rates.

1 / (r+x)

The higher r, the smaller value of future consumption, pollution or other things discounted.

Question 20

Warning. Do we find the assumption about a constant rate of decay misleading, when we look at the reality?

Answer 20

Yessssss

The optimum condition (5.20) assumes that the pollution stock A
decays at the constant rate no matter how large the pollution stock
is. In effect this assumes that the environment has an “unlimited
carrying capacity”. For many pollutants and receptors this assumption may not hold.
- For example, it may be that the environment loses its capacity to
break down the pollutant when the pollution stock exceeds a critical
level.

Further, this loss of carrying capacity may even be irreversible.

When such threshold effects exist, it is important that the pollution
stock is not allowed to exceed the thresholds.

Question 21

How can you illustrate a threshold effect in the decay rate/pollution stock relationship?

Answer 21

Draw it

See slide 26.

The graph features a horizontal dashed line extending from the left vertical axis, at a certain height, to the right. This suggests a constant rate of decay (α) when the concentration of the pollutant is below a certain threshold.

However, there is a point where the dashed line drops vertically down to the horizontal axis, indicating a sharp decrease in the decay rate to zero. This suggests that once the concentration of the pollutant reaches a certain threshold, the rate of decay suddenly reduces to zero, implying that the pollutant no longer decays beyond this point.

Question 22

How can we represent this figure if there is an irreversibility combined with a threshold effect?

Answer 22

Draw it

se slide 28

Same explanation as before, but with an extension:

The pollutant is “irreversible” after this threshold; it will persist in the environment without diminishing.

The red arrows along the horizontal axis indicate that this process is a one-way street—once you reach the threshold where decay stops, you cannot go back to a state where the pollutant decays again. This is what is meant by “irreversibility.”

The graph demonstrates a concept often discussed in environmental science and economics: there can be a point of pollution concentration beyond which the damage cannot be reversed, known as a “tipping point.” Before this point, the pollutant is being decayed or mitigated at a constant rate, but beyond this tipping point, the environment can no longer mitigate the pollutant effectively, leading to potentially permanent damage.

Question 23

Question from student in relation to The Double Dividend hypothesis:
Why is the labor supply reduced?

Answer 23

We made the following statement: “The tax interaction effect” (environmental tax on a polluting good):

1) The higher consumer prices of polluting goods 2) reduce labor supply,
3) thereby reducing the revenue from the income tax and other
consumption taxes => 5) welfare decreases 4) as the government has to
raise some taxes to make up for the lost revenue.

Explenation:
1) Enviromental tax on polluting good makes the production cost more expensive. The firms send the cost further to the consumer, why the consumer prices for the this polluting good has increased. Maybe the firm take some of the cost themselves.
2) Reason for reduced labor supply: Distortions in the labor market, e.g. sectors can be extra affected by the enviromental tax, increasing the production prices. Therefor they maybe need to cut wages or employees. Empirical support argue the wage elasticity is positive, meaning when wages increase people want to work more, not less. Also people without a job has a high incentive to get a job. In conclusion this support the statement outline above.
3) people work less, then the cake is smaller.
4) to reach the same stable amount, the government has to increase the taxes.
5) Wellfare fall, due to lower wages possibly because of distortions in the labor market and higher income taxes. Assumption