EBF 200
Introduction to Energy and Earth Sciences Economics

 

Dealing With Externalities

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Reading Assignment

For this lesson, please read the section entitled "Public Goods and Why They Pose a Problem for the Market" in Chapter 5 ("Difficult Cases...").

In this lesson, we will describe a real-world use of Coasian policy to deal with an externality and provide an example of how such systems work in general. We will also talk of other methods and why they are less attractive than Coasian methods.

We will now focus on the topic of attempting to reduce the emissions of Sulfur Dioxide (SO2) from power plants and steel mills that consume coal. We mentioned in the last lesson why SO2 emissions are "bad" - they create acid rain, which renders lakes incapable of supporting life. Acid rain also damages buildings, as any of you who have been to Pittsburgh can readily see.

There are three general ways in which SO2 emissions can be reduced. These all involve attempting to move from the private to the socially optimal level of pollution. We should note at this point that the socially optimal level of pollution is not zero, but is the point where the marginal benefit of pollution equals the marginal cost.

You might ask, what is the social benefit of pollution? Well, pollution itself does not have any benefit, except perhaps to companies selling pollution-control equipment and to class-action lawyers. However, we need to remember that it is merely a by-product of an industrial process that creates something we find to be very useful: electricity. Without burning coal, electricity would be much more expensive in the US. Therefore, when we consider the benefits of using electricity, we have to consider this as a benefit that comes from emitting SO2 into the environment.

As mentioned above, there are three general ways we can proceed:

1) Command and Control. This is exactly what it sounds like: governments issue commands in order to control the amount of pollution. If emitters fail to comply with these rules, they face criminal sanction and the possibility of fines and imprisonment.

2) Coasian permit trading. This is a system whereby the government delegates to itself the property right to emitting sulfur dioxide and then sells (or gives away) these property rights. A company needs a permit for every ton of SO2 they wish to emit into the environment, and the quantity of those permits is controlled by the government. This method has the benefit of allowing firms to trade permits so that firms that have a high cost of emitting can buy rights from firms that can reduce pollution at lower costs, which means that as a society we can have the same amount of pollution reduction as in the command and control method, but at a lower cost to society. This will be illustrated a little later. This method is called "cap and trade," because the government will set a cap on the amount of SO2 that can be emitted each year and then allow emitters to trade amongst themselves to obtain the socially efficient result.

3) Pigouvian taxes. These are taxes on pollutants, and got their name from the first person to propose them, a British economist called Arthur Pigou. This method contrasts with cap and trade in this way: with a Coasian system, we are setting the socially optimal quantity, and then allowing the price to find the market equilibrium. In theory, this is equivalent to the "social cost," the difference between the two supply curves in our social versus private equilibrium diagram. The good thing is, we do not have to try to figure out this cost, which can be extremely difficult to discover, but, instead, we can simply let the market find the level. A Pigouvian tax moves the equilibrium from the private to the social one, but it does so by setting a fixed cost (the tax), and then allowing quantity to adjust in the marketplace. The problem with this system is that it requires more information. If the tax is too high, the quantity emitted will move to a quantity below the socially optimal value, which means that some wealth is destroyed. If the tax is too low, then we will not reduce pollution by very much, and we will be producing at a level above the socially optimal amount, which is also not a wealth maximizing situation.

So, in theory, all three methods get the same results, but, in reality, the cap-and-trade method can be shown to work better than either alternative.

The first attempt to limit sulfur emissions, the Clean Air Act of 1970, used command and control regulation, and relied upon government to specify and administer all aspects of pollution control (i.e., micro-management). The Environmental Protection Agency (the EPA), the government agency charged with administering environmental policy, would determine performance standards applicable to each pollution source. Typically, standards were set in rates: quantity of pollution emitted per hour, or per unit-of-energy, etc. Sources then would have to find a way to meet these fixed, general standards. Each could choose one of two methods of compliance:

  1. Install pollution control equipment
  2. Reduce the number of hours of production (in the extreme, shutting down completely)

Both of these methods of compliance are very expensive. Old plants have high emission rates (because they were designed without pollution control in mind) and need to install A LOT of pollution control equipment to come into compliance. According to the law of diminishing returns, each next unit of pollution reduction costs more than the previous unit. This translates into HUGE costs to old sources, and huge costs for middle-aged sources. Another large cost comes from the fact that most industrial facilities are very valuable to society - in the hundreds of millions of dollars each. Completely abandoning a facility, even if it has been paid for, necessitates construction of a replacement facility. As a result of these high costs, industry would choose to endlessly litigate new environmental policy in the courts rather than comply, and the environment was never very adequately protected. The Clean Air Act of 1970 required all coal-fired plants to install pollution-control devices called "scrubbers," but the legal fight back was great - to this day, 40 years later, the majority of power plants built before 1970 still do not have scrubbers.

The result was that by the end of the 80s, the rates of SO2 emission were still much higher than what was thought to be the socially optimal amount, and acid rain was still a problem. At the urging of economists, the government adopted a different approach, one consistent with the teachings of Coase. In the Clean Air Act Amendments of 1990, Congress adopted a cap and trade program for sulfur dioxide, known as the Title IV program, based on the chapter in the law.

Under Title IV, every year, the EPA would decide how many permits were to be issued. This number shrank every year. The number started at about 17.3 million tons in 1991, and was down to about 9 million tons/year by 2000. The EPA would allot the permits to plants based upon their emissions in some base year, and the firms could either emit SO2 and surrender permits to the government, or it could sell the permit and then release less SO2. This aligns the incentives of the firms with the goals of reducing pollution - it would award firms for innovating and reducing pollution by being able to "sell," and hence benefit from, their pollution control efforts.

The accounting behind this system is very complex, so I will use some simple numerical examples to illustrate how such a system works.

Let us say that there are three firms: Awful Industries (Firm A), Bigbaddirty Inc (Firm B) and the Crud Corporation (Firm C). In the beginning of our problem, there are no pollution laws, and each firm is polluting at their maximum level. For each firm, this is 5 tons per hour. The air is getting terribly polluted, and the government hires a group of biologists, who say that there should never be more than 9 tons per hour emitted.

1. Using Command and Control

Firstly, the government decides to limit each firm to 3 tons each. The following are the firm profits at each level of pollution:

Table 7.5: Total Firm Profits at Various Pollution Levels
Units of pollution 0 1 2 3 4 5
Firm A 0 100 190 270 340 400
Firm B 0 150 270 360 420 450
Firm C 0 160 240 280 300 310

From Table 7.5, we can see that each firm makes the maximum profit at 5 units of pollution, so that is what they will do if there are no controls - emit the maximum amount. This is because reducing pollution costs money: firms have to spend to clean up their waste, and they are not able to produce as much stuff. Another way to look at this is to reverse Table 7.5 and look at the TOTAL COSTS of reducing pollution (this is also called “Pollution Abatement”):

Table 7.6: Total Costs of Reducing Pollution
Units of pollution 0 1 2 3 4 5
Firm A 400 300 210 130 60 0
Firm B 450 300 180 90 30 0
Firm C 310 150 70 30 10 0

Table 7.6 tells us how much it would cost to move from the uncontrolled situation to a certain amount. For example, if Firm A had to move to 1 unit, they would have to give up 300 in profit.

So, what are the costs to the firms if they are each forced to emit only 3 tons each? Well, we just add up the total costs in the column headed by “3 units.” The total loss is 130 + 90 + 30 = 250. Remember this number.

This is the same as the government giving 3 pollution permits to each firm, and telling the firms that they may not trade the permits amongst them.

2. Cap-and-Trade

What if the government gives three permits to each firm, and says that the firms can trade them? Well, Firm A will make 70 more in profits if they can pollute 4 units. Firm C will make 40 less units of profit if they go to two units. So, we have a potential trade. Firm A is willing to pay up to 70 for an additional permit, and Firm C is willing to accept more than 40 for a permit. Since we can find a mutually beneficial amount between 40 and 70, then the trade will happen. This means that Firm A will now emit 4 units (because it has 4 permits) and Firm C will emit 2, as it now only has 2 permits.

The result is that we will have Firm A polluting 4, at a total cost of 60, Firm B will still pollute 3, at a total cost of 90, and Firm C will pollute only 2 units at a cost of 70. So, the total cost for all three firms is now 60 + 90 + 70 = 220.

So, now we have the same amount of pollution, but the total cost to the firms is reduced from 250 to 220. This benefits society: either the firms can make more profit, or they can lower their prices. Both of these things are good for the economy.

There is one more benefit to having a permit system: if a person wants to reduce pollution, all they have to do is buy a permit and then not use it. This reduces the total amount of pollution in the world.

In this market, permits will trade for between 40 and 70. If we have a larger market, with more firms, we can expect more trades and we can expect the equilibrium price for permits to converge to a single value. This value will be the value of the Pigouvian tax we need to have the same result, but, as I mentioned above, this would likely require quite a bit more trial-and-error on behalf of the tax-setter. Simply setting a cap and letting the price equilibrate based upon firms trading in their own best interest is a more effective way to reduce pollution.

A Market Approach to Dealing with Externalities

Let's assume 5 firms, and no environmental regulation. Each firm pollutes 4 "units" (say tons) of "guck," an environmental bad. Abatement is costly.

Scenario 1) The Environmental Protection Agency (EPA) announces each firm must reduce pollution 2 units. So, each firm gets a non-tradeable right to pollute 2 units.

Scenario 2) EPA gives each firm tradeable rights to pollute 2 units (in our example, 10 in all).

So how much does it cost firms?

A small detour:

MC(X)=TC(X)-TC(X+1);

But…let Z=the “no regulation” state. This implies TC(Z)=0.

So, MC(Z-1)=TC(Z-1)+TC(Z)=TC(Z-1);

TC(Z-1)=MC(Z-1)

MC(Z-2)=TC(Z-2)-TC(Z-1)=TC(Z-2)-MC(Z-1);

TC(Z-2)=MC(Z-2)+MC(Z-1);

We can show that:

TC(Z-3)=MC(Z-3)+MC(Z-2)+MC(Z-1) and so on.

This all implies that we can calculate total costs by simply adding up the marginal costs from right to left.

Back to the problem…

Given the data below, calculate the marginal cost of pollution abatement.

Table 7.7 Cost of Pollution Abatement
Amount of Firm 1 Pollution 0 1 2 3 4 5
TC of Abatement 35 26 18 11 5 0
Amount of Firm 2 Pollution 0 1 2 3 4 5
TC of Abatement 60 44 30 18 8 0

Click here for answer

Answer

Table 7.7b Cost of Pollution Abatement
Amount of Firm 1 Pollution 0 1 2 3 4 5
TC of Abatement 35 26 18 11 5 0
MC of Abatement 9 8 7 6 5 0
Amount of Firm 2 Pollution 0 1 2 3 4 5
TC of Abatement 60 44 30 18 8 0
MC of Abatement 16 14 12 10 8 -

Now, the EPA decides that each firm must reduce its pollution to 2. How much will this cost?

Reading off the total cost tables, we get 18+30=48.

Allowing Trading Between Firms

Or: The EPA gives each firm 2 pollution “credits,” which are tradeable. To pollute x units, each firm must own x credits. Since Firm 2 is the “high cost” firm, we’ll ask: Should Firm 2 buy a credit from Firm 1?

Firm 2's marginal cost of abatement (going from 2 to 3 units of pollution) is 12. Firm 1's marginal cost of abatement (going from 2 to 1) is 8. So, if Firm 1 sells a credit to Firm 2, abatement costs will go down by 4.

Check: For Firm 1, if x=1, total cost = 26

For Firm 2, if x=3, total cost = 18, 18+26=44. Cost went down by 4.

What price should they trade at? It costs Firm 1 8 “units” to abate one more unit, so that is the lowest they should accept. Firm 2 gains 12, so that is the most they should be willing to pay. So, the price of this credit will be in the range [8, 12].

Should Firm 2 buy a second credit from Firm 1? Firm 2's marginal cost of abatement (going from 4 to 3) is 10. Firm 1's marginal cost of abatement (going from 1 to 0) is 9. So, they should trade, reducing total costs by 1 (you’ll want to check this), at a price in the range [9,10].

Market Trading of Permits to Pollute

Let's assume 5 firms, and no environmental regulation. Each firm pollutes 4 "units" (say tons) of "guck," an environmental bad. Abatement is costly.

Scenario 1) EPA announces each firm must reduce pollution 2 units. So, each firm gets a non-tradeable right to pollute 2 units.

Scenario 2) EPA gives each firm tradeable rights to pollute 2 units (in our example, 10 in all).

So, how much does it cost firms? Assume 5 firms, as in the next table.

Marginal Cost of Pollution

Table 7.8 Amount of Pollution
Firm 0 1 2 3
1 4 3 2 1
2 8 6.5 4 2
3 6 3.5 2.5 0.5
4 12 9 6 2.5
5 8.5 7 5.5 3.5

From this, we need to calculate a total cost table. To do this, just add up the marginal costs from right to left. Thus, the total cost for firm 1 of 3 units of emission is 1. The total cost of 2 emissions is 1+2=3. The total cost of 1 emission is 1+2+6=6, and so on.

This results in a total cost table:

Table 7.9 Amount of Pollution
Firm 0 1 2 3 4
1 10 6 3 1 0
2 20.5 12.5 6 2 0
3 12.5 6.5 3 0.5 0
4 29.5 17.5 8.5 2.5 0
5 24.5 16 9 3.5 0

So, the total cost of Scenario 1 (no trading, 2 units guck emissions per firm) is the sum of the total costs at 2 units of pollution:

3 + 6 + 3 + 8.5 + 9 = 29.5

The Benefits of Allowing Trading

Now, let’s go to scenario 2, where trading is allowed:

We need to derive supply and demand curves for permits.

What does our supply curve look like? Q=10. There is always a supply of 10 in the market.

What does the demand curve look like? Simply rank marginal pollution control costs from high to low:

Table 7.10 Marginal Pollution Control Costs Ranking
Number Marginal Cost
1 12
2 9
3 8.5
4 8
5 7
6 6.5
7 6
8 6
9 5.5
10 4
11 4
12 3.5
13 3.5
14 3
15 2.5
16 2.5
17 2
18 2
19 1
20 0.5

With 10 permits available, the market price will be the average of the 10th and the 11th value. Here, that is 4.

The top 10 demanders will get the pollution units—at a market price of 4.

How much will each firm make from the market?

Table 7.11 Firm 1:
Emissions 0 1 2 3
MC 4 3 2 1

If this firm could not trade, it would have costs = 3.

With a market price of 4, it sells 1 (or 2) pollution rights, has abatement costs 1 + 2 + 3 (+4) = 6 (10) and sells 1 or 2, revenues 4 (8)

TC = 6 – 4 (= 10 – 8) = 2. So, Firm 1 makes 1 off the market.

How much does Firm 2 make?

Table 7.12 Firm 2:
Emissions 0 1 2 3
MC 8 6.5 4 2

Before trading cost = 6. After trading cost = 6

Exercise:


Calculate the net wealth increase (across all 5 firms) created by the market.

A Practice Question

You are the incredibly greedy owner of Guck, Unlimited, a major polluter. Currently, in the “free” state of the world, you emit 5 units of pollution. Your costs of pollution abatement are below:

A) Fill in the marginal cost portion of the table below (4 points).

Table 7.13 Units of Pollution
Units of Pollution 0 1 2 3 4 5
Total Cost 119 72 44 24 10 0
Marginal Cost ? ? ? ? ? ?

B) Explain what Guck’s net costs (costs of abatement plus the costs of permits bought, minus the cost of permits sold) would be if

  1. Pollution permits cost $30/unit, and you must buy any you want from the market; you are allocated none;
  2. Pollution permits cost $40/unit on the market, and the EPA allocates you 4.

Click here for answer

Answer

A)

Table 7.13b Units of Pollution
Units of Pollution 0 1 2 3 4 5
Total Abatement Cost 119 72 44 24 10 0
Marginal Cost 47 28 20 14 10 ?

B) Explain what Guck’s net costs (costs of abatement plus the costs of permits bought, minus the cost of permits sold) would be if

  1. Pollution permits cost $30/unit, and you must buy any you want from the market; you are allocated none;

One value is greater than $30, so you buy one permit at a cost of 30. You therefore have 1 unit of pollution, with total abatement costs of 72. Your total costs are 30+72=102.

  1. Pollution permits cost $40/unit on the market, and the EPA allocates you 4.

Again, you only have one value greater than 40. So you pay $40 for a permit, and have $72 in abatement costs, for a cost of $112. HOWEVER, you have 3 permits remaining, which can sell for 40*3=$120. So your total costs are 112-120=-$8. In other words, your profits went up by 8!

A Problem for You

There are four firms in an industry, with total costs of pollution abatement as described below. The government decides that to pollute, a firm requires one permit per unit of pollution. The government also will auction off 7 permits. Given this, what is the market price of permits, and which firms will buy how many permits?

Table 7.14 TC-Amount of Pollution
Firm # 0 1 2 3 4
1 580 430 290 160 70
2 770 470 250 100 30
3 535 285 150 70 10
4 630 450 290 150 50

Click here for answer

1st: Calculate the marginal costs:MC(X)=TC(X)-TC(X+1)

For example, for firm 1 MC(3)=TC(3)-TC(4)=160-70=90.

2nd: Put the MCs in order from high to low.


Table 7.14b MC Amount of Pollution
Firm # 0 1 2 3 4
1 150 140 130 90 70
2 300 220 150 70 30
3 250 135 80 60 10
4 180 160 140 100 50

There are 7 permits. So, take the midpoint of the 7th and 8th values (here, 145). Now, recover the MC table and allocate the permits to all.

MCs>145

Table 7.14c # and MC
# MC
1 300
2 250
3 220
4 180
5 160
6 150
7 150
8 140
9 140
10 135
11 130
12 100
13 90
14 80
15 70
16 70
17 60
18 50
19 30
20 10

Find where MC>145.

Then calculate costs per firm.

Firm 1 buys 1 permit, at a cost of 145. Its abatement costs at 1 are 430, for a total cost of 575.

Firm 2 buys 3 permits, at a cost of 145*3=435. Its abatement costs at 3 are 100, for a total cost of 535.

Firm 3 buys 1 at 145. Its abatement costs at 1 are 285, for a total of 430.

Firm 4 buys 2 permits at 145. Its abatement cost at 2 are 290, for a total cost of 580.

Total costs are 575+535+430+580=2120.

Another Practice Question

There are four firms in an industry, with total costs of pollution abatement as described to the right. The government decides that to pollute, a firm requires one permit per unit of pollution. The government also will auction off 7 permits.

Given this, what is the market price of permits, and which firms will buy how many permits? What is the total cost of abatement?

Table 7.15 Amount of Pollution
Firm # 0 1 2 3 4
1 56 36 20 8 0
2 62 41 24 9 0
3 45 30 17 7 0
5 60 40 24 10 0

How do you do this problem?

  1. Calculate MCs.
  2. Rank order MCs from high to low.
  3. To find the market price, take a number halfway between the 7th and 8th MC.
  4. Allocate the permits to the firms with the 7 highest MCs.
  5. Figure out the total cost of abatement by firm.
  6. Add up TCs across all firms.