Externalities

Underprovision is likely

Resources

Slides:

Content

Introduction to Externalities

Moving from Public Goods to Externalities

For the last part of class, we are jumping to the next set of slides, which cover Lecture 8 on externalities. Most students have been introduced to externalities in their principles of economics class, but it is valuable to give a brief reminder and dive deeper into the mathematics and concepts of externality analysis.

Definition and Conceptualization of Externalities

What exactly is an externality? The precise definition is that an externality occurs when the production or consumption of a good has a positive or negative effect on the value obtained by a firm or household that is external to the decision of how much to produce or consume. However, there is a simpler definition that might better capture the concept: an externality is when value goes to someone external to the decision-making process. External means they were not the decision maker making the original production or consumption choice. The better definition is that there are spillovers in value from one party to another.

The instructor notes that environmental economists may have done themselves a disservice using the word “externality,” because it sounds nerdy and hard to understand. There is a more intuitive word available: “spillover,” which is more accurate and gets the idea across better. Perhaps in future years, the terminology will shift to use “spillover” everywhere, but for now, the terms will be used interchangeably. A spillover exists when there is positive or negative value that spills over to someone who was not the decision maker.

Negative Production Externalities

The classic definition is a negative production externality: when production inflicts spillover costs on someone else. A negative production externality is a cost of production incurred by someone external to the original production decision. The key problem that recurs throughout all externality analysis is that the market’s marginal costs, as represented by the supply curve, do not match the true marginal cost to society.

When a firm produces and pollutes, they have direct costs of production—coal purchases, wages, and other inputs—but they ignore other costs. Polluted air lowers value for nearby residents, and climate damages accrue to everyone. The firm’s costs are less than the true costs to society. The implication of this divergence is that the market, left to its own devices, will over-allocate resources to that good and generate deadweight loss.

Marginal Cost Terminology

To properly analyze externalities, we need different terminology for understanding the various cost concepts. First is MPC: marginal private cost. This is the set of costs felt directly by the producing firm. In contrast, there is MEC: marginal external cost. These are costs imposed by the production of the last unit on external people—people not involved in the production decision. The sum of these two gives us MSC, or marginal social cost: MSC equals MPC plus MEC. This is the total cost to society of producing one more unit.

Graphical Analysis of Negative Externalities

Graphically, this creates a divergence between costs felt by the individual producer and true social costs. For cars, the ordinary supply curve represents marginal private costs that the car manufacturer faces. But the true marginal social costs are higher because of pollution and congestion. For each unit of cars produced, there is additional marginal external cost imposed on society. Adding the marginal private cost and the marginal external cost gives us the marginal social cost curve, which lies above the private supply curve.

To see the deadweight loss created by this externality, we need to consider marginal willingness to pay. The demand curve shows willingness to pay based on private benefits of consuming the good. But consumers do not account for the negative value from additional cars—more congestion, more pollution, more wear on roads. They would prefer a lower quantity, Q*, instead of the market quantity, Q_M. The area labeled ABC represents deadweight loss: areas that should have been provided at positive value but were not because the market overproduced. With negative externalities, we get overproduction relative to the social optimum.

Positive Externalities and Under-Provision

There is also the flip side of externalities: positive externalities. Suppose someone has a nice backyard with 10 acres of wetlands that provide clean water services to people living downstream. It is nice of that person to provide that environmental service, but the value they get from the wetland is less than the value society gets, because the individual does not see the benefits to downstream residents. When someone chooses what is optimal for them individually, they ignore benefits to others, resulting in under-provision of the positive externality.

Connection Between Public Goods and Positive Externalities

It turns out that public goods are basically just positive externalities. We could use the exact same graph to discuss everything we covered about public goods before. It is a little different because here we are dealing with positive rather than negative effects, but nonetheless, next class will talk about the similarities between public good provision and positive externalities. The ultimate externality to address is carbon emissions, which will be the focus of future lectures.

Closing Remarks

Are there any questions on the material covered today? The session has covered public goods, market failures, spillovers, and the foundations of understanding externalities. The next session will build on these concepts and examine how they apply to specific environmental issues, particularly climate change and carbon emissions. Have a good rest of your day and come prepared to go deeper into externality analysis in the next lecture.

Day 2 Content

Introduction and Course Administration

Welcome to this lecture where we will finish our discussion of externalities and then move on to the Prisoner’s Dilemma. Before diving into the content, there are several administrative matters to address.

Mid-Semester Evaluation Feedback

Thank you for taking the mid-semester student evaluation. The results were extremely helpful. One particularly encouraging finding was that almost every single person explicitly wrote that they liked the games and interactive visualizations. This feedback confirms that these teaching methods are landing well, and we will continue using them throughout the course.

Upcoming Schedule and Assignments

Several updates have been made to the class schedule. Assignment 2 is now posted and due on the 18th. As before, this assignment will serve as preparation for the micro quiz that will also be on the 18th. The quiz will be similar but slightly different to what appears on the assignment. This assignment will take longer than the previous one, so students should not start it late.

The assignment will also be made available as a PDF in addition to the web page format. On the topic of PDFs, there is a request from the teaching assistant: please do not submit multiple files to Canvas for an assignment. Some students were submitting multiple pictures, all differently rotated, which makes grading surprisingly difficult. For an easy solution, students can still take phone pictures but should paste them into a Word document and upload that single document. For the best approach, save the document as a PDF before uploading. This will speed up grading and ensure no points are accidentally lost because submissions are hard to read when they are upside down or out of order.

Course Structure and Upcoming Topics

Looking at the overall framing for the course, we are currently working through the micro-foundations section. We finished optimal pollution and then moved to micro failures, which is an extension of micro-foundations applied to the classic three market failures that characterize much of environmental economics: market failures and open access, externalities, and the commons.

After completing these topics, the course will shift gears again. What makes this course unique is that it is not just a hodgepodge of environmental and natural resource tools lumped together, as is traditional in courses of this type. Instead, it ties everything together in a global macroeconomic framework. We had a little bit of that at the beginning with the planetary donut concept, but we quickly lost that perspective when we got into the nitty-gritty of consumer utility optimization and similar topics. All of that foundational work will be revisited as we come back to questions of environmentalism in the whole economy and how indicators like GDP and wealth play out in this context. That is the overall arc of the course.

Guest Lecturer Announcement

On February 23rd, there will be a guest lecturer. Famara Diouf is the executive director of NATCAP Teams, our research center, and he will be leading us through some of his really interesting work. He is literally a negotiator for the country of Gambia at the UNFCCC, which is the hosting convention for all the climate change negotiations that make international news. He literally has to put on a suit and argue over words about what the international agreements will have written in them. This will be a fascinating experience. There will be a couple of other guest lecturers later in the semester, but this will be the first one.

Quiz Distribution and Grading

The quizzes are being handed back. Students did very well overall. If there are any specific grading concerns, students should take them up with the TA, Ryan, who did the actual grading. His email is on the website for scheduling meetings to discuss any concerns.

Externalities: Review and Applications

Recap of Positive Externalities

Moving back into externalities, we went quickly through the introduction last time, so here is a quick review before exploring more specific applications with a new web application.

The example being used is the provision of clean water through having a wetland on your property. This wetland has benefits to you as the landowner—you like the wetland, and it makes your water cleaner. But it also has benefits to people downstream from you. They get cleaner water, but they are external to the decision on whether or not you should keep that wetland or how much of that wetland you should keep. This is a classic externality, specifically a positive externality. Last class covered negative externalities, where the classic example is pollution like sulfur dioxide. Here, we are talking about a positive externality, where the wetland is providing external value—a gain, not a loss.

Graphical Analysis of Positive Externalities

The vertical axis on our graph represents dollars. We are going to try to express the value of this wetland in dollars. The question of how we express the value of wetlands in dollars will be addressed in three whole lectures on ecosystem service methodology. For now, we simply assume we can put a dollar value per unit of wetland on the horizontal axis.

This is a positive consumption externality. The previous example we had was a negative externality on the producer side, where we took the marginal cost curve and placed the externality there. Now, because we are talking about something that is benefiting a person rather than being a cost of production, it is the marginal benefits or the demand curve that we will modify.

The marginal cost curve is straightforward. It is just the cost of providing wetlands, perhaps the purchase price or the foregone sales price of those hectares of land. But we are going to have an externality defined by the fact that the marginal private benefit is going to be less than the marginal social benefit. This difference is going to be the externality, except it is positive value instead of negative value like we had with production.

The punchline is that if you let the free market with no augmentation solve this, it would set quantity where marginal benefit equals marginal cost. That is what markets always do. But here it depends on what costs are being included. In the free market with no fixes, the only cost that matters to the decision maker is the private one, so we call that QM, indicating it is the market solution. This is in contrast to the fact that when you think about everybody’s benefits—not just the private ones—the actual correct utility and surplus-maximizing quantity is the socially optimal QS.

This difference between these two quantities represents under-allocation. The instinct should develop that under-allocation can probably be expressed as deadweight loss. Indeed it can, and students will be working with that concept in the problem set.

Connection Between Externalities and Public Goods

An important point that was not always made explicit when these classes were originally taught is that the three different market failures we are discussing are actually more tightly linked than it might seem. The particular linkage worth discussing is how externalities, specifically positive externalities like this wetland example, are actually quite similar to what we started with in the market failures section: public goods.

The idea that under-provision is happening here might sound suspiciously familiar, because that was essentially the same conclusion we had with public goods. When we had a public good, it was only provisioned according to one person’s marginal benefits, and that was way below what it should have been.

What is that connection? They are ultimately the same basic idea. When you have a public good such as the value of a park, whoever ends up producing that unit of park—in this example, the person who paid for buying that park and then the private company came in and built it—they are getting value that was optimal to them, but then everybody free-rides on them. Another way of expressing the exact same thing is that they just created a decision providing a positive externality.

Public goods and externalities tend to differ in scale. Public goods tend to have lots and lots of people—millions of people, all of society—benefiting from them, whereas externalities are better framed when thinking about a localized effect like a watershed. But they are basically the same thing, and both have the same conclusion: the deadweight loss by only considering private benefits and costs is a bad thing. Some solution, which the rest of the course will address, involves thinking about solutions to that problem. Both framings will be used.

Climate Change as an Externality

The other theme in this course is climate change, the gigantic elephant in the room. Climate change can be thought of in many different ways, but we are going to regard it as an externality. In this case, it is a negative production externality, leading to massive overproduction. The scale of climate damages represents one of the most significant externalities in human history.

Solutions to Externalities

Legal Solutions and the Coase Theorem

The first bucket of solutions would be legal solutions. If we have good property rights, that alone will lead to fixing the externality. You may have come across Ronald Coase, a Nobel Prize winner, who developed something called the Coase Theorem. He showed, with excellent mathematical rigor, that as long as there are not a lot of transaction costs, externalities can and will be fixed by just letting people negotiate.

If there was an externality like your neighbor had a barking dog, Coase argued that as long as you two can negotiate, you could essentially pay each other to resolve it. The dog owner would probably pay you to be okay with the barking.

The key thing to know here is that this is the fundamental argumentation under the correct and very useful conservative argument on environmental protection. This argument does not always apply, and that is where conservatives and liberals might differ on whether externalities can actually be fixed by legal extension of property rights. But if you accept the assumptions, Coase’s argument is true. If there are no costs and people have clear lines of communication—that is just another way of saying low transaction costs—then the free market with better property rights can solve environmental issues.

Negotiation-Based Solutions

The second solution is tightly related to legal solutions: negotiation. This could happen through the legal system using the government to extract payments through lawyers, or through direct negotiation where, for example, the dog owner negotiates with the person who does not like that dog and offers a payment to compensate them. These are the free market solutions.

Government Interventions

Much more time is spent thinking about government interventions, simply because historically, for better or worse, most of our solutions have been government policy driven. There are a few different types of policy buckets to discuss, and we will start to fill these out with examples.

Command and Control

The first type goes by the phrase “Command and Control.” The etymology of this phrase is curious because it just sounds bad—it sounds like a bad idea. Whoever phrased this was probably an anti-environmental policy person.

The example of command and control would be emissions standards. The government could say, okay firm, you can only produce this amount of pollution, and fine them or send them to jail if they break that law. That is what the government can do. We call that command and control because there is no market incentive used to induce this behavior. It is just a law that the government says you have to follow.

There is nuance here. We have spent time showing that a uniform standard applied to all firms would not be as good as one that was differentiated for different firms according to their marginal cost of abatement. But subsequent lectures will start to move towards market-based solutions.

Market-Based Solutions

Market-based solutions are still government interventions—the government will set up the market-based solution—but the underlying mechanisms are not just requiring firms to follow the law. Instead, something about incentives, markets, and prices will drive the desired behavior.

An example is Cap and Trade, which is a policy that says you can only emit pollution if you have a permit to emit it, and the government will cap the total number of permits. But the flexibility comes in when different firms can trade those permits. If you set it up that way and let the firms trade, you will both achieve your emissions target and do it in a cost-minimizing way. This is very important because the costs of pollution reduction are huge.

Pigouvian Taxation

Definition and Concept

The policy type we will discuss in detail today is Pigouvian taxation. This is really central in a lot of discussions of what government policy should actually be implemented. It is considered by many economists to be probably the best answer to the climate challenges we face. It would be a Pigouvian tax in the form of a per-unit tax on carbon.

There is another important point of consensus: if you ask conservative economists, there is overwhelming agreement, both among left-leaning and right-leaning economists, that a carbon tax would be a very good way of solving climate change, or at least way better than what we are actually doing. Even if you do not think climate change is a problem, you might still want to look at the argumentation from conservative economists that a carbon tax would actually just be better for everybody, especially if you did it in the context of replacing other taxes.

You can actually be a pro-tax cut advocate and still be in favor of the carbon tax because you fix the externality but can use the revenue to eliminate other taxes. The revenue generated means you do not have to tax people so much in other ways. This is called revenue-neutral taxation. There is huge consensus that a carbon tax would be way more cost-effective to reach whatever climate goal we have than our current mismatch of policies and emissions targets.

A Pigouvian tax is a corrective tax designed to induce private decision makers to take into account the things that they would otherwise ignore. The marginal private benefits is the only thing the private agent considers when choosing their market quantity to produce. A Pigouvian tax is a corrective tax that says, well, this difference in value—if we say that is the tax rate for each unit—and this person cannot get away from paying it, we literally just change their benefit or cost curve appropriately. This is named after Arthur Pigou, and the idea is really straightforward.

Taxes and Subsidies

We call it a tax when it is something on a negative externality, meaning we are taking money from the individual and giving it to the government. The concept is identical, except for a positive or negative sign, to what we call subsidies. Subsidies and taxes are basically the same thing. A subsidy is a flow of value from the government to the individual.

That is what we had with the wetland example. We would subsidize the owner who has these wetlands, paying them some amount of money and hoping that changes their behavior. It does change their behavior—it makes them want to produce more wetland area.

Interactive Demonstration of Pigouvian Taxation

Let us explore these concepts interactively with a web application. A good methodological approach is to have your graph on your screen mimic what is being done on the board. But it is still valuable to write it down on the board, even though we have a nice visualization, so we can talk through the process.

We are going to have a negative production externality. The marginal cost curve is the private marginal cost. It is a production negative externality, meaning that the private costs are less than the marginal social costs. We also need to have our demand curve for whatever is being produced—it could be cars or electricity—because it still provides value, and we cannot just say do not do it.

The idea is that if we did not have any corrective to this situation, we can calculate the deadweight loss. The key steps are to identify the two equilibria, figure out which one is the market solution and which one is the social one, and see what the surplus triangles would look like.

We can see that surplus value is anywhere where the actual benefit is above the actual cost. But if we go out to the market solution, we have the opposite. The cost is greater than the benefit at the margin, and this would all be negative value. The deadweight loss is calculated by looking at this triangle and subtracting it from the total. This is graphically what we want to get rid of.

So the straightforward question is: what is the deadweight loss here? We basically want to reduce production until we eliminate all that negative value. The socially optimal point is better than the market point simply because it does not have any of this negative value. So how do we set a tax that gets rid of that?

Finding the Optimal Tax Rate

On the web application, you can adjust the line for the size of the tax. If you start to increase the tax a little bit, you see a new equilibrium happening. If the tax is, say, level 8, it is going to start to reduce the quantity, but it did not go far enough. The deadweight loss triangle got smaller, but it is still there. This reflects the fact that we have only made it part of the way to the optimal solution.

What if we set a tax of 42, really loving our environment? Actually, that does not really love the environment. You are probably going to make people angry, and they will probably rebel against your environmental policy. Here, if we had a tax of 42, we see it pushes the actual cost curve to be above the marginal social cost, and now we have a new type of deadweight loss. We just taxed it so much that we really hurt people, and now we are underproducing compared to what would be optimal.

If you are a total environmentalist who believes in only pristine environments, you might still negotiate for this outcome. But from a welfare economics perspective, we have more deadweight loss. The optimal tax is the one that sets MPC plus T equal to MSC, completely eliminating the deadweight loss.

With these demonstrations, the web application reports out various values like the deadweight loss, the tax revenue, and other metrics. You can figure out what the producer surplus, consumer surplus, and the amount of revenue being generated by this policy are.

The Pigouvian tax is going to shift the MPC curve around, and the correct Pigouvian tax is just one such that the T added to the MPC equals MSC. It is hard to draw because the ideal one is just right on top of the MSC curve, making it so that the after-tax private cost equals the social cost.

Application: The Gas Tax

Upcoming lectures will talk about carbon taxing and will actually run models to calculate what the optimal carbon tax is, given the literal complexity of the climate system. But there are all sorts of other Pigouvian taxes out there. One that is related but not actually a carbon tax is the gas tax. It is a really good example of a Pigouvian tax.

The thinking is that it is actually a pretty significant tax, but it represents the fact that the purchase and consumption of gasoline has an external cost beyond just climate change. Burning fossil fuels produces greenhouse gases, so it has an external impact in terms of more climate change and climate damages.

But actually—and this is something that becomes clear when working with government workers on transit and transportation—that is really not what people talk about at the policy level. What they talk about is the external cost of accidents and primarily congestion.

This reflects the fact that even at the scale of a county, the climate impacts that are attributable to local action are very small, because they are divided by everybody in the world. But the external costs of having congested highways are really easy to observe.

The fact that the more you drive, the more you clog up the highways has a cost to you because of congestion—we hate traffic. But it is also increasing the hatred of traffic that other people have. So every person, unless there is some sort of fix to the congestion, will be overdriving—driving too much. Even though they hate the traffic, most of that cost is being felt by other people rather than them. We get this nefarious situation where everybody overdrives. A way to fix that is a gas tax.

Quantifying External Costs of Driving

There are estimates from Perry and Small, who wrote an article around 2000. Correcting for inflation, congestion was causing 32 cents per gallon of damages. Accidents caused 27 cents per gallon of damages, and pollution—so climate change and local smog and haze—caused only 24 cents per gallon of damages.

So just to put some dollar values on it: there are lots of reasons to not drive a car, and it is not just climate change. There are significant external costs from congestion and accidents that justify gas taxes from a pure efficiency perspective.

Revenue Use and Policy Implications

Governor Walz controversially increased the gas tax in 2018. Many Republicans really disliked him for this, but it did raise a ton of revenue, and a lot of it was able to go towards improved infrastructure.

That is the other side of this equation with the Pigouvian tax. Not only does it have the value of closing the externality and providing more total surplus by getting rid of the deadweight loss, but there is a whole other potential benefit: what did you do with the tax revenue?

The presumption in basic analysis is just that a dollar of tax revenue is the exact same relative value of importance as a dollar of consumer or producer surplus. But evidence shows that that is not the case. It is often true that the revenue generated by the tax, if it is spent on something like improving infrastructure or subsidizing e-bikes, can have a greater return than what it would have been if it was just consumer or producer surplus.

Mathematical Framework

There is a mathematical appendix that provides a more formal treatment. The mathematical setup involves a supply and demand framework with more flexible functional forms with coefficients, where the marginal social cost is the summation of private costs and external costs, and they actually have different slopes, so calculations get even more complicated.

This mathematical framework sets up literal functions for marginal benefits, private costs, and social costs, and we can solve algebraically for the different equilibrium price and quantity. This indicates a cool feature of economics: it is not just a decision-making framework in loose terms. You can actually calculate optimized outcomes—at least optimized if you got your assumptions right and your equations were right.

Introduction to Game Theory and the Commons

The Commons as a Market Failure

We are now moving into our third of the three common market failures, which is that of the commons. The commons itself is an ancient term. It actually goes all the way back to feudal times. The king would have land that was partly owned by individual families and peasants. But he would also have the commons, which was typically a forest or land held in common that the king would let people access to hunt.

Hunting was a common form of providing food for your family. In the history of economic thought, peasants would often spend time doing a production activity that they gave to the king, essentially, and then get their well-being from going on the commons and hunting for their actual day-to-day consumption goods. Not all kings were that bad—maybe they would only take a portion as tax. But that idea of Robin Hood—the king overtaxing everybody—is the classic example. The commons was actually the solution for a lot of peasants in this situation.

Why Game Theory is Needed

The commons is hard to understand without a new set of tools. So far we have just been using supply and demand essentially. But the decisions for how optimal behavior will be computed in a commons situation does not work so well with supply and demand. So the new set of tools that we are going to use here fall under the category of game theory.

John Nash and Game Theory

John Nash was a singular genius and one of the most important single figures in economics. He identified what we will call Nash Equilibria, which is a really powerful predictive mathematical result that can be used in situations like the commons to make a prediction about how people will operate. For those who have seen the movie A Beautiful Mind with Russell Crowe, it depicts his life and contributions.

Elements of Game Theory

Game theory involves several key elements. The first is players. Players could be anything—it could be two individuals, or it could be companies like Airbus and Boeing.

The second element is strategies. For each player, we define two or potentially more strategies that they could play. In a price-cutting game example, Boeing or Airbus would decide whether to cut prices or keep them the same.

The third and final element is payoffs: a set of pairwise numbers indicating if the two players play a particular combination of strategies, what is the payoff to each of the different players or firms.

The Payoff Matrix

Let us draw a payoff matrix. In this example, we will use the Prisoner’s Dilemma, which is the most famous game theory example and lies at the core of many sustainability challenges.

The original formulation was this: you had two prisoners, Player A and Player B, charged with a crime. Police put them in separate rooms because this is actually a good strategy when trying to negotiate with criminals so they cannot talk to each other. The police are going to negotiate to try to get a confession by offering a reduced sentence. We see this play out even in recent cases—prosecutors trying to negotiate for testimony on condition of clemency. This is a common thing. The payout in this case is number of years of prison.

We have the first two elements of game theory: players and strategies—confess or not confess. The final element is what are the payoffs.

The notation we follow is that we have two numbers per cell. Let us call one cell 10 and 5, or another cell 3 and 3. This indicates the payoff to Player A and Player B respectively. The convention is to put the number closer to whoever gets that payout, making it a little easier to see.

Looking at the payoff matrix, if Player B confesses and Player A confesses, the payoffs might be 3 years for each player. But there will be a bunch of other values in the rest of the payoff matrix depending on whether one confesses and the other stays silent, or both stay silent.

Preview of Next Class

We will return to this game theory framework and show where it gives us really strong, powerful predictive tools about what, in other examples like Airbus and Boeing, the players would do if we got the model right. And then we will apply it to the environmental context of the commons dilemma. Game theory will allow us to formally model situations where multiple decision-makers interact strategically, which is essential for understanding commons problems.

Introduction to Externalities

Moving from Public Goods to Externalities

Definition and Conceptualization of Externalities

Negative Production Externalities

Marginal Cost Terminology

Graphical Analysis of Negative Externalities

Positive Externalities and Under-Provision

Connection Between Public Goods and Positive Externalities

Closing Remarks

Transcript (Day 1)

NOTE: Part of transcript 9 has Lecture 07 day 2 and Lecture 08 day 1. It is unclear to me the split before this or if you would like the transcripts to be split.

Transcript (Day 2)

All right, let’s get started. Welcome to Lecture 08B, where we will finish externalities, and then hopefully move on to the Prisoner’s Dilemma.

First, just a few things on the agenda to get caught up on. Thank you so much for doing that mid-semester student evaluation. The results were extremely helpful. One of the things I liked was that almost every single person explicitly wrote that they liked the games and interactive visualizations. I was worried those were hitting flat, and so I’m glad they’re not. We’re going to continue on with them.

In terms of schedule for the upcoming lectures, just a few things to point to. I’ve updated a few things. Key thing to note is this is Assignment 2, that one’s now posted, and it is due on the 18th. As before, this one will be preparation for the micro quiz that will also be on the 18th, which will be similar but slightly different to what you see on this one. This one will take a little bit longer than last time, so don’t start this one late.

I also realized I didn’t print it off as a PDF. Right now, it’s just as a web page, but there’s workspace. I think I’ll make it also a PDF so you can do it that way.

On PDFs, I have a request from our TA, and I guess it’s a request from me too. Please do not submit multiple files to Canvas for an assignment. There were some people that were submitting a bunch of pictures, all differently rotated, and that’s surprisingly hard to grade. If you want an easy solution, you can still take those phone pictures, just paste them into Word or something like that, and upload that document instead. And if you really want to do it nice, save it as a PDF and upload that document. That will make things a lot faster and make sure you don’t accidentally miss points, because it’s hard to read upside down and out of order.

Looking ahead to the overall framing, we’re working through our micro-foundations section. We finished optimal pollution, and then we moved to micro failures, which is kind of like an extension of the micro foundations, but applied to the classic three market failures that characterize a lot of environmental economics. The fuller title for this is market failures and open access, and then externalities and commons are where we’re going next.

After that, we’re going to shift gears again. This is going to come back to what is unique about this course, is that it’s not just going to be a hodgepodge of environmental and natural resource tools lumped together, as I kind of think is traditional in this type of course, but it’s really going to come back to the question of tying them together in a global macroeconomic framework. We had a little bit of that at the beginning with the planetary donut, but then we quickly lost that when we got into the nitty-gritty of consumer utility optimization and such. But that’s all the core that we will then start to revisit as we come back to questions of environmentalism in the whole economy, how indicators like GDP and wealth play out in this. So that’s the arc.

In terms of scheduling, this is when that micro quiz is. Some of these titles will change around a little bit, but on the 23rd of February, we’re going to have a fun guest lecturer. Famara Damfa is the executive director of NATCAP Teams, our research center, and he’ll be leading us through some of his really interesting work. He’s literally a negotiator for the country of Gambia at the UNFCCC, which is the hosting convention for all those climate change negotiations that you see. He literally has to put on a suit and argue over words about what the international agreements will have written in them. We’ll have a couple of other guest lecturers later on in the semester, but this will be our first one.

[Quiz distribution section omitted]

For those who have grading concerns, remember, take it up with our TA, Ryan. He’s the one that actually did the grading, and so I won’t have many informed opinions on why you got what you got. His email is on the website, so you can email him and meet with him whenever.

But onwards to the materials at hand.

Back into externalities. We went quickly through the introduction, so I’ll do a quick review, and then we will actually try it out with some more specific applications and a brand new web app.

We’re using the example of the provision of clean water through having a wetland on your property. That has benefits to you. You like the wetland, it makes your water cleaner, but it also has benefits to people downstream from you. They get cleaner water, but they are external to the decision on whether or not you should keep that wetland, or how much of that wetland you should keep. So it’s a classic externality.

Except this one is a positive externality. Last class, we talked about negative externalities, and there, the classic example is polluting something, like sulfur dioxide. But here we’re talking about a positive externality. This wetland is providing external value, but it’s not a loss, it’s a gain.

The vertical axis is dollars. We’re going to try to express the value of this wetland in dollars. You might be wondering, how do we express the value of wetlands in dollars? We’re going to have three whole lectures on that when we talk about ecosystem service methodology. But for now, just trust me. Suppose that we can put a dollar value per unit of wetland. That’s a heroic task, but for now, just assume it.

It’s a positive consumption externality. The previous example we had was a negative one, but also it was on the producer side, and what that meant is we took the marginal cost curve and had that be where we put the externality. Now, because we’re talking about something that is benefiting a person, rather than being a cost of production, it’s the marginal benefits, or the demand curve, that we’re going to modify here.

Thus, the marginal cost curve is the easy one, it’s just going to be this. Providing wetlands has some marginal cost. Maybe that is the purchase price or the foregone sales price of those hectares of land. So it’s pretty easy to see that one.

But we’re going to have an externality defined by the fact that the marginal private benefit is going to be less than the marginal social benefit. This difference is going to be the externality, except it’s positive value instead of negative value like we had with production.

The punchline that we came to last lecture is that if you let the free market with no augmentation solve this, it would set where marginal benefit equals marginal cost. That’s what markets always do. But here, it depends on what costs are being included. If it’s the free market with no fixes, the only cost that matters to the decision maker is the private one, and so we’re going to call that Q star M, indicating it’s the market solution. This is in contrast to the fact that when you think about everybody’s benefits, not just the private ones, the actual correct utility and surplus maximizing one is the socially optimal quantity QS star. This difference between these two is under-allocation.

You should be getting that instinct that under-allocation is probably going to be able to be expressed as deadweight loss. Indeed, it can. You’ll be working with that in your problem set.

But where I want to go, and this wasn’t done when I took these classes, so maybe it’s going out on a limb, is that the three different market failures we’re talking about are actually more tightly linked than it might seem.

The particular linkage I want to talk about is how externalities, but specifically positive externalities like this, are actually quite similar to what we started with in the market failures section, which was public goods. The idea that under-provision is happening here might sound suspiciously familiar, because that was essentially the same conclusion that we had with public goods. When we had a public good, it was only provisioned according to one person’s marginal benefits, and that’s way below what it should have been.

What is that connection? They are ultimately the same basic idea. When you have a public good, such as the value of a park, whoever ends up producing that unit of park, the “sucker” who paid for buying that park and then the private company came in and built it, they are getting value that was optimal to them, but then everybody free-rides on them. Another way of expressing the exact same thing is they just did a decision that was providing a positive externality.

Public goods, maybe where they are different is public goods tend to be ones that have lots and lots of people, like millions of people all of society benefiting from it, whereas externalities, this framing is maybe more better when you’re thinking about a localized effect, like a watershed. But I think it’s kind of cool that they’re basically the same thing, and both of them have the same conclusion, that the deadweight loss by only considering private benefits and costs is a bad thing, and that some solution, which we’ll spend the rest of the course talking about, will be thinking about solutions to that. We’ll use both of these framings.

The other theme in this course is climate change. It’s just the gigantic elephant in the room. And this can be thought of in a lot of different ways, but we’re going to regard it as an externality. In this case, it’s a negative production externality, leading to massive overproduction.

But let’s now shift gears to solutions, and we’re going to outline a few of them. How can we fix this?

The first bucket would be legal solutions. The idea is, if we have good property rights, that alone will lead to fixing the externality. You may have come across Ronald Coase, winner of the Nobel Prize, and he has something called the Coase Theorem. He actually showed, with excellent mathematical rigor, that as long as there aren’t a lot of transaction costs, externalities can, and he even went so far as to say will, be fixed by just letting people negotiate.

If there was an externality, like your neighbor had a barking dog, he argued that as long as you two can negotiate, you could essentially pay the dog owner, or the dog owner would pay you to just be okay with the barking. Coase argued there could be a payment as long as there’s a good legal system.

The key thing to know here is that this is the fundamental argumentation that is under the correct and very useful conservative argument on environmental protection. I think it doesn’t always apply, and that’s where conservatives and liberals might differ, is can this actually be fixed by legal extension of property rights. That’s a debate. But if you accept the assumptions, Coase’s argument is true. If there are no costs, and people have clear lines of communication, that’s just another way of saying low costs, the free market with just better property rights can solve all of environmentalism. I think that’s an important point, because there are plenty of cases where that is the right way to look at it.

These are both essentially related to the Coase theorem, that some sort of negotiation can work. The legal system is you’re going to use the government to extract that money, using lawyers, but the Coase theorem also applies to negotiation, letting that dog owner negotiate with the person who doesn’t like that dog and offer a payment to compensate them. Those are the free market solutions.

But then there’s this whole bucket of government interventions. Actually, much more time is spent thinking about this, simply because, historically, for better or worse, most of our solutions have been government policy driven.

There’s a few different types of policy buckets that I want to talk about, and we’ll start to fill these out with examples. The first goes by the phrase Command and Control. I would love to know the etymology of this phrase, because it just sounds bad. It sounds like that’s going to be a bad idea. Whoever phrased this was probably an anti-environmental policy person, because even the environmentalists start with this, which frames government as commanding and controlling.

The example of this would be emissions standards. The government could just go ahead and say, firm, you can only produce this amount of pollution, and fine them or send them to jail if they break that law. That’s what the government can do. But we call that command and control because there is no market incentive that is used to induce this behavior. It’s just a law that the government says you have to do it.

Interestingly, we saw in our lectures that there’s still a little bit of nuance here. We spent all that time showing that a uniform standard applied to all firms would not be as good as if we had one that was differentiated for different firms according to their marginal cost of abatement. So there actually is a fair amount of nuance there.

But in subsequent lectures, we’ll start to move towards market-based solutions. This is still a government intervention, insofar as the government is going to set up the market-based solution, but the underlying mechanisms are not just you have to follow the law, but something about incentives and markets and prices that is going to drive that behavior.

An example for now is Cap and Trade, which is just a policy that says we’re going to pass a law that says you can only emit pollution if you have a permit to emit it, and we’re going to cap the total number of permits. But the flexibility is going to come in, and we’re going to say you different firms can trade them. We’ll spend a whole lecture on this, talking about how if you set it up that way and let the firms trade, you will both achieve your emissions target and do it in a cost-minimizing way. And this is very important, because the costs are huge.

But the one we’ll talk about today is Pigouvian taxation. This is one that is really central in a lot of the discussions of what government policy actually should be done. It’s considered by many economists to be probably the best answer to the climate challenges that we face, in the form of a per unit tax on carbon.

Here’s another point of consensus. If you ask conservative economists, there’s overwhelming agreement, both on left-leaning and right-leaning economists, that a carbon tax would be a very good way of solving this, or at least that it would be way, way, way better than what we’re actually doing.

Even if you don’t think climate change is a problem, you still might want to take a look at the argumentation from conservative economists that a carbon tax would actually just be better for everybody, especially if you did it in the context of replacing other taxes. You can actually be a pro-tax cut advocate and still be in favor of the carbon tax, because you fix the externality but can use it to eliminate other taxes. The revenue generated from it means you don’t have to tax people so much. This is called revenue-neutral taxation.

Either way, I just want to point out that there’s huge consensus on this point, that it would be way more cost-effective to reach whatever climate goal we have than our current mismatch of policies and emissions targets.

So what is a Pigouvian tax? It’s just a corrective tax designed to induce the private decision makers to take into account the things that they would otherwise ignore. Thinking over here, we’re saying my marginal private benefits is the only thing the private agent considers when they’re choosing their market quantity to produce. A Pigouvian tax is just a corrective tax that says, well, this difference in value, if we say that’s the tax rate for each unit, and this person can’t get away from paying it, we literally just change their benefit or cost curve appropriately.

This is named after Arthur Pigou. The idea is really straightforward. We call it a tax when it’s something that is on a negative externality. That just means that we’re taking money from the individual and giving it to the government, but the concept is identical, except for a positive or negative sign, to what we call subsidies. Subsidies and taxes are basically the same thing, it’s just going to be a flow of value from the government to the individual. That’s actually what we had here. We’re going to subsidize, pay the owner who has these wetlands some amount of money, and hope that changes their behavior, and we find out it does. It makes them want to produce more.

Let’s explore those interactively. I’ve got another web app for us to play with. A good methodological way for you to approach it is to have your graph on your screen mimic what I’m doing on the board. But I still want to write it down on the board, even though we’ve got a nice visualization, so we can talk through the process.

We’re going to have a negative production externality. I’ll try to roughly match the lines, but what’s nice about the web app is the lines are exactly right, because I didn’t draw the line, I just defined the function. We’re going to have our marginal cost curve, but the private marginal cost. I realize I made a mistake. I called it PMC on the screen. Just know that that’s the same as what I called over here the marginal private cost.

It’s a production negative externality, meaning that the private costs are less than the marginal social costs. And then we also need to have our demand curve, for whatever it is that they are producing. Because it could be cars or electricity, it’s still something that provides value, and so we can’t just say don’t do it.

But the idea would be if we didn’t have any corrective to this situation, we can calculate the deadweight loss. At the end of this lecture, we’ll be doing this more algebraically, but basically the key steps are to identify the two equilibria, figure out which one’s the social one, and see what the surplus triangles would look like.

We can see that a surplus value is anywhere where the actual benefit is above the actual cost. This is all benefit. This part does not benefit, because that’s only with respect to the one person. This is the true one. This is the positive benefit.

But if we go out to the market solution, what do we have? We have the opposite. The cost is greater than the benefit. This would all be negative value, and so you’d calculate the total surplus by looking at this triangle, and you have to get the area of this triangle, because you’re going to subtract it from there, but graphically we could see it would offset some of that. And this is the deadweight loss. That’s what we want to get rid of.

It’s sort of an easy question, but what’s the deadweight loss here? We basically just went down until we eliminated all that negative value, and this point is better than this point, simply because it doesn’t have any of this negative. So how do we set a tax that gets rid of that?

Interactively, on the web app, you can wiggle around the line for the size of the tax. I’ve captured a few screenshots here. If you started to increase the tax a little bit, what do you see? A new equilibrium is going to happen. And if the tax is a little bit of an increase, like level 8, it’s going to start to reduce the quantity. But it didn’t go far enough, and so the deadweight loss triangle has gotten smaller but it’s still there. This is just reflecting the fact that we’ve only made it part of the way to the optimal solution.

What if we really loved our environment and set it to a tax of 42? I would say you don’t really love the environment. You’re probably going to make people angry, and they’ll probably rebel against your environmental policy, so you may be shooting yourself in the foot. Here, if we had a tax of 42, what do we see? It’s going to push the actual cost curve to be above the marginal social cost, and now we’re going to have a new type of deadweight loss. We just taxed it so much that we really hurt people, and now we’re underproducing compared to what would be optimal.

If you’re a total environmentalist who believes in only pristine environments, you might still negotiate for this one. There’s debate on this. I would say you still wouldn’t. Unless you think the framework is flawed, you’re basically saying let’s hurt some people in order to improve the environment because I really want it. And that could be construed as selfish.

Regardless, we can see it’s too high simply from our welfare economics perspective, that we’ve got more deadweight loss. The optimal tax is 25. With these demonstrations, the web app will report out various values, like the deadweight loss, the tax revenue, and the other things you can do would be to figure out what is the producer surplus, consumer surplus, and what is the amount of revenue being generated by this.

The Pigouvian tax is going to shift the MPC curve around, and the correct Pigouvian tax is just one such that T added to the MPC equals MSC. The ideal one literally makes it so that it is equal to the marginal social cost.

We’ll talk in upcoming lectures about carbon taxing, and we’ll actually run models to calculate what is the optimal carbon tax, given the literal complexity of the climate system. But there’s all sorts of other Pigouvian taxes out there. The gas tax is a really good example of a Pigouvian tax.

The thinking there is that it’s actually a pretty significant tax, but it represents the fact that the purchase and consumption of gasoline has an external cost, and it’s more than just climate. Pollution from burning fossil fuels produces greenhouse gases, and so it has this external impact in terms of more climate change and more climate damages.

But actually, and I know this because my wife has been a government worker on things related to transit and transportation, that’s really not what they talk about. What they talk about is the cost, the external cost of accidents and primarily congestion.

This is just reflecting the fact that even at the scale of Hennepin County, where she works, the size of the climate impacts that their action is attributable to is very small, because it is divided by everybody in the world. But the external costs of having congested highways is really easy to observe.

The congestion, the fact that the more you drive, the more you will clog up the highways, has a cost to you that it’s congested. We hate traffic, but it also is increasing the hatred of traffic that other people have. Every person, unless there’s some sort of fix to the congestion, will be over-driving, driving too much, because although they hate the traffic, most of that cost is being felt by the other people rather than them. And so we get this situation where everybody overdrives. A way to fix that is a gas tax.

Here are some estimates. These are old estimates, but I think they’re roughly the same, from Perry and Small. In 2000 dollars, correcting for inflation, congestion was causing 32 cents per gallon of damages, accidents 27 cents, and pollution only 24 cents. And actually, the pollution is both climate change pollution but also local smog and haze. I’ve got links to the articles if you’d like to dive into them.

That’s an interesting finding, that there’s lots of reasons to want to not drive a car, and it’s not just climate change.

I love my bike, and it’s an e-bike, so it’s literally as fast as these cars, so I feel like I’m hacking at life or something. The best is on the State Fair days. The State Fair site is just right over there, and I was driving up Raymond to get to here once, and it was a parking lot for about 2 miles, and it took me 55 minutes to make it to work. The next year, and every year after, I have my favorite day biking of the year, which is me cruising at 26 miles per hour, the speed limit essentially, alongside all of these cars who are averaging half a mile per hour.

This continues to make news. In 2018, there was controversy when the gas tax was increased. A lot of Republicans really disliked this, but it did raise a ton of revenue, and a lot of it was able to go towards improved infrastructure. That’s the other side of this equation, which is the Pigouvian tax not only has the value of closing the externality and providing more total surplus by getting rid of the deadweight loss, but that’s ignoring a potential whole other benefit, which is what did you do with the tax revenue?

The presumption of surplus here is just that a dollar of tax revenue is the exact same relative value of importance as a dollar of consumer or producer surplus, but evidence shows that that’s not the case. It’s often true that the revenue generated by the tax, if it’s spent on something like improving infrastructure or subsidizing e-bikes, can have a greater return than just what it would have been if it was consumer or producer surplus.

That’s Pigouvian taxation. Super straightforward, but it’s so dominant in solving problems that it’s worth a full-on treatment.

There’s a mathematical appendix. I’m not going to have a question on this on the exams. This is basically going to be our supply and demand setup, but given more flexible functional forms with coefficients, where we’re going to have the marginal social cost as the summation of those two, and actually have different slopes, so it gets even more complicated. You can refer to it or not. There’s a lot of peer pressure among environmental econ professors to still teach this stuff. But the point is, there is the mathematics that can say this is not just graphic. We have literal mathematical functions for marginal benefits, private costs, and social costs. And we can solve algebraically for the different equilibrium price and quantity, and this indicates the cool feature of econ, that it’s not just a decision-making framework in loosey-goosey terms, you can actually calculate optimized things, at least optimized if you got your assumptions right and your equations were right.

What I want to pivot to is the other slides. We are now moving to Commons and Prisoner’s Dilemma. We are going to move into our third of the three common market failures, which is that of the commons.

The Commons itself is an ancient term. It actually goes all the way back to feudal times. The king would have land, some of which would be owned by individual families and peasants. They would also have the commons, and the commons was typically a forest. But it was land held in common that the king would let people go and access to hunt. Hunting was a common form of providing food for your family.

In the history of economic thought, the peasants would often spend time doing a production activity that they give to the king, essentially, and then get their well-being from going on the commons and hunting for their actual day-to-day consumption goods. Not all kings were that bad. Maybe they would only take a portion of the tax, but that idea of Robin Hood, the king overtaxing everybody, that’s the example. And the commons was actually the solution for a lot of peasants in this situation. That’s what the Commons is, an area where the king, or whoever, says that anybody can go here and do what you want. In that case, hunting was something that people did.

The Commons, though, is hard to understand without a new set of tools. So far, we’ve just been using supply and demand, essentially, but the decisions for how optimal behavior will be computed in a commons doesn’t work so well with supply and demand. The new set of tools that we’re going to use here fall under the category of game theory.

This is John Nash, and he is a singular genius, one of the most important single figures in economics. He identified what we will call Nash Equilibria, which is a really powerful predictive mathematical result that can be used in situations like commons to make a prediction on how people will operate. Here’s a much more attractive John Nash when he was much younger, looking at numbers, from the movie A Beautiful Mind with Russell Crowe.

Game theory is what we’re going to learn. We’re just going to introduce the concept today of what’s called the payoff matrix, and we’ll use those next class.

The payoff matrix is going to define a few things. It’s going to show, first off, players. Players could be anything. It could be me and you, or it could be companies like Airbus and Boeing.

Then strategies. For each player, we define two, or potentially more, different strategies that they could play. In this case, we’re going to be playing a price-cutting game, where Boeing or Airbus will decide, should I cut my prices or keep them the same?

And finally, the payoffs. This is going to be a set of pairwise numbers indicating if the two players play this combination of strategies, what is the payoff to each of the different firms?

Let’s draw one. The two things are the players and their strategies. In this particular case, we’re going to be building to the prisoner’s dilemma. The prisoner’s dilemma is going to be called that because the choice of Player A is to confess or stay silent on whether or not the other player, who is their co-conspirator in an alleged crime, committed the crime as well.

This is the most famous game theory example and lies at the core of many sustainability challenges. The original formulation was just this. You had two prisoners, Player A and Player B. They’ve been charged with a crime. Police will put them in separate rooms, and we know from crime dramas on TV this is actually a good idea when you’re trying to negotiate with criminals, so they can’t talk to each other. Then they’re going to negotiate with them to try to get a confession. A confession is saying, yes, we did it.

As you probably also know from crime dramas, they will often try to lure one of the criminals in their individual room into admitting they committed the crime by offering a reduced sentence. The payout in this case is number of years of prison.

So we’ve got the first two elements of game theory: players, strategies (confess or not), and then the final one is what are the payoffs. I’m not going to talk about why the numbers are what they are. Next class, we’ll put some intuition to them, because the actual values will totally change the dynamics of the game. I just want to show the approach.

The payoffs are going to be two numbers, like 10 and 5. This is going to be the payoff to Player A, and Player B. We’ll have specific values. In this example, we’ll have a 3 and a 3. This 3 is closer to Player B, so that’s what they get if Player B confesses and Player A confesses. But we’re going to have a bunch of other values in the rest of the payoff matrix.

That’s where I’m going to leave it, because we’re at time. We’re going to return to this and show where, number one, game theory gives us some really strong, powerful, predictive tools about what, in this example, Airbus and Boeing would do if we got the model right. And then we’re going to apply it to the environmental context of the commons dilemma.

We are good. Thank you, and have a good day.