In this lesson, we reach the end of the topic of market failures. The last market failure mechanism for us to address, which is perhaps the most important to the topics of energy and sustainability, is the market failure known as an "externality," which is a violation of the assumption of free entry and exit into a market. The most important type of externality is the existence of air and water pollution. In this lesson, we will take a look at how we can use economics methods to "internalize" externalities. We will also speak of goods that are under-provided or over-exploited in an uncontrolled marketplace due to the absence of well-defined property rights.
By the end of this lesson, you should be able to:
This lesson will take us one week to complete. Please refer to Canvas for specific time frames and due dates. There are a number of required activities in this lesson. The chart below provides an overview of those activities that must be submitted for this lesson. For assignment details, refer to the lesson page noted.
Requirements | Submitting Your Work |
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Read Chapter 5 in Gwartney et al., OR Chapter 12 in Greenlaw et al. Plus other assigned readings linked to in the lesson text |
Not submitted |
Lesson Quiz and Homework | Submitted in Canvas |
For this lesson, please read the sections entitled "Externalities - A Failure to Account for All Costs and Benefits," "External Costs," and "External Benefits" in Gwartney et al. Chapter 5 - "Difficult Cases for the Market." Or read Greenlaw et al. Chapter 12
“Externalities” are the last type of market failure we will talk about. They are a form of free entry/exit market failure. When a trade is made, there are normally two people affected by the trade: the buyer and the seller. But, sometimes, a trade or some other piece of economic activity has an effect on people who are not directly involved. Because these effects are on a person who is external to (or outside of) the trade, we call them externalities. Externalities can be either positive or negative; that is, the economic activity of one person or group can have either a positive or negative "spill-over" onto other people.
An externality is when the welfare (utility) of a person depends not only on his activities, but also on the activities of an “outside” person. An externality exists whenever an individual or firm undertakes an action that impacts another individual or firm for which the latter is not compensated (a negative externality, e.g., pollution), or for which the latter does not pay (a positive externality, e.g., voluntary vaccination). This occurs when property rights are NOT well-defined. When externality exists, the competitive market does not achieve the efficient allocation of resources in society (i.e. the market fails) because no market exists in which the affected party can express his/her preferences for the externality. The presence of externalities means we are ‘missing a market’ for the externality. Because externalities are often co-produced with other market transacted goods (e.g., emissions and electricity) this distorts the markets of the transacted goods as well as the markets connected to them.
This is the most common type of externality, and the one that will be addressed most frequently in this course and in real life. It can take many guises. For example, think about a case where a village makes its living from catching and selling fish from a river. Now, if a chemical plant opens 25 miles upriver and decides to discharge chemical waste into the river, then the fish all die and the people in the village lose their ability to make a living. In this case, the chemical plant (and, by extension, its customers) is not being forced to cover all of the costs of its operation. If it was required to dispose of hazardous waste in some way that did not involve dumping it into a river, then it would be faced with higher costs, and if it has higher costs, then the price of its products will be higher. If the price is higher, then consumers will purchase less.
Air pollution is one of the key externalities that has been addressed in the US over the past 40 years. And coal has been the largest source of some of the worst air pollution. In 1998, coal power plants were responsible for:
In the Industrial Heartland of the US - places like Michigan, Ohio, and Pennsylvania - a lot of industrial facilities have burned coal over the past 150 years. The coal that is burned in these power plants, steel mills, and factories contains sulfur. When sulfur burns, it forms a compound called Sulfur Dioxide, SO2. The SO2 is carried into the environment by the exhaust stacks connected to the boilers of these plants. When the SO2 mixes with water vapor in clouds, it forms Sulfuric Acid, H2SO4, and eventually, this falls as part of rain. This is what is known as Acid Rain, and was responsible for lowering the pH of many lakes and rivers in the north-eastern part of the United States to the point where these bodies of water were unable to sustain any life. Another form of air pollution comes from the burning of gasoline in motor vehicles, which gives us several undesirable compounds: unburned hydrocarbons and partially reacted oxygen, in a form called ozone, which, in the presence of sunlight, creates photochemical smog, which can be severely damaging to the lungs. We also get particulate emissions - another word for soot - which consists of very fine particles of partially burned hydrocarbon that float in the air and get inhaled by people, and we also get Carbon Monoxide, a poisonous gas that can cause nausea at low concentrations and death at not so high concentrations. These emissions have all been the target of environmental legislation over the past 40 years, and we will talk at length later of attempts to regulate them.
A common form of water pollution is runoff of fertilizer from fields. In the central part of the US, known as the "Bread basket" (think of places like Illinois, Iowa, Kansas, and so on), farmers use a great amount of chemical fertilizer to ensure large crops of corn and soybeans. Since fertilizer is relatively cheap, farmers have an incentive to over-apply, as opposed to under-applying it. Any fertilizer that is not absorbed by the plants runs off with rainfall into rivers, and these rivers all end up flowing into the Mississippi River. As you go downstream, the concentration of the Mississippi river increases. The result is that in the Gulf of Mexico, just off the coat of Louisiana, there is a large "dead zone' several hundred square miles in size which is caused by the excess fertilizer in the water. This fertilizer accelerates the growth of algae in the water, and the algae consumes all of the oxygen in the water, meaning that nothing else can live in the water. One of the reasons that the damage from the recent oil spill in the Gulf was not larger was that it occurred in this "dead zone," so there was not a lot of marine life to kill to begin with. This situation creates a benefit for everybody who consumes corn or soybeans - which is, basically, all of us, in the form of cheap food, but it has a significantly negative effect on the biodiversity of the Gulf of Mexico, with secondary effects that are scarcely understood by humans.
This is an example of a positive externality: bee keepers take part in a market for honey; they raise and keep bees in order to harvest honey and sell it to the public. In the process of creating honey, bees fly around and pollinate plants, which enables them to grow. This is very beneficial to people who grow flowers and vegetables for a living. Without bees, these vegetable or flower growers would have to manually pollinate their plants - a very tedious and labor intensive process, or develop hybrid plants that are self-pollinating. These are both costly propositions. Indeed, these businesses rely upon the presence of bees to enable their business models to work - without them, their products would be more expensive, and thus there would be less consumed. So, the presence of bees to pollinate commercial plants is a positive externality that arises from the presence of honey farmers.
Pollution does not simply refer to dirty air or water, but it also refers to other bespoilments of the environment, and one of these is noise pollution. Noise pollution can come from a variety of sources: highways, airports, factories, construction sites, nightclubs, railroads. (I live close to a railway level crossing, and the sound of sirens and horns as the trains pass the crossing several times a day can be very annoying. Fortunately, one grows accustomed to this noise, and after a while, you don't really hear it.) It is basically another by-product of economic activity, and if the noise was forced to be reduced in some way, then the firms generating it would have one of two choices: reduce the amount of economic activity (this is common, such as airports being forced to be closed overnight), or install expensive equipment to reduce the amount of noise emitted. Once again, this has the effect of raising costs, and the raising of costs means that the equilibrium price is higher, and there will be less consumed. Sometimes the economic activity gets shut down completely - for example, a lot of bars and clubs in New York City have been forced to close because the buildings they occupy have become residential areas, and the clubs get fined for excessive noise so frequently that they are unable to continue doing business.
There can be positive and negative externalities, but since positive externalities do not present a large economic problem, economists concentrate on negative ones - positive externalities do not really present much of a market failure issue.
The general issue here is one of costs: there are costs that are borne by the participants in the economic transaction, and then there are costs that are borne by non-participants - the external costs. The costs that the participants bear - the costs to the seller that are transferred to the buyer via the price mechanism - are what we call "private" costs. In an ideal world, all economic costs will be private - they will be all borne by the people who derive utility from the transaction. However, in reality, there are many cases where there are some costs that are transferred to non-participants - such as fisheries destroyed by acid rain, or the ill-health that comes from breathing dirty air, or the problems of trying to sleep near noisy factories or railroads. These costs, which are not carried by the manufacturer or purchaser of the goods in question, are what we call "social costs," because they are borne by society. They are illustrated in the following supply and demand diagram:
In the above diagram, we have the "private" equilibrium (Q1, P1), which is the intersection of marginal private costs (MC) or supply curve (for example marginal cost of producing each kWh of electricity) and market demand. We also have the "social" equilibrium (Q2, P2), which is the intersection between Social Marginal Cost and demand curve. Social Marginal Cost is the sum of marginal private plus Marginal External Cost (Social Cost). We can define the Marginal External Cost (MEC) as for example the additional external cost from each additional kWh of electricity that is produced. We can assume the Social Marginal Cost a line parallel to the marginal private costs but above that, because it bears the social cost (for example cost of harm to the people).
The difference between these two equilibria comes from the upward shift of the supply curve when we include the social costs, which are costs that are paid by society in general, or by people "external" to the transaction, versus the private supply curve, which is the one that contains all the private costs. Therefore, "social" equilibrium would be at higher price and lower quantity. It should be clear that the true social optimum is not (Q1, P1), but instead (Q2, P2) once we account for the costs of the negative externality on society. Note that the competitive equilibrium leads to too much pollution being produced and less total wealth. If we ignored external costs from producing electricity from coal and consumed at (Q1, P1), we would obtain gains in consumer and producer surplus equal to the green trapezoid, however we also incur marginal external costs equal to the purple parallelogram. So, society experiences a wealth loss equal to the blue triangle.
I may be over-simplifying things here, but, basically, the entire field of environmental economics is concerned with trying to shift the equilibrium from the private one, (Q1, P1), to what we call the "socially optimal" equilibrium, (Q2, P2). This is often referred to as "internalizing" an externality.
In the next lesson, we will discuss methods for performing this shift, how these methods are implemented, and how effective they are.
When we talk of one person's actions affecting another person negatively, we sometimes hear about something called a "fiduciary externality." This can be boiled down to the following: if one person buys a good, they are moving the demand curve outwards. This act of moving the demand curve outwards will result in movement of the equilibrium to a point where the price will be higher than it would be without that person buying. Put another way, if I buy a good, you cannot buy it, and if you want to buy it, you may have to pay a higher price. This is most obvious in an auction scenario. Just last night, I was watching an auction for exotic cars, and, in one case, there were two bidders for a certain vehicle. Each person kept increasing their bid, that is, causing the other person to pay more. This is not a market failure. Another example could be travel at Thanksgiving: because more people want to fly, and because the number of airplanes is finite, fares tend to increase over Thanksgiving. Similarly, more people want to drive over this period, and thus roads are more congested (and thus, the opportunity cost of using them increases). These are all situations where increased demand raises prices, so that any one person is adversely affected by everybody else's economic choices, but this is not an externality in the sense that it is not a market failure - it is merely a dynamic realignment of the market equilibrium as a response to a temporary change in demand, much like the fact that roses are more expensive on February 14th than they are on February 21st, gasoline is more expensive around Memorial Day than around Columbus Day (ceteris paribus), and hotel rooms are a lot more expensive at Rehoboth beach, DE in July than in November. I reiterate: these are not market failures, except in cases where market power comes into play, but that is a separate issue.
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 previously mentioned 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. This approach is simply to require that all firms employ some abatement or emissions control technology or equipment (think “scrubbers”—devices that one can attach to the end of a smokestack to pull out bad emissions from the stack). If emitters fail to comply with these rules, they face criminal sanction and the possibility of fines and imprisonment.
Command and Control approach may involve some distortions:
Thus Command and Control is unlikely to be the most efficient solution.
2) Pigouvian taxes. These are taxes on pollutants, and got their name from the first person to propose them, a British economist called Arthur Pigou [2]. 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.
3) 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. Cap and trade contrasts with Pigouvian tax method 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. Cap and trade method seeks to creates a market for externalities. This a possible solution to the missing market problem of externalities. Once we create a market for the externality, it is no longer external to the market. Hence we say we have “internalized the externality.”
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:
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.
Firstly, the government decides to limit each firm to 3 tons each. The following are the firm profits at each level of pollution:
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 7.1, 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 7.1 and look at the TOTAL COSTS of reducing pollution (this is also called “Pollution Abatement”):
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 7.2 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.
In order to calculate the numbers in table 7.2, we can start from the last column and move to the left. The last column to the right is when firms make no effort in reducing units of pollution. In that case, the total cost of pollution reduction is zero. Then, we move to the next column, where firms reduce only one unit of pollution (producing 4 units of pollution each). Total cost of reducing only one unit of pollution can be calculated as: (total profit at 5 unit of pollution) – (total profit at 4 unit of pollution). The next column (moving to the left) is when each firm produces only 3 unites of pollution (removing 2 units). We can calculate the total cost of producing only 3 unites of pollution as: (total profit at 5 unit of pollution) – (total profit at 3 unit of pollution). And if we continue this method to get to the first column, we will have Total cost of producing zero unit of pollution = (total profit at 5 unit of pollution) – (total profit at 0 unit of pollution).
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 . 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.
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 .
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.
Here is a story about two guys sharing an apartment. We’ll call them Bert and Ernie. It turns out that Bert is a big fan of Megadeth, and can't get enough of their music. However, Ernie does not like this music so much. Ernie likes quiet. So, we have a bit of a problem: two people sharing the same apartment, one who likes loud, raucous, heavy metal, and one who cherishes peace and quiet. Is there a solution? This being an economics course, we are inclined to ask, is there some application of “economics” that would allow us to define just how much music can be played and keep both people happy? Is there some way we can "optimize the social wealth" in the apartment, some way to maximize happiness in the entire in-apartment community, which consists of Bert and Ernie. (We'll not worry about any externality effects the music might have on the neighbors for now.)
Well, in economics we are fond of stating things, especially utility and happiness, in terms of money, if only for the ease of accounting and measurement it allows us, so we have to define Bert and Ernie’s “happiness” in numbers. These numbers represent happiness in money terms. Let us suppose that the happiness for between zero and 5 songs is given on the following table:
Number of songs played | Bert's Happiness | Ernie's Happiness |
---|---|---|
0 | 0 | 0 |
1 | 10 | -2 |
2 | 18 | -6 |
3 | 24 | -13 |
4 | 28 | -20 |
5 | 30 | -32 |
The above table contains the "total" amount of happiness for each number of songs. As you can see, the more songs played, the happier Bert gets and the more unhappy Ernie gets. We can assume, for simplicity, that all of the "happiness" numbers are denominated in dollars.
What is the “best” number of songs? Well, we want to know at which number total social happiness is maximized. Since our society here consists of two people, it's pretty easy to do - we add together everybody’s happiness and find out what the highest total is for everybody added up:
Number of songs played | Bert's Happiness | Ernie's Happiness | Total Happiness |
---|---|---|---|
0 | 0 | 0 | 0 |
1 | 10 | -2 | 8 |
2 | 18 | -6 | 12 |
3 | 24 | -13 | 11 |
4 | 28 | -20 | 8 |
5 | 30 | -32 | -2 |
So it appears that 2 is the “best” number of songs played. It is the “socially optimal” amount.
Now, how do we get to this amount?
Let us assume that this apartment belongs to Bert, and Ernie is his guest. So Bert has the “property right” to play music. Since he has the right, and he is happiest when playing 5 songs, then this is how much he will play in the beginning.
This being economics and all, Ernie decides that maybe he can buy a little bit of peace and quiet. So, he offers Bert some money to go from 5 songs to 4. If we go to 4, Ernie's happiness increases from -32 to -20, so he is 12 dollars better off. So, he would be willing to offer up to 12 for one less song. If we go from 5 to 4, Bert's happiness decreases from 30 to 28. He will be giving up 2 dollars of happiness to listen to one less song. So, if he is being offered more than \$2 to not play the 5th song, he should accept if he is a rational utility maximizer, and, of course, we assume that he is. For this drop in music, he must gain back at least \$2 to be better off. So, we will have a trade. Ernie will pay less than 12, but more than 2, to go from 5 songs to 4. Both guys are happy with between 2 and 12 dollars being exchanged for one less song.
We can repeat the same thing for 4 to 3 songs and 3 to 2 songs.:
From 5 to 4 songs, the payment is between \$2 and \$12
To go from 4 songs to 3 a payment of between \$4 and \$7 will satisfy both Bert and Ernie.
Now, if we have negotiated a total of three songs, and Ernie wants to go down to 2, he will offer up to 7, and Bert will accept anything over 6.
So, to date, we have had three opportunities to make trades where both people are better off - Bert is willing to give up music if he is compensated more than the happiness he is losing from not hearing music, and Ernie is willing to pay if he pays less than the amount of happiness he gains from each less song. These trades are mutually beneficial, and are "wealth generating" - both guys are better off if these "trades" are made.
So, what about going from 2 to 1 song? Well, to do this, Bert needs to get at least \$8, because that's how much value he places on the second song. However, Ernie is only willing to offer 4, since that is how much he values the extra silence. Since there is no number that is above 8 AND below 4, this trade will not be made. We will stop at 2. So, if we add up the trades, we can say that:
“We will go from 5 songs to 2 for an exchange of between \$12 and \$26.”
Note that we stop at 2 songs, which is the “socially optimal” amount.
OK, now what if we assume that the opposite is true: that Ernie owns the flat, and Bert is his guest. In this case, Bert is happiest with 0 songs. So, that is where we start. In this case, Bert is willing to offer Ernie some money in order to be able to play some music. To go from 0 songs to 1 song, he will offer up to 10. Ernie will be happy with anything more than 2.
So, we will go from 0 to 1 songs with a payment between \$2 and \$10. This will be a mutually beneficial trade, so both are willing to make it.
Now, if we want to go from 1 song to 2 songs, Bert is willing to offer up to \$8, and Ernie is willing to accept anything over \$4. Once again, there is an opportunity for a trade to be made, and it will be made.
So, what about going from 2 to 3 songs? Well, Ernie needs to get at least \$7 to want to do this trade. However, Bert is only willing to offer \$6. Since there is no number that is above 7 AND below 6, this trade will not be made. We will stop at 2. So, if we add up the trades, we can say that:
“We will go from 0 songs to 2 for an exchange of between \$6 and \$18.”
Note that we stop at 2 songs, which is the “socially optimal” amount.
You will notice that we started in two different places - in one case we started with 5 songs being played and, with voluntary exchange, we got to 2. In the other case, we started at 0, but with mutual, wealth-generating trades, we also got to 2. No matter where we start, we end up at the same place, and that place happens to be the socially optimal amount of Megadeth tunes.
OK, so this example seems a little silly. But let’s say I changed the table above to “Tons of Hideous Guck Emitted into Stream by Steel Plant Near Your House,” “Payoff to Steel Plant,” “Payoff to People in Your Town.”
Number of Junior Whoppers | PH Total Value | NR Total Value |
---|---|---|
0 | 0 | 0 |
1 | 9 | 8 |
2 | 16 | 14 |
3 | 21 | 18 |
4 | 24 | 20 |
6 | 25 | 20 |
Paris Hilton and Nicole Ritchie are stuck in a room at the Motel 6 for the next 3 hours. Both are hungry. Paris has a bag of 5 Junior Whoppers, while Nicole has no food. Nicole does have money. Here are their TOTAL value of Junior Whoppers. All values are in \$ million
Assuming that Nicole does not use force, and that neither party acts out of spite (ok, let’s pretend), explain any deal that will take place. Some hints: 1) Calculate marginal values; 2) Remember, don’t have the sum of Junior Whoppers that Paris and Nicole eat exceed 5!
Eric and James are locked in the locker room at the Jordan Center for the next five hours. Eric has 6 “mini-Mac” burgers in a bag. James has money. Each of them has total value of mini-Macs consumed (in shekels, of course) as outlined below.
# of Macs | Eric's Valuation | James's Valuation |
---|---|---|
1 | 40 | 90 |
2 | 70 | 160 |
3 | 95 | 215 |
4 | 116 | 265 |
5 | 131 | 301 |
6 | 140 | 333 |
A: Assume that neither party acts out of spite, and all trades are voluntary, explain what trades will be made.
B: Let us make this a little harder. Assume that every time Eric sells a mini-Mac to James, Eric has to pay 50 shekels to the government authority. How many shekels will the government collect from Eric, and why?
If transactions costs are not “too high,” the market will find the optimal (best, wealth maximizing) solution.
But what constitutes “transactions costs?”
What could be a transactions cost?
This theory was first elaborated by a professor by the name of Ronald Coase [3], who won the Nobel Prize in Economics for his work in 1991. He was the first person to observe that if property rights were well defined, and could be enforced, it was possible for a society to move to the socially optimal equilibrium in cases of pollution, or other externalities. In his honor, this has become known as the "Coase Theorem," and is the foundation of a large part of environmental legislation in the United States.
If you are a little bit more interested in this, you can read the article at the following link, which was written at the time of Coase being awarded the Nobel Prize. It is written at a slightly higher technical level than most of the course content, but is not so obtuse that anyone taking this course should have difficulty reading it.
The most important underlying assumption of using a "Coasian" solution to an externality problem is that property rights need to be well defined and enforceable. That means that we have to know who owns what, and that the people who own those things should be able to enforce their rights, and stop unauthorized users from using resources that they own. After a little bit of thinking, this becomes self-evident. Externalities arise because an economic actor is able to off-load some of his costs onto another person, and if the afflicted person had well-defined and defendable property rights, this would not happen, or at least, it would not persist. Coase was able to home in on the underlying, root problem of externalities, and shows how such problems can be solved.
The Coase Theorem states that assigning property rights for the affected resource will result in the socially optimal quantity being produced.
It DOES NOT MATTER to which party the rights are assigned; to get the socially optimal quantity, all that is required is the clear definition of property rights.
When the producer has the property rights:
When the affected party has the property rights:
This can only work with low transaction costs, which is not the case:
Another issue facing application of the Coase Theorem is that of equity: it assumes that an affected party has the ability to pay a polluter to pollute less, which is not always the case. There is also a social issue here: the notion of paying a person in order to not perform a "bad deed' seems very wrong to many people. Looked at from the other perspective, allowing a company to make a payment to government in order to be able to emit pollution is seen by some people as wrong. This notion is described in the article at the following link, which I would like you to read:
Read the article: It's Immoral to Buy the Right to Pollute [5] by Michael J. Sandel
We will talk a little bit more about this issue later. These are issues that can, and have been, addressed. The difficult part then boils down to the notion of defining property rights. Who has a property right to a river, or to the air, or to peace and quiet?
Let's assume 2 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:
;
But…let Z=the “no regulation” state. This implies .
So, ;
;
;
We can show that:
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.
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 |
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 .
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 ,
For Firm 2, if , , . 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].
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.
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 . The total cost of 1 emission is , and so on.
This results in a total cost table:
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:
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? . 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:
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?
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 and sells 1 or 2, revenues 4 (8)
. So, Firm 1 makes 1 off the market.
How much does Firm 2 make?
Emissions | 0 | 1 | 2 | 3 |
---|---|---|---|---|
MC | 8 | 6.5 | 4 | 2 |
Before trading cost = 6. After trading cost = 6
Calculate the net wealth increase (across all 5 firms) created by the market.
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.
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
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?
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 |
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?
Firm # | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|
1 | 56 | 36 | 20 | 8 | 0 |
2 | 62 | 41 | 24 | 9 | 0 |
3 | 45 | 30 | 17 | 7 | 0 |
4 | 60 | 40 | 24 | 10 | 0 |
In this lesson, we examined the last of our market failures: the externality. We described several different cases where economic costs can be transferred onto people who are not willing participants in an economic transaction.
We then looked at methods of internalizing externalities, or how to move from some private equilibrium to a "socially optimal" equilibrium. As we saw, externalities typically exist because of poorly-defined or non-existent property rights. By instituting a system of property rights, and allowing self-interested exchange between elements of society, we are often able to move to the socially optimal equilibrium at the lowest possible cost to society.
We examined various methods of pollution-abatement schemes, including command-and-control and Coasian Cap-and-Trade schemes. We demonstrated why cap-and-trade systems can be more effective than command and control, and easier to operate and more accurate and effective than Pigouvian tax schemes.
We continued in the theme of poor property rights, looking at public goods and common pools, and we described ways of addressing the problems associated with the undesirable results of these property-rights failures.
You have reached the end of Lesson 7! Double check the list of requirements on the first page of this lesson to make sure you have completed all of the activities listed there.
Links
[1] https://creativecommons.org/licenses/by-nc-sa/4.0/
[2] https://www.econlib.org/library/Enc/bios/Pigou.html
[3] https://www.econlib.org/library/Enc/bios/Coase.html
[4] http://www.daviddfriedman.com/Academic/Coase_World.html
[5] https://www.nytimes.com/1997/12/15/opinion/it-s-immoral-to-buy-the-right-to-pollute.html