Content
Public Goods and the Free-Rider Problem
The Public Goods Game and Behavioral Economics
In the previous class, a public goods game was played where the best strategy for maximizing individual payout was giving zero every time. This particular class’s data is consistent with findings from one of the most widely studied behavioral economics experiments. Lab experiments have demonstrated this pattern across a wide variety of settings, at different income levels and in different countries. People typically start out contributing 40 to 60 percent of their tokens to the public good, but the contribution always seems to fall over time. This behavior appears to be something fundamental about human nature.
Rivalry, Excludability, and Market Failures
To understand public goods, it is necessary to tie this concept back to market failures and the broader framing of economics. The spectrum of rivalry and excludability is key to categorizing different types of goods. When players in the game had the choice on how to spend their public tokens, putting them into a personal account made it a standard good that was completely rival and fully excludable. The catch was that it was less valuable per token than the other option available.
In the game, any tokens put into the group account were rewarded twice as much, so they were more valuable. However, they had the attributes of being both non-rival and non-excludable. Even if someone free-rode and did not contribute their tokens, they still got their even share of the public good payout. This is why it is advantageous to do the privately optimal thing and hope that others will contribute. However, there is nuance in this debate because people are not just trying to maximize their own welfare. Some players in the game played a strategy that was good for everybody, and that really is how humans work in reality.
The Spectrum of Goods and Under-Provision
On the spectrum of goods, when tokens are put in the private good, the good is down at the end with full rivalry and excludability. When tokens are put in the public good, it has both attributes of non-rivalry and non-excludability. This is what causes the key conclusion about public goods: they will be under-provided unless something fixes it. There are two different ways to think about fixing this problem. First is how individuals can fix it through their own choices and strategies. Second is how society or governments can fix it through policy interventions. This class is not just about environmental doom and gloom, but about thinking through the policies that can address these problems.
Solutions to Public Goods Under-Provision: Individual Strategies
Playing Games Against Programmed Bots
For individuals, there is another game that was created to explore different strategies. There is a QR code so participants can play it on their phone, though it is probably better on a computer if one is available. Participants can go to the website and navigate to the game.
In this game, each participant plays a separate game against some bots that were programmed to behave like players do in class. The participant and the bots each choose how much of their tokens to put into the private good versus the public good. For now, the simplest case with default settings is being used. The key feature is a slider bar, which indicates how many of the 20 tokens each round will be contributed to the public good. If a participant contributes 10 of their 20 to the public good, they will keep the other 10 as private reward.
Participants choose a strategy and update it each round, playing 10 rounds quickly. As participants click and make choices, they see their own choice as well as the choices of the three bots they are playing against. The game interactively plots cumulative earnings and the contributions of all players over time. The goal is to keep playing until the round goes to 10.
Strategic Interaction and Observable Behavior
This is a tricky game because the bots are observing what the participant does and reacting accordingly. Even if a participant knew the bots were reacting to them, they would not know exactly how the bots would respond. Would the bots be selfish or would they ignore the participant’s actions? In this case, the bots showed realistic behavior: starting with high contributions and decaying over time, with not much interactivity between the participant and the bots.
However, in the next assignment, participants will play with different options. If the opponents are conditional cooperators, the optimal strategy changes completely. It is no longer optimal to be selfish; instead, it is closer to showing good faith efforts by contributing to the social good in order to encourage the bots to do the socially optimal thing. For now, with the default setting, going selfish gives the best payout.
Beyond Homo Economicus
The point being made is that we are not working only with Homo economicus, which is a phrase describing an ultra-rational individual who is perfectly utility maximizing. However, that is not reality. When the class was surveyed after playing the game, most participants, except for one group, had some degree of non-Homo economicus behavior. They did something for a reason other than maximizing their individual welfare. In reality, there are other considerations that influence behavior: what will people think of me, and could I get my opponent to react positively?
So participants could still be selfish but have strategic reasons to play differently. This represents the first way to solve the public goods game: using strategic interaction. Behavioral economics shows interesting richness in these kinds of scenarios. Game theory will be returned to later in the course, and concepts like the Coase Theorem will be discussed to illustrate other approaches. For now, the key point is that private solutions to the public goods game can involve playing strategically and considering the reactions of others.
Solutions to Public Goods Under-Provision: Government and Society
Need for Graphical Analysis
The more interesting question, which will receive more time in the course, is how society can fix the under-provision of public goods. If we really want to fix this problem, we need to understand it, which means drawing some graphs. Another web app has been created and is accessible by QR code on the website. It is probably best to access it on a laptop so that participants can play along with the graphs being presented.
Public Goods Analysis: The Parks Example
Suppose we are considering a specific public good: parks. The quantity Q represents the quantity of parks in the area, though we leave it ambiguous whether that refers to the total size, the number of parks, or something else. The vertical axis represents dollars, which signify the price or marginal cost of producing parks. Let’s assume there are no increasing returns to scale in park production. Instead, it is a constant marginal cost of, say, $5 per unit of park.
To figure out the optimal amount of parks to provide, we need to know the marginal benefit for individuals. The marginal benefit curve shows the marginal benefit for the ith individual, denoted MB_i. It follows a standard marginal benefit curve: it starts high because one park would be very popular, but more parks provide less benefit each additional unit. This marginal benefit curve also represents the price someone would be willing to pay for each additional park.
With only one person, the optimal amount of parks would be where marginal costs equal marginal benefits. This person would be willing to pay $5 for that amount, and it costs $5 to build, so it is optimal. However, that scenario is too simple and not really a public good because there is no public. So let’s consider the case with multiple people.
The Publicly Optimal Solution with Multiple Individuals
Let’s say N equals 2, with two individuals having identical marginal benefit curves. To determine the socially optimal outcome, we need to calculate the aggregate marginal benefit, which is done through vertical summation. With two people, we simply double the height of the individual marginal benefit curve. The aggregate marginal benefit curve equals the sum over all individuals i of the marginal benefit of each individual.
If we express MB_i in inverse demand function style as a parameter A minus B times Q, then the societal marginal benefit becomes two times this, because it is identical for each person. We can calculate the optimal quantity by setting this aggregate marginal benefit equal to marginal cost.
Market Failure: Under-Provision Without Government
Before calculating the optimal quantity, let’s discuss what would happen without government intervention. Suppose a private park-building company wants to come in and provide parks. Like any profit-maximizing firm, they would only produce if they can make a profit. One person would be willing to pay $5 for the first park, and they might build it. However, because this is a public good, there is a free-riding problem. As soon as someone pays for access, the marginal value for the other person goes to zero, because they already have access to the public good. So they will not pay anything extra.
What we see in this market failure scenario is that the first unit gets built, then nobody buys anything else. It stops at a very low quantity. Some parks exist, but not enough compared to what society would want. This leads to deadweight loss.
Calculating Deadweight Loss
To calculate deadweight loss, we look at the area under the marginal benefit curve but above the marginal cost curve. If we only have Q_M from the market solution, we get only a small area below marginal benefit. But if we had Q* for the societal optimum, we would get a much larger area of total welfare. The triangle remaining between what we have and what we could have is the deadweight loss from under-provision.
As N increases, the deadweight loss also increases. With N equals 3, deadweight loss grows from 3.1 to 8.3. With N equals 20, there is enormous deadweight loss from the under-provision of this public good. This demonstrates that as society gets bigger and more people benefit from public goods, it becomes increasingly costly not to provide them at the socially optimal level. The more people that can benefit from a public good, the greater the welfare loss from under-provision.
Policy Solutions to Public Goods Under-Provision
Privatization as a Market Solution
How do we solve the under-provision problem? Well, one solution involves privatization of the public good. Consider indoor playgrounds as an example. These are provided by the market, even though we said earlier that private markets would not provide parks in general. The key difference is that firms charge an admission fee of $10 to get in, thereby privatizing the space and making it excludable. They can make a profit because they collect fees from users, so the market provides it willingly.
However, this solution only works when you can actually privatize the good. What about things that you cannot privatize, like climate reduction, military protection, or research and development? These goods have characteristics that make privatization impossible or impractical. In those cases, we must move into government solutions.
Subsidy-Based Solutions
On the web app showing the parks example, there are a couple of policy options available to explore. The first is a subsidy approach. A lot of environmental economics involves calculating optimal subsidies to correct market failures. If private parks undersupply the socially optimal amount, the government can pay private firms a subsidy for each park they produce. As the subsidy rises, deadweight loss decreases. If a government sets the subsidy at exactly the right level, it can eliminate all deadweight loss and achieve the socially optimal outcome.
Direct Public Provision
The second, and often more common, solution is direct public provision. Rather than subsidizing private firms to produce the public good, the government can simply provide the good itself using tax dollars. The government chooses exactly how much to provide to the population. If the government provision is well-designed, it can minimize deadweight loss and achieve efficiency. This approach takes the good entirely out of private markets and under government control.
Optimal Pollution Control and Firm-Specific Emissions Reduction
Introduction to Asymmetric Firm Pollution Abatement
The instructor began the lecture content by revisiting pollution, which is clearly a central issue in environmental economics. The focus was specifically on what happens when you have multiple firms with different characteristics attempting to reduce emissions. Rather than treating all firms equally, the lecture addressed the question of what the optimal policy should be when firms have asymmetric marginal abatement costs. The instructor wanted to move away from discussing how to aggregate marginal abatement cost curves and instead focus on determining the correct policy response when firms differ in their ability to reduce emissions cost-effectively.
Graphical Representation of Multiple MAC Curves
The instructor set up a graphical framework with emissions on the horizontal axis and costs on the vertical axis. Two marginal abatement cost curves were drawn, one starting at an intercept of 6 and another starting at 12, with both curves sloping downward. The question posed was what policy would be optimal when facing this situation.
The aggregation of curves was explained by noting that where only one firm operates in a certain range, the aggregate curve reflects only that firm’s costs. However, once both firms are operating, the aggregate marginal abatement cost curve is constructed by adding the width of one firm’s curve onto the other. Alternatively, the aggregate curve can be calculated mathematically using the intercepts of the individual firm curves.
The EPA Emissions Reduction Mandate
To make the problem concrete, the instructor presented a scenario where the Environmental Protection Agency has set a goal to reduce total emissions from the current level of 12 units down to 9 units. The key question then becomes: what is the cost-effective way to achieve this 3-unit reduction in total emissions?
Mathematical Solution for Optimal Emissions Reduction
The lecture then moved into the mathematical details using specific functional forms for the marginal abatement cost curves. The curves were given as MAC A equals 12 minus 2 times emissions from Firm A, and MAC B equals 6 minus emissions from Firm B. The instructor explained that to solve for optimal emissions reduction, one must first aggregate these curves together, but then apply a decision rule.
The key decision rule for optimal pollution is to set the marginal abatement cost curves equal to each other. The instructor emphasized that this is another example demonstrating why economists think in marginal terms. While thinking about total costs and total benefits can become very complex, following this simple rule of equating marginal abatement costs allows one to determine the optimal emissions reduction for each firm.
Solving the Optimization Problem
Setting MAC A equal to MAC B, the equation becomes 12 minus 2 times EA equals 6 minus EB. Solving this equation involves moving the 6 to the left side to get 6 equals 2 times EA minus EB, which yields the relationship EB equals 2 times EA minus 6.
The EPA’s mandate provides the constraint that EA plus EB equals 9, representing the total allowable emissions after reduction from the current 12 units. Substituting the expression for EB into this constraint gives EA plus (2 times EA minus 6) equals 9. Combining like terms yields 3 times EA minus 6 equals 9, which simplifies to 3 times EA equals 15, and therefore EA equals 5.
Once EA is determined to be 5, and given that the total must be 9, it follows that EB equals 4. Therefore, Firm A is required to reduce its emissions by 1 unit, having started from an initial level of 6, while Firm B is required to reduce its emissions by 2 units, having started from an initial level of 6.
Explanation of Differentiated Reduction
The reason the two firms have different amounts of reduction is that one firm is inherently better at reducing its emissions than the other. Specifically, Firm B is more efficient at emissions reduction because its marginal abatement cost curve has a slope of negative 1, whereas Firm A’s curve has a slope of negative 2. This means that for Firm B, each additional unit of emissions reduction costs less than it does for Firm A. Therefore, it is more cost-effective to require Firm B to do more of the reduction.
Graphical Decision Rule and Conclusion
The decision rule shown graphically is that efficient emissions reduction requires the marginal abatement cost curves of all firms to be set equal to each other at the margin. In straightforward English, this means cleaning up pollution until the last unit cleaned up costs exactly as much as the damage it avoids. The instructor noted that an interactive tool is available where students can explore different optimal strategies and experiment with various curves, though it was not demonstrated during the lecture.
Market Failures: Theoretical Framework
Transition to a New Course Topic
The instructor indicated a major pivot in the course content, announcing entry into a new unit about market failures. Market failures are extremely common in areas relevant to environmental economics, making this a crucial topic for understanding environmental policy. The instructor wanted to provide a general theoretical framing before diving into specific examples and applications.
Definition of Market Failure
A market failure is defined as any case where individuals pursuing their self-interest does not result in a socially optimal outcome. When individuals pursue their private interests through utility maximization, specifically by setting their indifference curves equal to their budget constraints, a market failure occurs when this behavior leads to suboptimal social outcomes. In other words, under conditions of market failure, the invisible hand does not work to guide the economy toward efficiency.
Connection to Welfare Theorems
The instructor reminded students that significant time had been spent on the welfare theorems because, under very restrictive assumptions, the first welfare theorem makes a strong argument that the free market, left unconstrained, will be guided as if by an invisible hand toward an outcome that is good for everybody. However, with more realistic assumptions that relax those restrictive conditions, we find examples where pursuit of private interest simply does not produce the best outcome. In these cases, the welfare theorem fails to hold, and markets fail to achieve efficiency.
Assumptions Underlying Market Efficiency
The instructor presented the assumptions necessary for the first welfare theorem and the invisible hand mechanism to function correctly. The key assumptions include perfect information, perfect competition, no externalities, divisible goods, and no transaction costs, among others. When we study market failures, we are systematically violating each of these assumptions. The instructor noted that examples of market failures include public goods or public bads, impacts on external parties not reflected in market prices, commons problems involving overuse of shared resources, market power situations such as monopoly, monopsony, or oligopoly, and asymmetric information where different parties to a transaction have different information.
Characterizing Goods: Rivalry and Excludability
Introduction to Two Fundamental Dimensions
The instructor explained that understanding market failures requires understanding two different spectrums along which we can characterize goods. These two dimensions, rivalness and excludability, help us understand why some goods are efficiently provided by markets while others are not.
The Spectrum of Rivalness
The first spectrum is rivalness, which refers to competition in consumption. For a rival good, one person consuming it lowers how much somebody else can consume. An apple is a classic example of a rival good because if I eat it, you cannot eat it. A hammer is also fairly rival, though hammers can be shared if people pass them back and forth.
On the opposite end of the spectrum are non-rival goods, where one person consuming or using the good does not lower how much somebody else can use it. In reality, almost all goods fall somewhere along the spectrum between perfectly rival and perfectly non-rival rather than at the extremes.
A highway provides an example of a good in the middle of this spectrum. If I am driving in the middle of the night when there is very little traffic, I am not affecting anyone else’s ability to use the highway, making it fairly non-rival under those conditions. However, a highway is not truly non-rival because when traffic becomes congested, rivalry begins to emerge as my use of the road directly affects others’ ability to use it.
Providing cell phone signal is another example of a good that is closer to non-rival. In normal circumstances, my use of the cell network does not noticeably reduce your ability to use it. However, at places like sporting events or the State Fair where demand concentrates, the service provider brings in extra cell towers to handle the demand, demonstrating that the good does have some rival characteristics even though it is closer to non-rival than many other goods.
Perfectly non-rival goods include academic research and fundamental scientific research. When Albert Einstein figured out that energy equals mass times the speed of light squared, this knowledge became endowed to everybody. My ability to use that equation in my own research and thinking does not reduce your ability to use the same equation.
The Spectrum of Excludability
The second spectrum is excludability, which concerns the ability to prevent people from consuming a good, based on access rather than on the consumption itself. With an excludable good, it is possible to prevent people from consuming it through various mechanisms like fences, property rights, or locking something in your house. However, excludability is also a spectrum rather than a binary characteristic.
On the highly excludable end are ordinary private goods like apples or private property. Some natural resources like rivers fall somewhere in the middle of this spectrum. In Minnesota, for example, property owners can legally exclude people from accessing rivers through their own land, but they cannot exclude people from walking down the river itself because the river is considered public property.
Safety from police presence is an interesting case on the excludability spectrum. Having a safe society because of police presence means you cannot exclude someone from benefiting from that safety, yet the police may be more effective in certain locations with higher property taxes, creating some excludability based on where you live.
On the fully non-excludable end, consider a factory that sets up equipment to do direct air capture of carbon dioxide from the atmosphere, thereby reducing climate change damages. The factory owner cannot capture all the benefits of their carbon removal efforts because everyone benefits from the lower global temperatures that result. The benefits are completely non-excludable.
Donations provide another interesting example of excludability. When the instructor donated to NPR, it did not change their ability to consume NPR content, nor did it unlock any paywall or exclusive access. From a pure utility maximization perspective, this behavior seems irrational, but the example highlights that humans are more complex and multifaceted than the simple utility maximization model suggests.
Four-Quadrant Classification of Goods
The instructor then presented a framework combining the two spectrums into a four-quadrant table with rivalness and excludability as the two axes, using environment-specific examples to illustrate each category.
High Rivalry and High Excludability: Private Goods
In the high rivalry, high excludability quadrant are bottled water and ordinary private goods. When water is taken from a lake and bottled, it becomes an ordinary market good with the characteristics of high excludability and high rivalry. If you drink one bottle of water, I cannot drink that same bottle, and we can exclude people from accessing it by charging a price that they must pay to obtain it.
A beautiful backyard provides another example in this quadrant. The property owner gets value from the backyard, and their neighbor also gets value from it by looking at it. However, the property owner can exclude the neighbor from enjoying the backyard by putting a fence around it and posting a no trespassing sign. In this way, an environmental good that was previously experienced as a public good becomes enclosed and converted into a rival private good through the establishment of property rights and excludability mechanisms.
Low Rivalry and High Excludability: Club Goods or Collective Goods
In the low rivalry, high excludability quadrant are collective goods, also called club goods. Cell phone signal is a perfect example because many people can simultaneously use the same signal without affecting each other’s ability to use it, yet it is relatively easy to exclude people from accessing it. When you go into a coffee shop and want to use the Wi-Fi, you need the password to access it. Similarly, the instructor pays Comcast a substantial amount of money every month for internet access, and Comcast has the ability to restrict access if the bill is not paid.
Low Rivalry and Low Excludability: Public Goods
In the low rivalry, low excludability quadrant are public goods, which are of significant relevance to environmental economics and the focus of considerable attention in this course. A wetland upstream of a city provides a good example of a public good with environmental value. As water flows through tributaries with wetlands, the plants literally clean the water by removing pollutants. Downstream, the city does not have to spend as much money on water treatment to make the water safe. Everybody in the downstream community benefits from this water purification service, and the city cannot exclude people from benefiting from it.
Clean air is another example of a public good. If I decide to emit less carbon dioxide, everybody benefits from the fact that I have reduced my emissions, and I cannot exclude people from benefiting from my emissions reduction. The benefits are non-rivalrous because your benefit from my reduced emissions does not diminish my benefit, and they are non-excludable because I cannot prevent anyone from benefiting.
High Rivalry and Low Excludability: Common Goods
In the high rivalry, low excludability quadrant are common goods, such as the commons or common-pool resources. A fishery is the best example of this type of good. The instructor described how their father owns a cabin on a lake in northern Minnesota because he loves fishing and values this activity highly enough to have purchased the cabin for this purpose. He particularly enjoys fishing at the beginning of the year when fish populations are at their highest levels.
However, professional anglers with expensive bass boats come to the same lake and compete for the fish. The professional anglers’ activities noticeably deplete the fish available for the instructor’s father to catch. This is an example of rivalness in the context of a common good because the professional fishers’ harvesting directly reduces the amount of fish available for others. This rivalry emerges because fish are a common good with low excludability, meaning that the lake owner or the state cannot easily prevent people from fishing there.
One main policy lever for addressing common goods problems is to restrict the number of fishing licenses issued. The Minnesota Department of Natural Resources can adjust the number of licenses sold when an area becomes overfished. In practice, they sell enough licenses that there is still some rivalry impact and some depletion, but this license system is how policy can begin to address the problem of overexploitation of common goods.
Key Conclusion About Market Failure and Individual Action
A key conclusion from this framework is that if market failure exists, which encompasses any of these situations where the welfare theorem assumptions do not hold, then individual actions pursuing self-interest will not lead to an efficient outcome. The invisible hand will fail, and some form of intervention or correction will be necessary to achieve socially optimal outcomes.
Political Economy of Environmental Protection
Balancing Objectivity with Values-Based Disagreements
The instructor acknowledged the challenge of teaching environmental economics while maintaining an objective stance on contentious political issues. In the introductory course, the instructor attempts to stay conceptually above rancorous political debate by illustrating the relevance of environmental economics concepts while allowing students to come to their own conclusions about policy. The instructor continues this approach in the environmental economics course, though it is more difficult because environmental protection issues tie closely to deeply held values that tend to be associated with one political party more than another.
Broad Agreement on Market Failure Existence
The statement that if market failure exists, individual actions pursuing self-interest will not lead to efficient outcomes is not controversial at all. The instructor estimated that ninety-nine percent of economists across the entire political spectrum would agree with this foundational proposition.
Disagreement on the Significance and Solution of Market Failures
What is different across the political spectrum is what comes next after acknowledging that market failures exist. Right-leaning economists acknowledge that market failures exist in theory because economic theory automatically leads to their existence. However, they argue that the specific conditions necessary for market failures to occur in practice are not common, so market failures are not a major problem requiring government action. In essence, their position is that while market failures may exist in theory, we do not need to do much about them in reality.
Another perspective from right-leaning economists is that while market failures certainly exist, government solutions to market failures might actually be worse than the market failure itself. In other words, the point is not to argue that a problem does not exist, but rather to argue that if your only proposed solution makes the problem worse than it was before, then that solution is not a good idea.
A positive approach that some right-leaning economists advocate focuses on fixing market failure problems through better assignment of property rights. The underlying idea is that clear and secure ownership of environmental goods gives people better incentives to care for them and use them efficiently. If water had no rivalness and people used it as a dump because nobody owned it, one potential solution is to increase property rights by taking things out of public access and putting them under individual or corporate control. Once property rights are clearly assigned and secured, people will have correct incentives to conserve the resource themselves without needing government intervention.
Government’s Role in Addressing Market Failures
In reality, the instructor noted that most market failures are fixed with government action. This is not a politically controversial statement across the political spectrum because it is simply true, whether people think it is good or bad. Governments create schools as public goods funded through taxes. They built and maintain roads, another public good. They establish military forces to provide national security, arguably the ultimate public good. They conduct antitrust enforcement to address market power issues and break up monopolies. They put mandates in place, such as requiring catalytic converters on cars to reduce air pollution. They use market mechanisms like taxes and cap-and-trade systems to address externalities. They employ liability rules where polluters are held liable for the damages they cause. But generally speaking, most of these methods assign property rights more clearly and then enforce those rights.
Nature of Solutions to be Studied
The instructor indicated that in the rest of the course, the analytical tools would be used to assess different solutions to market failures. The course would examine these various government approaches in detail in the second half of the semester.
Summary of Market Failure and Environmental Goods
Effectiveness of Markets for Ordinary Goods
With ordinary private goods in competitive markets, markets provide clear value signals so that price is a good metric for how valuable something is to consumers. Price accurately reflects the marginal utility and marginal cost of the good. Markets work well for ordinary goods, and we do not need special tools or policies to make sure ordinary goods are provided efficiently.
Failure of Markets for Environmental Goods
However, markets do not provide clear signals for most environmental goods because environmental goods have characteristics that violate the welfare theorem assumptions. Normal market logic that handles ordinary goods fine is completely inadequate for environmental goods. Environmental goods, where market failure exists due to public good or common good characteristics, need special treatment beyond what standard markets provide.
Systematic Undervaluation of Environmental Benefits
Without fixing our standard market approach, we will systematically undervalue or ignore the benefits that nature provides to us. Environmental goods provide massive benefits to human welfare but because they lack clear market signals and prices, these benefits are often not reflected in people’s decision-making. This leads to overexploitation of common goods and underprovision of public goods in the environmental sphere.
The Public Goods Game
Introduction to the Game
To illustrate the first market failure that would be discussed in detail in the course, public goods, the instructor organized an interactive game. Students would earn class points instead of money, which the instructor noted is actually more valuable to them. The game was designed to illustrate decision-making among individuals and how people choose between private-leaning and socially minded options.
Game Setup and Rules
The class would be divided into pairs or small groups for the game. The game would consist of six rounds total, with the first round being a practice round and the remaining five rounds being scored. Whichever team accumulated the most points would earn that many class points as a reward.
The setup involved giving each group 10 imaginary tokens at the beginning of each round. Collectively, each group had to decide how many tokens to invest in a private good and how many to invest in a public good. The payoff structure was designed to highlight the tension between private incentives and social efficiency.
Private Good Option
If a group invested tokens in the private good, each group member would receive 20 cents per token that they invested in the private good. Each group member was to write down on their table how many tokens they were allocating to the private good and immediately calculate and write down their earnings from the private account by multiplying the number of tokens by 20 cents per token.
Public Good Option
For the group good, every token that any group member contributed would generate 40 cents of aggregate value. However, the key feature of the public good is that the total value generated is summed across all contributions and then distributed evenly among all group members, regardless of how much each member contributed.
Practice Round
The instructor asked the class to debate among themselves and decide how many tokens each group would allocate to the public good and how many to the private good. They were instructed to write down a number large enough for the instructor to see indicating how many tokens they were allocating to the public good.
After collecting the contributions from the practice round, the total was 24 tokens across all groups. This meant 24 divided by 5 groups equals 4.8 tokens per group on average. At 40 cents per token, this yield $1.92 for each group member from the public good.
The instructor worked through the calculation for someone who kept 5 tokens for themselves. Those 5 tokens in the private good would be worth 5 times 20 cents equals $1.00. Adding the $1.92 from the public good gives a total of $2.92 for that person. The instructor asked if everyone understood the mechanics before proceeding to the real rounds.
Round 1 Results
For Round 1, which counted toward the final score, the total contribution to the public good was 17 tokens. Divided by 5 groups, this equals 3.4 tokens per group on average. At 40 cents per token, each group member received $1.36 from the public good. Students were asked to write down how many tokens they had kept for themselves but were instructed to keep this information private, as sharing would change the dynamics of the game.
Subsequent Rounds and Declining Contribution Trend
The instructor moved through the subsequent rounds quickly. Round 2 had a total of 15 tokens contributed to the public good, yielding an average of 3 tokens per group and $1.20 for each member from the public good. Round 3 came in at 11 tokens total, yielding an average of 2.2 tokens and earnings of 88 cents from the public good. Round 4 had 13 tokens contributed, yielding an average of 2.6 tokens and $1.04 from the public good. For the last round, described as being like the NPR Fund Drive coming to an end, the total was 18 tokens, yielding 3.6 tokens per group on average and $1.44 from the public good.
Calculation of Total Earnings and Public Revelation
Students were asked to sum up their total earnings across all rounds in a cumulative column. Then the instructor had each group publicly report their total earnings. The amounts reported were $8.28, $8.20, $13.92, $14.72, $9.72, and $16.28.
Winner and Explanation of Strategy
The two groups with the highest earnings, each getting 16 class points, reported earnings of $14.72 and $16.28. When asked about their strategy, one of these groups revealed that they contributed zero tokens to the public good every single round. When asked why they pursued this strategy, they explained that they could maximize their payoff by contributing nothing to the public good while still getting a share of the public good contributions made by everyone else.
Recognition of Free-Riding
Everyone else in the class was asked what they would call these two people. The response was “free riders,” and the instructor confirmed this identification. The instructor noted that ignoring considerations of morality, ethics, laws, or anything else about what is socially appropriate, the utility-maximizing thing to do in this game is indeed to always contribute zero to the public good while hoping others contribute. Therefore, the instructor said with a touch of dark humor, congratulations to the free riders for being true Homo economicus, the self-interested rational maximizer assumed in economic models.
Historical Pattern in the Game
The instructor showed a plot of average tokens contributed in this game over the last several years. The pattern showed that average contribution started relatively high in the first round but declined over subsequent rounds. The instructor noted that in past years, there have been some very nice people who contributed a lot to the public good, displaying altruistic behavior. Interestingly, the instructor mentioned that in all the years of playing this game, they had never seen anybody play a pure zero contribution strategy every single round until this particular class.
Discussion of Taxes as a Solution
One student raised an excellent point about taxes. In the game, a higher tax rate that forced people to contribute to the public good would encourage contribution to the public good provision. The instructor acknowledged this good observation and noted that the class would think about exactly that in the next sessions, after discussing all the different types of market failures. Taxes are definitely one very effective solution to public goods problems, among other solutions they would examine.
Conclusion of Game and Class
The instructor thanked the class for staying a few minutes after the scheduled end time to complete the game. The instructor noted that the game took longer than expected. The class would continue this discussion in the next session, thinking about how we can fix the problems illustrated by the game and how different solutions address the public goods problem.
Overview and Course Administration
Welcome and Lecture Structure
Welcome to Lecture 07B and 08. There is always some difficulty in aligning the lecture number with the slide numbers, which is the convention being used in this course. The lecture 7 slides were split into parts A and B, and this session will finish up part 7B before moving on to lecture 08, which covers externalities.
Today’s Agenda
The agenda for today involves picking up on the public goods question that was illustrated with an interactive game in the last class. Graphical analysis will be added to show how different demand curves can be aggregated, and in the case of a public good, how this will result in under-provision. An early semester course evaluation will be conducted to gather feedback on what is working and what is not in the course. Most of the day will hopefully be spent on externalities.
Assignment and Quiz Deadlines
Weekly Questions 3 was assigned in the last class, and the assignment deadline is the 16th. This information can also be seen on Canvas or in the Assignments tab. A new assignment will be assigned in class with a due date of Wednesday, the 18th of next week. Assignment 2 is due on the 18th, and the corresponding micro-quiz 2 will be held in class on the same day. The course uses a predictable micro-quiz structure where what will be on the quiz depends on what assignments students have completed, which helps with test preparation and studying.
Public Goods and the Free-Rider Problem
The Public Goods Game and Behavioral Economics
In the previous class, a public goods game was played where the best strategy for maximizing individual payout was giving zero every time. This particular class’s data is consistent with findings from one of the most widely studied behavioral economics experiments. Lab experiments have demonstrated this pattern across a wide variety of settings, at different income levels and in different countries. People typically start out contributing 40 to 60 percent of their tokens to the public good, but the contribution always seems to fall over time. This behavior appears to be something fundamental about human nature.
Rivalry, Excludability, and Market Failures
To understand public goods, it is necessary to tie this concept back to market failures and the broader framing of economics. The spectrum of rivalry and excludability is key to categorizing different types of goods. When players in the game had the choice on how to spend their public tokens, putting them into a personal account made it a standard good that was completely rival and fully excludable. The catch was that it was less valuable per token than the other option available.
In the game, any tokens put into the group account were rewarded twice as much, so they were more valuable. However, they had the attributes of being both non-rival and non-excludable. Even if someone free-rode and did not contribute their tokens, they still got their even share of the public good payout. This is why it is advantageous to do the privately optimal thing and hope that others will contribute. However, there is nuance in this debate because people are not just trying to maximize their own welfare. Some players in the game played a strategy that was good for everybody, and that really is how humans work in reality.
The Spectrum of Goods and Under-Provision
On the spectrum of goods, when tokens are put in the private good, the good is down at the end with full rivalry and excludability. When tokens are put in the public good, it has both attributes of non-rivalry and non-excludability. This is what causes the key conclusion about public goods: they will be under-provided unless something fixes it. There are two different ways to think about fixing this problem. First is how individuals can fix it through their own choices and strategies. Second is how society or governments can fix it through policy interventions. This class is not just about environmental doom and gloom, but about thinking through the policies that can address these problems.
Solutions to Public Goods Under-Provision: Individual Strategies
Playing Games Against Programmed Bots
For individuals, there is another game that was created to explore different strategies. There is a QR code so participants can play it on their phone, though it is probably better on a computer if one is available. Participants can go to the website and navigate to the game.
In this game, each participant plays a separate game against some bots that were programmed to behave like players do in class. The participant and the bots each choose how much of their tokens to put into the private good versus the public good. For now, the simplest case with default settings is being used. The key feature is a slider bar, which indicates how many of the 20 tokens each round will be contributed to the public good. If a participant contributes 10 of their 20 to the public good, they will keep the other 10 as private reward.
Participants choose a strategy and update it each round, playing 10 rounds quickly. As participants click and make choices, they see their own choice as well as the choices of the three bots they are playing against. The game interactively plots cumulative earnings and the contributions of all players over time. The goal is to keep playing until the round goes to 10.
Strategic Interaction and Observable Behavior
This is a tricky game because the bots are observing what the participant does and reacting accordingly. Even if a participant knew the bots were reacting to them, they would not know exactly how the bots would respond. Would the bots be selfish or would they ignore the participant’s actions? In this case, the bots showed realistic behavior: starting with high contributions and decaying over time, with not much interactivity between the participant and the bots.
However, in the next assignment, participants will play with different options. If the opponents are conditional cooperators, the optimal strategy changes completely. It is no longer optimal to be selfish; instead, it is closer to showing good faith efforts by contributing to the social good in order to encourage the bots to do the socially optimal thing. For now, with the default setting, going selfish gives the best payout.
Beyond Homo Economicus
The point being made is that we are not working only with Homo economicus, which is a phrase describing an ultra-rational individual who is perfectly utility maximizing. However, that is not reality. When the class was surveyed after playing the game, most participants, except for one group, had some degree of non-Homo economicus behavior. They did something for a reason other than maximizing their individual welfare. In reality, there are other considerations that influence behavior: what will people think of me, and could I get my opponent to react positively?
So participants could still be selfish but have strategic reasons to play differently. This represents the first way to solve the public goods game: using strategic interaction. Behavioral economics shows interesting richness in these kinds of scenarios. Game theory will be returned to later in the course, and concepts like the Coase Theorem will be discussed to illustrate other approaches. For now, the key point is that private solutions to the public goods game can involve playing strategically and considering the reactions of others.
Solutions to Public Goods Under-Provision: Government and Society
Need for Graphical Analysis
The more interesting question, which will receive more time in the course, is how society can fix the under-provision of public goods. If we really want to fix this problem, we need to understand it, which means drawing some graphs. Another web app has been created and is accessible by QR code on the website. It is probably best to access it on a laptop so that participants can play along with the graphs being presented.
Public Goods Analysis: The Parks Example
Suppose we are considering a specific public good: parks. The quantity Q represents the quantity of parks in the area, though we leave it ambiguous whether that refers to the total size, the number of parks, or something else. The vertical axis represents dollars, which signify the price or marginal cost of producing parks. Let’s assume there are no increasing returns to scale in park production. Instead, it is a constant marginal cost of, say, $5 per unit of park.
To figure out the optimal amount of parks to provide, we need to know the marginal benefit for individuals. The marginal benefit curve shows the marginal benefit for the ith individual, denoted MB_i. It follows a standard marginal benefit curve: it starts high because one park would be very popular, but more parks provide less benefit each additional unit. This marginal benefit curve also represents the price someone would be willing to pay for each additional park.
With only one person, the optimal amount of parks would be where marginal costs equal marginal benefits. This person would be willing to pay $5 for that amount, and it costs $5 to build, so it is optimal. However, that scenario is too simple and not really a public good because there is no public. So let’s consider the case with multiple people.
The Publicly Optimal Solution with Multiple Individuals
Let’s say N equals 2, with two individuals having identical marginal benefit curves. To determine the socially optimal outcome, we need to calculate the aggregate marginal benefit, which is done through vertical summation. With two people, we simply double the height of the individual marginal benefit curve. The aggregate marginal benefit curve equals the sum over all individuals i of the marginal benefit of each individual.
If we express MB_i in inverse demand function style as a parameter A minus B times Q, then the societal marginal benefit becomes two times this, because it is identical for each person. We can calculate the optimal quantity by setting this aggregate marginal benefit equal to marginal cost.
Market Failure: Under-Provision Without Government
Before calculating the optimal quantity, let’s discuss what would happen without government intervention. Suppose a private park-building company wants to come in and provide parks. Like any profit-maximizing firm, they would only produce if they can make a profit. One person would be willing to pay $5 for the first park, and they might build it. However, because this is a public good, there is a free-riding problem. As soon as someone pays for access, the marginal value for the other person goes to zero, because they already have access to the public good. So they will not pay anything extra.
What we see in this market failure scenario is that the first unit gets built, then nobody buys anything else. It stops at a very low quantity. Some parks exist, but not enough compared to what society would want. This leads to deadweight loss.
Calculating Deadweight Loss
To calculate deadweight loss, we look at the area under the marginal benefit curve but above the marginal cost curve. If we only have Q_M from the market solution, we get only a small area below marginal benefit. But if we had Q* for the societal optimum, we would get a much larger area of total welfare. The triangle remaining between what we have and what we could have is the deadweight loss from under-provision.
As N increases, the deadweight loss also increases. With N equals 3, deadweight loss grows from 3.1 to 8.3. With N equals 20, there is enormous deadweight loss from the under-provision of this public good. This demonstrates that as society gets bigger and more people benefit from public goods, it becomes increasingly costly not to provide them at the socially optimal level. The more people that can benefit from a public good, the greater the welfare loss from under-provision.
Policy Solutions to Public Goods Under-Provision
Privatization as a Market Solution
How do we solve the under-provision problem? Well, one solution involves privatization of the public good. Consider indoor playgrounds as an example. These are provided by the market, even though we said earlier that private markets would not provide parks in general. The key difference is that firms charge an admission fee of $10 to get in, thereby privatizing the space and making it excludable. They can make a profit because they collect fees from users, so the market provides it willingly.
However, this solution only works when you can actually privatize the good. What about things that you cannot privatize, like climate reduction, military protection, or research and development? These goods have characteristics that make privatization impossible or impractical. In those cases, we must move into government solutions.
Subsidy-Based Solutions
On the web app showing the parks example, there are a couple of policy options available to explore. The first is a subsidy approach. A lot of environmental economics involves calculating optimal subsidies to correct market failures. If private parks undersupply the socially optimal amount, the government can pay private firms a subsidy for each park they produce. As the subsidy rises, deadweight loss decreases. If a government sets the subsidy at exactly the right level, it can eliminate all deadweight loss and achieve the socially optimal outcome.
Direct Public Provision
The second, and often more common, solution is direct public provision. Rather than subsidizing private firms to produce the public good, the government can simply provide the good itself using tax dollars. The government chooses exactly how much to provide to the population. If the government provision is well-designed, it can minimize deadweight loss and achieve efficiency. This approach takes the good entirely out of private markets and under government control.
Transcript (Day 1)
Alright, let’s get started with Chapter 7, Market Failures and Public Goods. I’ve done a little bit of reorganizing; this used to be externalities, but I decided I wanted to do public goods before externalities because I really like them, both the concept and actually most public goods I tend to like.
That’s what we’ll talk about today. But first, before we dive into that, we need to finish up one last thing from optimal pollution, which is the firm-differentiated optimal pollution thing that we started talking about last class.
Then we’re going to introduce the general concept of market failure. You almost certainly saw this in your principles class, but we’re going to dive in with more detail because it’s so central to environmental topics.
Then we’re going to play a game, for real this time, and it will be illustrating what we’ll talk about next, which is public goods, the first of our environmentally important market failures.
A couple logistical updates. Unfortunately, due to high demand for earth economy modeling, I was not able to post the homeworks on Friday, so you don’t have anything due. If you don’t see it go up on Canvas, assume it’s not going to be due. I’ll assign the weekly update after class here, so expect to get a Canvas announcement about that.
Secondly, I wanted to update on class points. This is a new thing I’m trying out again. Remember, you can spend them: 10 points gives you a free pass with full credit on an assignment, or 5 points if you just want an extension without any explanation. I added them all up. Our current standings are: Riley has 2, Alex has 1, Jackson has 2, Victoria has 6, Gabby has 2, and Jordan has 2. That’s where we’re at.
Any questions? We all good? All right.
The other thing is, I forgot, I do still want to implement the early semester course evaluation. I didn’t get the Google Form together in time, so we’ll do that tomorrow.
Diving right in. We spent a whole lot of time the last couple of lectures talking about pollution. That’s a very central issue in environmental economics, obviously. But I want to revisit what we’ve done, which was aggregating the MAC curves for multiple firms, but I want to jump straight to the question of what’s the right policy when you have asymmetric firms.
So let’s get a quick reminder of what we’ve got. We’re going to have emissions on one axis and dollars or costs on the other. In this particular case, we’re going to have two MAC curves. One that starts at 6, and one that starts at 12. And they’re both going to slope down to the main point.
Our question is going to be: what is the optimal policy? That’s basically where we got to, now adding a bit more detail. One thing we did add last lecture is we talked about how we’re going to be summing these. The aggregate curve, marching down the dollars, has only one firm in this area, so it’s here, but as soon as we cross that point of 6, now we’re going to be adding however wide this line is onto that line. So the graphical way to do it is we take that much and add it there. But another, perhaps better way of doing it is calculating the intercept. That becomes our aggregate MAC curve.
Now, what I want to do is take that and address the situation where we have a goal. The EPA says that we need to get emissions reduced from the current amount, which is 12 (that’s the current level with business as usual), down to 9 units. What’s the cost-effective way of doing this?
The first thing I want to show is what would happen if they didn’t consider cost-effectiveness and instead just said that every firm needs to reduce by a certain fixed amount. We’re going to show that that’s not optimal, and that having firm-specific reduction amounts will be better.
Let’s do it in math using these curves. The actual curves are: MAC A equals 12 minus 2 times emissions, and MAC B equals 6 minus E sub B.
The first step is to aggregate these together. But I’m just going to go straight to the rule for solving the optimal emissions.
The key decision rule is this: for optimal pollution, set the MAC curves equal to each other.
So here is another example of why economists love thinking on the margin. It gets really complex if you think about it in totals, but if you just follow this simple rule, optimal pollution can be figured out. What is the optimal emissions reduction for each firm? You find it by solving for the situation where the two different firms have equal marginal abatement costs.
What does this look like? Well, we’ve got these curves, so we’re just going to set them equal to each other. So 12 minus 2 times E sub A is going to be equal to MAC from firm B, which is 6 minus E sub B.
You can solve this one pretty easily. Let’s move the 6 over, so 12 minus 6 is 6. And the minus 2 times E sub A goes over there, so that becomes positive. We get E sub B equals 2 times E sub A minus 6.
The last thing we need to solve this is the mandate. We know that the EPA wants to reduce emissions from 12 down to 9, so we have one extra equation: E sub A plus E sub B equals that desired 9.
We’re going to substitute in the definition for E sub B. We get E sub A plus (2 times E sub A minus 6) equals 9. We combine like terms. 3 times E sub A equals 15, so E sub A equals 5.
Once we get E sub A equals 5, we also have what we need for E sub B, because of our rule from the EPA that E sub A plus E sub B equals 9. Plugging in E sub A equals 5 implies that E sub B equals 4.
And so in this particular case, Firm A is going to reduce emissions by 1, and Firm B reduces by 2, because they were both producing 6, and now they’ve gone down to 5 and 4, respectively.
The reason for having a different amount of emissions reduction from each of these firms is simply that one of the firms is better than the other one at reducing its emissions. In fact, it’s B. We can really see that because the slope of the MAC curve was only negative 1 instead of negative 2.
The decision rule, put graphically, shows that the MAC curves are set equal to each other for the two firms. The numbers in the example may differ, but it shows the same results: we’re going to get different levels of abatement according to how good the two firms are.
So the conclusion all comes down to this: efficient pollution reduction is achieved where the MAC curves are all equal to each other. In addition, the firm MACs should be set equal to each other.
Put in straightforward English, that simplifies down to: we should clean up pollution until the last unit cleaned up costs exactly as much as the damage it avoids.
Any questions on this?
I do have a fun little interactive tool. I’m still building these out, but haven’t incorporated them into the course fully, so you can find that under the games. This one will show you solving for different optimal strategies with different curves you can play around with, but I won’t pull that up dynamically.
Moving right along then to the big pivot in the course. We’re actually entering a new part of the course, and this will be about market failures.
Market failures are super common in things relevant to environmental economics. In particular, we’re going to be talking about different types of them. But I want to give a general framing of them first.
The definition is just any case where individuals pursuing their self-interest doesn’t result in a socially optimal outcome. Individuals pursuing selfish behavior, or let’s just call it private interests, and this literally just means doing their utility maximization in the way that we’ve said. So basically, if individuals are setting their indifference curves equal to their budget constraint, that’s pursuing their private interests. A market failure is saying that this will lead to suboptimal social outcomes.
In other words, the invisible hand is not going to work. We spent all that time on the welfare theorems because under those really restrictive assumptions and considerations, the argument was strong that the free market left unconstrained will be pulled as if by an invisible hand to something that is good for everybody.
Here now, we’re going to start to have more realistic assumptions. And in this particular case, it’s going to basically be that there are examples where this private interest, just letting it happen, does not produce the best. So it’s basically saying the welfare theorem does not hold here.
I just copied and pasted those assumptions. You don’t have to write them down again, but those are the assumptions that were necessary for the first welfare theorem and the invisible hand to work.
When we’re going to talk about market failures, it’s basically systematically violating each one of those different assumptions. So the examples of market failures are things like public goods or public bads, impacts on external parties, commons problems, market power like monopoly, monopsony, oligopoly, or asymmetric information. These are all examples where we’re basically violating the welfare theorem. And so it’s not too surprising that the welfare theorem doesn’t hold anymore.
Market failures, that’s the definition in words. But it’s all going to come down to two different spectrums of what type of good we are thinking about.
Spectrum 1 is rivalness. What is rivalness? Well, rivalry just means we’re in competition. Now, in this case, for a rival good, it’s just the sort of ordinary case where one person consuming it lowers how much somebody else can consume it. This is the ordinary case.
An apple might be an example of a rival good. If I eat that apple, you can’t eat that apple. A hammer is also pretty rival; maybe we could pass it back and forth. But it’s really a spectrum, from these rival goods, where my consumption lowers how much somebody else can consume it, to on the other end, non-rival goods, where one person consuming it doesn’t lower how much somebody else can use it.
In Econ 101, we usually talk about just the two extremes, but in reality, almost all goods are somewhere in between.
Getting a little closer to a non-rival good is a highway. If I’m driving down the highway in the middle of the night and there’s not much traffic, I didn’t affect anybody else’s ability to use it. And maybe when there’s medium traffic, it’s still true that everybody’s still able to drive their preferred speed. But at some point, it starts to get congested. So this would be an example where it’s not really fully non-rival. There starts to be some rivalness.
Another one might be providing cell signal. Me using my cell phone doesn’t reduce your ability to use your cell phone. Except, have you ever been at a sporting event where actually it does? Usually they do a pretty good job, but you might have noticed outside of Huntington Stadium or the State Fair, they bring in extra cell towers. So they do a decent job of mitigating it, but it’s closer on the end of the spectrum to being non-rival.
Some examples of perfectly non-rival goods would be academic research, fundamental research. When Einstein figured out E equals MC squared, that became something that is endowed to everybody. You might try to protect it with things like patents, but eventually information becomes free, and my ability to use that equation certainly doesn’t reduce your ability to use that equation.
So that’s the definition of rivalness.
Spectrum 2 is excludability. Excludability is not about the consumption of the thing, but about the access to the thing. If you have an excludable good, it’s possible to prevent people from consuming it. That’s pretty straightforward, like a fence, or property rights, or it’s locked inside my house. Those are all good ways to exclude somebody from consuming it. If I have my apples and they’re inside my house, you can’t get them.
But indeed, it is a spectrum. On the excludable end of things would be ordinary goods like apples, maybe even the ability to use public space or a river. Rivers can be sort of excluded. Here in Minnesota, you can legally exclude people from getting access to the river through your land, but you can’t exclude them from walking down the river to get to that same part, because the river itself is considered public. So it’s a little bit less excludable.
Safety from police presence is another example. Having a safe society, you can’t exclude somebody from benefiting from that. But maybe you can to some extent, because maybe the police are more effective in certain locations than others where they have high property taxes.
Then on the other end, fully non-excludable, is if somebody sets up a factory and does a bunch of direct air capture of carbon in our atmosphere. It’s going to reduce damages from climate change, but that one person doesn’t get all the benefits. They get a tiny bit, but everybody gets the benefits because it lowers the global temperature for absolutely everybody. So that’s on the other extreme end.
I put donations here because of donations to NPR. Who’s ever donated to the NPR Fund Drive? I did once, and I don’t know why. It doesn’t change anything about my behavior. The marginal impact on my ability to consume NPR did not change. It’s not like it unlocked a paywall or something. I just did it. I was totally irrational from the perspective of utility maximization. I just wasted money.
I’m kind of joking, because this is just highlighting the true fact that we’ll deal with throughout: humans are actually more complex beings than simple utility maximizers, because if I was a pure utility maximizer, I shouldn’t have given to NPR.
So those are the two spectra. I want to now put them together and give some environment-specific examples.
This is what’s typically taught. It’s going to be a table where we have rivalness (high and low) and excludability (high and low).
Going through here, but using environmental goods as an example: bottled water. We can get water from the environment for free. If it’s in a lake, it would be pretty hard to exclude people, and there’s so much of it that maybe me drinking that water doesn’t much prevent somebody else from drinking. There’s an extreme circumstance where if we really depleted the lake, it could start to be rival.
But let’s use the simplest example: bottled water. We did something to it. We took it out of the lake, we bottled it, and now suddenly it’s an ordinary good. It’s rival. If we’re talking about just the single bottle of water, certainly me drinking it means you can’t drink it. But also it would be very easy for us to exclude people from having it, like having it have a price at the convenience store. It’s not free. So that’s the standard good.
Another one we’ll talk about when we get more into ecosystem services is what if I have a beautiful backyard and I get a ton of value from it, and also my neighbor gets a ton of value from it. Is this a private good? It depends. Could I exclude them from viewing it? If I put a fence around it and say no trespassing in this beautiful land, I’ve now taken something that might have been public and made it rival. And so that’s a way that you can enclose an environmental good and make it a private good.
Collective goods (sometimes called club goods): I said I would use environmental ones, but I couldn’t think of a good one here. So ignoring the case where we are at the State Fair and we’ve actually run out of cell phone signal, cell service is a perfect example of a collective good. It’s one where it is not very rival. A lot of people could be using it and hardly affect somebody else’s ability to use it. But it’s really easy to exclude people. You go into the coffee shop and you have to get the Wi-Fi password. I pay a lot of money to get access to Comcast’s services. Even though it doesn’t deplete other people and their ability to use that service, Comcast definitely is able to restrict me from using it if they didn’t want me to. So that would be an example of a collective good.
The next one is going to be super relevant to where we go next in this course: common goods. A common good is anything that is like a commons if you’ve ever heard that word. A fishery is the best example of that: an open access fishery.
My dad has a cabin on a lake in northern Minnesota because he loves fishing. He enjoys catching these fish with a high dollar value; he expressed that value by buying the cabin in the first place. But the nature of fish, if you’ve ever asked a fisher person, is they can be overfished. So he loves going at the beginning of the year when the populations are full.
They actually have tournaments on his lake where a bunch of really professional anglers will come in with their super expensive bass boats and will noticeably deplete the number of fish available for him to catch, and he doesn’t like this.
This would be an example where there is definitely rivalness. These professional fisher people are depleting that resource; he now has less of them to get, and that’s because it’s a common good with low excludability. If he could somehow have the whole lake to himself, there’d be no boat fishing tournaments going on.
Student question: Could you restrict the number of fishing licenses?
Exactly, and so it is a spectrum. You certainly could restrict the number of fishing licenses out there, and in fact that’s one of the main policy levers that people would use. If the DNR, Department of Natural Resources here in Minnesota, discovers that an area is overfished, that’s a really easy thing to do: just dial back the number of fishing licenses they’re willing to sell.
In reality, they often sell so many that it still has a rivalness impact on him. But that’s a great point, and we’ll come to policy as we go throughout this course. Generally speaking, it’s pretty low on the excludability spectrum. They have public boat launches. Another way would be to get rid of the public boat launches so only the people who live on the lake can do it, but our government has decided that’s not a good thing.
The last one, with low excludability and low rivalness, is called a public good. An example from the environment would be a nice wetland. Why might that be a good public good? If there is a wetland upstream of a city, it’s real easy to show it provides value to that city insofar as it cleans up the water. As water comes from the tributaries and goes through watersheds that have wetlands in them, the plants will literally clean the water. The benefit is that downstream you don’t have to spend as much money on treating that water to make it drinkable. But the presence of that public good is something that everybody will benefit from, so it’s low rival. And there’s no way to exclude people from benefiting from it.
Another one that’s probably better is the idea of clean air. I just didn’t have a good picture of clean air because it turns out you can’t see clean air. But if I clean up air, if I emit less carbon, everybody benefits from it, and I am not able to exclude them.
A quick side note on there being spectra involved: a lot of these are mixed goods. They’re not going to actually fall cleanly into the four categories. You could probably get rid of those lines. It’s not a table; it’s like an actual plot. Any given good could be somewhere on this, and apples would be farthest up here, and different things like the climate commons would be down here.
The key conclusion is that if market failure exists, if any of these things happen, or if any of those assumptions that we put forth don’t hold, then individual actions will not lead to an efficient outcome.
Let’s talk about politics. When I teach my 101 course, I try to stay conceptually above the rancorous political debate you often see. I’ll try to elucidate it because it’s super relevant, but let people come to their own conclusions. I’m going to continue that in environmental economics.
Even though it’s a little harder. It’s harder because we’re talking about environmental protection, which itself is tied with a common set of values that is more likely to be held by one political party than the other, just statistically speaking. But I’m going to argue throughout, and try to be clear on this, that the tools themselves are really quite agnostic. We’ll try to expose the underlying value differences.
And that’s important. But I can’t argue with somebody saying their values are wrong. If somebody really likes private access and lower provision of public goods, that’s their right to prefer that. But I’m still going to try to clarify where the environmental economic precepts that we can get from this hold.
On that note, I just want to say that this statement that if market failure exists, individual actions won’t lead to efficient outcomes, is not controversial at all. 99.9 percent of economists would agree with that from all different parts of the political spectrum.
What’s different is the things I’ve listed below. Right-leaning economists would acknowledge that market failures exist. The theory automatically leads to it. It’s just that the conditions for it to happen aren’t that common. And so it’s not really a big problem, and so sure, it exists theoretically, but we don’t really need to do much about it.
Or another view is that maybe market failures do exist, but the government solution might just be worse. It’s one thing to say a problem is bad, but if your only solution will actually make it worse, that doesn’t seem like a good idea either, so maybe we should just let the market failure fail.
I’m underlying that key point, but they don’t question, even under those two cases, that the market failure, if it exists, still leads to inefficiency.
The final one, and this is on a more positive note, is people on the right side of the economic spectrum of political beliefs tend to focus on the idea that you can fix the problem by better assigning property rights. We’ll return to this, but the idea is if you have clear ownership of environmental goods and services, people will have better incentive to take good care of them.
If we had an environmental good like water that had no rivalness to it, people might use it as a dump, putting pollution into it. But what would one solution be? Increase property rights on who owns that. In essence, take things out of public access, put them in the hands of individuals. The conservative-leaning economists would argue that once those property rights are secured, people will have the correct incentives to do the conservation themselves.
So that’s property rights. In reality, most market failures are fixed with government action. This is not politically controversial either. I’m not saying it’s right or wrong, but it is true that most market failures are fixed by government action, and the environment is no exception to that.
In the rest of the course, you don’t need to write these down, we’ll be using our tools to assess these, but just to give you a few examples to motivate us: the government creates schools, roads, armies, those are all public goods that our taxes go towards.
They also do antitrust enforcement, they break up monopolies (although less and less). They simply put mandates in place, like saying cars have to have catalytic converters. That reduces the emissions, but it’s just a law; you have to do it. You can’t produce a car or sell a car in the U.S. without this thing that reduces the emissions.
They might try market mechanisms like taxes or cap and trade, which we’ll learn a lot about. They might have liability rules, like if you pollute my yard, you are liable for the damages it causes me.
But in general, most of these will be methods to properly assign property rights and then enforce them. That’ll be the second half of the semester when we dive into those.
To summarize this all up: with ordinary goods, with private goods, markets do provide a clear signal of value for these goods, and that means we can use the price as a good metric for how valuable the thing is.
But markets do not provide clear signals for most of the environmental goods. Another way of saying this is, fundamentally speaking, normal goods we don’t really need to worry about with these special tools we’re going to learn in environmental economics, because ordinary market logic handles them pretty well.
But these ones, where there is failure, this is where environmental goods tend to be. And so that’s the fundamental reason why, if we don’t do something to fix our standard market approach, we will systematically undervalue or ignore what benefits nature gives to us.
With that, I want to play a game. Let me pass this out. This is a game that’s going to illustrate the first of our market failures, which we’re going to talk about, public goods.
It says you’re going to earn money, but instead of money, you’re going to earn class points, because then I don’t have to pay for them. The class points are even more valuable.
The first thing is we’re going to pair up. We have an even number. Could you two pair up? You two? And you two? Go ahead and relocate yourself so that you can sit next to the person. You don’t need to bring your computer or anything.
This is going to be a game in which we illustrate how decision-making among individuals works, and how people might choose to be private-leaning or socially-minded. We’re going to play this game six rounds. The first round will be a practice round, just so we make sure we got the rules right. And then if you notice on the back of your sheet, there’s a table. We’re going to record the results of what you do. There’s the practice round and then five real rounds.
After we finish the game, whichever team has the most payoff gets that number, as class points. So you might get out of one or two or even three assignments if you want, if you do a good job here.
What’s the setup? We have 10 people, so the math will be easy. It’s going to be split into 5 groups.
At the beginning of each round, I’m going to give you 10 imaginary tokens. Just keep track of it in your head. I don’t actually print out tokens, but you could. And you’re going to make a choice, collectively as a group. Each pair of people will decide, of those 10 tokens, how much should be invested in a private good or a public good.
If you invested in the private good, you get 20 cents for each token you invested. You’ll jot it down on your table in the back: how many tokens you put towards your private account versus the group account. Then you can write down your earnings from your private account right away, because that’s just 20 cents times however many tokens.
But to get the amount you get from the group, we’re going to see how much the whole class contributes to the public good. And the sort of catch is, for every token that is invested in the group good, it generates 40 cents of value. So it’s just better at producing value than the private good. The catch is we’re going to sum up how much value was generated from all of the group commitments, and then distribute it evenly among everybody. Once we get the total, then I’ll tell you what you can put in your column for earnings from your share of the group account.
So that will be one round. You can sum up the round, and then you’ll also keep track of the cumulative. Whoever has the most cumulative points at the end, that’s how many class points you will get.
One last logistical note: technically speaking, you’re not supposed to be able to see how much other people contribute. This is like contributing to NPR, but I guess they have those stickers you can put on your car, so it’s not quite that way. What you’re going to do is write it on a sheet of paper big enough for me to see, and that will be how many tokens you contribute to the group good.
Alright, so let’s try that practice round. Everybody, debate amongst yourself and decide how many tokens should go to the public and how many should go to private accounts.
I’m going to cut discussions short because it’s just a practice round. If you could write down a number big enough for me to see for how many you are contributing to the group. Can you hold up your numbers please?
5, 5, 4, 14, 19… So we got to 24. So 24 divided by 5, you can write 4.8. In your earnings from the group, that’s your payout of the group contribution split evenly among all the people, and then whatever you got yourself.
When you did 5 and 5, you would get $4.80 from the group, from your payout of the group contribution split evenly among all the people, and then whatever you got yourself. If you kept 5 for yourself, each one of those is worth 20 cents, so you’d get an additional dollar, and so you would write in the total earnings $5.80 in that case. That was the practice round. Everybody got it?
Alright, let’s do it for real. This is for real class points. Make a new decision for your Round 1 allocation of public versus private. I’ll give you 10 seconds. And this time, write it a little bigger if you could. This time, I also won’t be saying what everybody got; I’ll just be keeping track of it.
For this round, we had 17 total contribution. We’re going to divide that by 5. That means on average it was 3.4, and each one of those is worth 40 cents, so 3.4 times 0.4, your earnings from the public component is $1.36. Everybody gets $1.36. And then however many you kept, you write that down.
Now we’re going to keep this information private. So you don’t have to tell anybody. Things might change if you did, but let’s do it again. Let’s do round two. Write down another number. We’re going to go a little faster this time.
This time we have 15 total. So that divided by 5 means it was 3 on average. 3 times 40 cents equals $1.20. Everybody gets $1.20. Write that down.
Let’s go fast so we don’t have to go over time. See you in the next round. Remember, whoever gets the best cumulative amount wins.
Round 3 went down to 11. 11 divided by 5 is 2.2 on average, times 0.4, 88 cents.
Doing another one. We are at 13. 13 divided by 5 times 0.4 is $1.04. Went up a little bit.
Now for the last round. This is round 5. Make your last contribution. The NPR Fund Drive is coming to an end.
We went up a little bit, 18! So 18 divided by 5 is 3.6 on average. 40 cents each, $1.44.
Sum up your totals. Hopefully you’ve been keeping track in the cumulative column. And now we are going to go public with the information. You’re going to say it out in front of everybody. How much did you all make?
$8.28. $8.20. $13.92. $14.72. $9.72. $16.28.
You both get 16 class points. I’m going to round it to 15, just… no, you can have 16, I’ll just keep track of that.
So what was your strategy? Zero every time. Why is that? What was your reason?
Because you could maximize your payoff by contributing nothing to the public good while still getting a share of the public good contributions made by everyone else.
Everybody else, can you think of a label or a word that you would call these people? Evil, okay, something more economics-y? Calculated, yeah. We have a special word for this: free rider.
You guys were free riders, and the unfortunate nature of this is if you ignore morality, evilness, or laws, or anything else, the utility-maximizing thing is indeed to always play zero. So congratulations, you are Homo Economicus.
I just want to end with here’s a plot of the last few years. This is expressed in average tokens. Every year, it’s gone down. I’ll plot these values again, but we were pretty similar. We started high. We actually had a little bit of very niceness. We had some people who contribute a lot to NPR.
Can you say anything about your strategy? You were very altruistic. And so that’s another finding here, is that in reality, though it is true that that’s the optimal from the standard economics perspective, real human behavior is rarely that straightforward. I’ve actually never had somebody play the zero-zero-zero strategy until now.
Student comment about higher tax rates.
Yep, would you argue for a higher tax rate? Is that related? Oh, in the game, yes! Excellent.
I have to encourage people… Yes. I will leave you with that thought, and that’s a very good point, and that’s where we’re going to go next, actually, so thank you for raising that. We’re going to start to think, after we’ve talked about all the different market failures, how can we solve them? And pro tip, tax is definitely one of the very effective solutions to this.
Alright, well, thank you everybody for staying a few minutes after. That took longer than expected. I should have given you markers so you could draw a big number easier and go around. But we will talk about this a little bit more next class, and think about what can we do to fix this.
Assignments are still being graded by the TA, but I should have them to you by Wednesday.
You can keep the paper.
Transcript (Day 2)
All right, everybody, welcome to Lecture 07B, and then on to 08. It’s a little hard always aligning the lecture number with the slides numbers, so that’s my convention. The lecture 7 slides were split into A and B, and so we’re just going to finish that up. That’ll be part 7B, and then we’ll move on to 08, which will be externalities.
Thinking about the agenda for today, we’re going to pick up on that public goods question that we illustrated with that interactive game last class. The thing we’re going to do is add some graphical analysis to it, showing how we can aggregate up different demand curves, and in the case of a public good, it will result in under-provision.
Then, I finally do have that quick early semester course evaluation, a chance for you to give feedback on what’s working and what’s not. And then hopefully we’ll spend most of the day on externalities.
Quick note about deadlines and stuff. There are slides from the first part of 7, and you can see 7B is under today’s thing. Hopefully you all saw that the Weekly Questions 3 was assigned last class, and the assignment deadline is on the 16th. You can also just see this on Canvas, or you can go over into the Assignments tab where deadlines and stuff are there too.
The new one that we’re adding is today. I will be assigning Assignment 2, and that again is going to be the one that you do at home however you want. Then on Wednesday of next week, the 18th, that’s when Assignment 2 is done, and the corresponding micro-quiz 2 will be had in class.
Any questions on the schedule?
Do you like this micro quiz structure, where it’s very predictable what it’s going to be, at least if you did those? Why am I asking now? I’m literally going to have a web form where you’re going to fill out this feedback, so I guess I shouldn’t just be ambling randomly. Nonetheless, let’s dive right in.
So yeah, where we left off last class, we played that public goods game, where the best strategy, it turned out, from the perspective of maximizing your payout, was giving zero every time. What I want to say is that this is data here from this particular class.
But this is one of the most widely studied behavioral economics experiments, and lab experiments have also shown this. They show it in a wide variety of settings, at different income levels, different countries. People start out contributing to the good. Between 40% and 60% of their tokens will go towards it.
But it always seems to fall, and so this seems to be something fundamental about human nature.
I want to tie this back to market failures and this broader framing we have. We talked about the spectrum of rivalry and excludability, and basically, when we had the choice on how to spend our little tokens, if you put them into your personal account, that essentially made it a standard good, right? Where it was both completely rival, you got that, nobody could take it from you, and it was fully excludable that you could prevent other people from having that score count towards them.
The catch was it was less valuable per token than the other option. In the game that we played, any of the tokens that were put into the group account rewarded twice as much, so they were more valuable, but they had this attribute of being both non-rival and non-excludable. That’s because even if someone free-rode, they still were going to get their share, their even share, of the public good payout. And so that’s why it’s going to be one where it’s advantageous to do the privately optimal thing and hope that there are some suckers who will contribute. But I also like that we already had the nuance in the debate of, yeah, well, we’re not just trying to maximize our welfare. I like that you both played, for instance, a strategy that was good for everybody, and that really is, in fact, how humans work.
Just putting it for a second on our actual spectrum of goods, all I’m saying is that when you put your tokens in the private good, you are down here with full rivalry and excludability. The problem is, when you put it in the public good, it had both of those attributes of non-rivalry and non-excludability, and that is what causes the key conclusion about public goods, which is that they will be under-provided unless something fixes it.
So I want to talk about two different ways that we might be able to fix this, because this class is hopefully not just going to be environmental doom and gloom, but thinking about the policies. We’ll get into that more and more as we go through the semester.
We’re going to talk about it first, how can individuals fix it, and then we’re going to move on to how can society or governments fix it.
For the individuals, I want to point to yet another one of our games. I’ll put up a QR code so you can play it on your phone. I’m actually curious if the user interface plays out well on your phone. It’s probably better on your computer if you have that out. You can just go to the website and navigate to it as you would like.
In this particular game, you’re each going to be playing a separate game, and you’re going to be playing against some bots that I have programmed. These bots are going to be playing strategies about exactly the same as we did in class, where you and the bots will be choosing how much of your tokens you would like to put into the private good versus the public good.
Just to orient you to the user interface, for now, we’re going to do the simplest case, where it’s just all the default settings here. If you’re on mobile, I think you have to scroll down a little bit because it collapses. The key thing that you’re going to have is this slider bar. This indicates how many of your 20 tokens that you get each round you’re going to contribute to the public good. So if we were to click the submit contribution button here, this is saying we’re going to contribute 10 of our 20 to the public good, and conversely, the other 10 will be paid out as the private reward.
So let’s just try this out quickly. Choose a strategy, you can update it each round, and I want you to play 10 rounds real quick, and I’ll do it too.
Don’t fiddle with these because then we’ll get different results. Just choose your amount. I’m going to be hopeful. And as you click, what you’ll see is your choice as well as the choices of the other three bots you’re playing against. I see that I was more generous than them. Better dial that back.
Then as you keep playing it, it’s going to interactively put out a plot of your cumulative earnings and the contributions of all the different players over time. Getting quite selfish here already. Just keep on clicking until the round goes to 10. We just have to stop there.
Now, when I’ve played that strategy, that sequence which is defined by the blue line, that’s my contribution, that’s my strategy. You maybe probably had a different one. As a result of that, we’re going to see the score up here. That’s what I scored. I got 223 utility, or whatever it is we’re measuring here. And hey, look, I slightly outperformed all of the bots.
First off, did that work on all your phones and computers? Cool, I’m getting better at web development, this is fun. Who got the best score? Who beat me at 223?
Anybody get higher than 223? Yeah? Anybody else? What did you get? 228, anybody beat that? You get 2 class points if you do. No one? What was your strategy?
Odders. Yes.
This is a tricky game because I didn’t really tell you what the bot behavior was, right? But you got the key thing, which is that the bots were observing what you did and reacting accordingly. But even if you knew that they were reacting to what you did, you don’t know how they were responding. Are they going to be selfish, or are they ignoring you?
In this particular case, what it illustrates… so nobody beat 228? Well, who got low? Anybody get really low? Nobody wants to say. Alright, you get two class points, I will mark that down. You can always, at any point, hit reset on the game.
Just to show you that the strategy that we had come out last class of contribute nothing at all to the public good, let’s just try this out. There’s a little bit of randomness in this, so we’ll see what it does, but let’s just play 10 quick rounds.
- So you can see, I got more by playing the zero every time.
You might be wondering, well, this all depends on the public behavior and how the bots are responding to you. So in the next assignment, which I’ll release shortly after class, it’s going to have you play around with some different options. And so maybe if you were looking at this closely, you might have assumed that the bot behavior was going to follow this realistic start high and then decay, so there wasn’t a lot of interactivity. They were looking at your strategies, but mostly they were just getting more skeptical over time.
But in the assignment, I’ll have you try out different ones, and sort of the punchline here is that if your opponents that you’re playing against are, for instance, conditional cooperators, then the optimal strategy changes. It’s no longer be selfish, it’s actually closer to what you said, that there’s going to be some degree of wanting to show good faith efforts, like having a lot go to the social good in order to encourage the bots to do the socially optimal thing as well. So the assignment will have you play around with those. I just wanted to orient you to the game.
For now, we’re just going to keep it at just that one run to show you how you can do it, and it illustrates in the default setting that just going selfish, indeed, with the assumption of these realistic bots, will give you the best payout.
What we’re talking about here is that, as individuals, we’re not working only with Homo economicus. That’s that phrase that describes this sort of ultra-rational individual who is perfectly utility maximizing. And perfectly utility maximizing means a lot of things. We’ve talked about all those assumptions. It includes that they can perfectly calculate what’s the best.
But it also includes that they only care about the utility as calculated by the utility function, so they’re not like you. You two were, and basically everybody here except for the group up here, had some degree of non-Homo economicus, non-rational behavior, meaning that you did something for a reason other than maximizing your individual selfish welfare. And it turns out, this matches reality. We are actually in reality, we are not in the sort of mathematical domain of economics.
And so there are other considerations, like what will people think of me? Or could I get my opponent to react positively to my strategy? So you could still be very selfish and still have reasons to believe that you might want to play strategically. And so that’s the sort of first bucket of how you can solve the public goods game, using strategic interaction. And the field of behavioral economics has shown us all sorts of really interesting richness there. We’ll return to this, and we’ll actually be using some game theory things. We’ll talk about the Coase theorem and other things that will further illustrate this, but for now, we’re just setting up that the private solutions to the public goods game is to play strategically.
The more interesting question that we’ll spend more time on here in this lecture is how can we, as a society, fix this under-provision of public good? And first, if we really want to fix this, we need to understand it, which is going to mean we should draw some graphs so we can do our standard econ thing. And for that, I have created another web app. I was prolific this weekend. So this is just on our website, QR code, but you can play along with my graphs that I will be showing. Again, it’s probably best on your laptop, but I’m glad to hear it’s working on phones.
And so I want to set this up. We’re going to spend some time here. I’ll actually draw it out too, but this is what is on the web app. Suppose we’re considering a specific public good of parks. Pretty classic public good.
And so Q is going to be the quantity of parks. We’re going to leave it a little ambiguous. Is that the size of the parks? Who knows? And we’re also going to have dollars up here. It’s going to be expressed in dollars. But this is going to be talking about it from the perspective of the price or the marginal cost of producing the park.
And so the first thing we will start with is the real easy one. Let’s just assume that in this particular case there really are no increasing returns. It’s a fixed cost to produce parks. Let’s say $5, maybe $5 million to make it more realistic, but let’s just say $5 costs the government or whoever is going to build these parks $5 per unit of park.
We want to figure out, though, what’s the optimal amount of public goods that would be provided, and for that we need to know a little bit more about the individuals and their marginal benefit.
And so this curve here is going to be the marginal benefit, but we’re going to subscript it with i, meaning for the ith individual. And the point here is it’s following a pretty standard marginal benefit curve. It starts high. If there’s just one park in the city, it’d probably be very popular. But eventually, you know, more and more parks gets less and less.
You’ll also notice that we’re doing the more intermediate, advanced econ thing of jumping straight to the marginals. You could think about this in total terms, like we’ve done a number of times before, but we’re going to skip that because now we’re getting good at thinking on the margin. And so we have this individual who has a marginal benefit. Note that it also is the price that they would be willing to pay for parks. That comes back to what we talked about, what goes into the demand curve. And so with just this information, let’s assume there’s only one person, and so this is the full-on marginal benefit curve. You would ask yourself, what is the optimal amount of parks?
And like much in economics, the optimal is where the marginal costs equal the marginal benefits. And so in this case, with one individual, it would be this amount of parks, because this individual is willing to pay $5 for that amount, for that next park, and it also cost whoever was building it the same $5, and so this is optimal.
But we’re going to take a more challenging case. That’d be so simple. But that’s not really a good example of a public good because there’s only one person, there’s no public. And so instead, you might guess where we’re going, is there’s actually not i equals 1, there’s going to be a bunch of different i’s. And so what if i is going to be either indexed 1 or 2? Let’s have a real simple case where n equals 2, because there’s only two different things in this list, right?
In a simple case, we’re also going to assume that every individual has exactly the same marginal benefit curve. And so marginal benefit for person 1 is here, person 2 is also there, right on top of it. But we’re going to jump to the punchline, which is we want to calculate the aggregate marginal benefit. And so this is going to be vertical summation.
And so because there’s two people, it’s really easy, it’s just we’ll go to twice as high. The point is we’re going to add up all the individuals. And it’s going to be the societal marginal benefit curve equals the sum over all i, the marginal benefit of each of the different i. So this is just sigma notation, it’s just saying this thing in here, try out all the different values of i, so 1 and 2, and sum them up. And so this is just equivalent to that, but it’s useful because you could have any number and plug in a million individuals.
Okay, so that’s the setup.
And if we add some specific numbers to it, let’s also say that the marginal benefit for all i people is going to be, we’re going to express it in the inverse demand function style that we have been using before, some parameter A, which would be here, minus B times Q.
We’ve already said there’s two people, and the marginal benefit for society is just summing those, so we could just write this again, but I’m just going to cut to the chase and point out that because it’s identical for each different one, that’d be the same as putting n outside of the equation. So if you had two of them, it’d be this plus this. That’s the same as 2 times this. And so we can simplify it further, if it’s useful, to something like that.
Alright, so those are the marginal benefit curves.
Before we jump to the question of what’s the optimal, I want to talk through the logic of what would happen if there wasn’t some government trying to fix this. We’ve got enough here to say what would happen, actually.
So for this, we’ll think, suppose some private park building company might want to come in and build a park. What would happen? Well, like any profit-maximizing firm, they would want to only produce if they can make profit. So what do you think would happen? What would this company do?
For the individual curve. Yeah, so right here. And why would that be? It’s because there’s one person that would be willing to pay at the price of 5. In fact, it could have been any of them because they all have the same curve, right? But what happens is one person will finally say, okay, yeah, I’ll buy that, and we’re going to build a park.
But because we’re assuming this is a public good, we’re going to get free riding, and what we see is that as soon as whoever of these two agents pays for it, now the marginal value for the other person who didn’t pay goes to zero, because they just got what they wanted for free. So they’re not going to pay anything else.
So in other words, some sucker would go ahead and buy that first unit whenever it was the case that their marginal benefit was equal to the price the market was offering, but then the next person won’t have to pay anything because they already have access to what they would have wanted to purchase.
So what do we see? We see that this first Q_M happens, and then nobody buys anything else, and so it doesn’t go higher.
A key conclusion, then, is that what happens is that there will be some parks, they did build the first park, it’s just that it’s going to be not enough. And that this alone leads to deadweight loss.
So to figure out the deadweight loss, you can basically do what we always do, the areas under the marginal benefit curve but above the marginal cost curve.
So those two graphs up there now are showing the same thing, but with different emphasis. Here I’ll combine them into one, is that if we only have, we’ll give it some labels now, where M is for markets, and we want to calculate what’s the surplus, it’s going to be all the area that is below marginal benefit, but it stops here because that’s what we produced. And it’s only that chunk.
And this is going to be less than what the amount of surplus we could have had if we instead went out to Q star. Just to make that more clear, this is the societal optimum.
So this whole area, this triangle here, is going to be representing deadweight loss. That’s bad, and you can actually calculate this using basic triangle formulas, but the point I want to make is that N, when it increases, the amount of deadweight loss also increases. And so you can play with this on the web app, there’s a slider bar that lets you change around N, and you can watch what changes. I’ve captured a few screenshots here. When you change N up to 3, the deadweight loss grows from 3.1 as it was in the default with 2, up to 8.3. Notice the y-axis is adjusting too. So it’s a pretty big reduction when you go to 3.
And here’s just with 20. There’s an enormous deadweight loss that dominates the calculation, and this shows you that as society gets bigger, if there’s more people who are benefiting from these public goods, it becomes increasingly costly to not provide them.
So how do we solve this?
Indoor playgrounds. That’s how we solve this. I’m sort of joking, but I have kids, I have been to a lot of indoor playgrounds, and I hate them passionately. They are loud, they are echoing around, they’re usually lowest possible quality construction materials, and so it’s just stress in a warehouse. And often they are in warehouses.
But my kids love them, and they are indeed provided by the market. But you might want to ask yourself, well, didn’t I just say that the private market wouldn’t actually provide parks? Why would this exist? Who knows why this does exist?
True. But why wouldn’t we just have the government provide it?
That’s the key thing, is you got to pay 10 bucks to get into this playground. And so the government didn’t provide it because it’s expensive to have indoor playgrounds to solve your winter predicament, which is a real one. So they have some, but not enough, I would argue. Why is this private firm making this expensive indoor thing? It’s because they get paid to have it, they have privatized the park.
And so we’re sort of seeing one of the additional solutions to this that also happens at the individual level, but here the individual supplier. If you have a public goods situation, one of the solutions is to privatize it by simply putting a price on the door, like QR code, and then you get the keypad number, and there’s literally nobody there. It’s all automated. It’s a great business. I would like to get into it if I was more mercenary. But yeah, they’ve figured out how to privatize the idea of a park, and therefore it’s profitable, and therefore the free market provides it.
So yay, free market wins.
But how do we better solve this? That only works under certain conditions where you can privatize it. What if it’s something you can’t privatize, like climate reduction, or military protection, or research and development, or all these other things?
Then we’re going to get into the domain of what might the government do.
So on your little web app, there’s also a couple of additional options. I’ll just go interactive with this one.
So here we’ve been playing around with no policy, and we saw that key finding that as N increases, the deadweight loss grows enormously.
The first of our two solutions will be the subsidy. A lot of environmental economics is dominated by calculating what is the optimal subsidy. Let me set this back to the default 2.
So when you click subsidy, you can play around with it. What we’re doing is we’re going to say, hey, private parks building companies, we know that in equilibrium you’re only going to provide a little bit because, here we’re back to the case where they can’t enclose it. So maybe I just kind of muddied the water by talking about indoor playgrounds, but when we’re back to the public good, we have the fundamental problem that the market will under-provide because of free riders.
One way we could fix it is as simple as saying, hey, private firms, for each park that you make, we’re going to pay you some subsidy. And so as you say your subsidy rises, you can see what happens to the deadweight loss. We start to provide more and more, and assuming you set the subsidy at the right amount, you can actually get rid of all of the deadweight loss.
We’ll work on the mathematics of this again because it’s going to be very similar, we’ll see, to externalities.
But the other one I wanted to say, and this is actually the more common one, is straight-up public provision. Let’s not mess around with trying to subsidize private firms to do things like protect our military interests, although we do kind of do that with some contractors. But there’s a really strong argument to be made that you wouldn’t want to try to subsidize defense. What does that sound like? That’d be like putting bounties on individuals and putting a subsidy, which is what a bounty is.
But instead, the government has found that, as a matter of fact, it’s just at least preferred by the government to do direct public provision. There’s no market force that they’re going to use. They’re simply going to provide it. And so they’re still going to pay people, you still pay your military generals, and you still buy the tanks.
But there’s no market incentive, it’s just that the government makes the direct purchase using your tax dollars. So it’s a pretty uninteresting plot, it just means to say that, yeah, if the government can choose exactly how much to provide of the public good, they’re going to do it. And if they’re a good government, they could totally minimize the deadweight loss.
Alright. Any questions on public provision and public goods?
That’s it for public goods.
Reminder, we’re going to return to this extensively. Right now, we’re in the phase of the arc of the semester where we are talking about the micro-level foundations, the tools that use market forces or corrections to market equilibria to try to make a better policy instrument. We’ll soon then be applying this to real-life situations of public goods, like climate policy. So we’ll return to this, but this is sort of the workhorse at the micro level.
We’ll transition to the other big of the three market failures, externalities, in a second, but I actually want to have this early semester evaluation I said. And so I care so much about this, and I realize one of the ways I could hopefully positively impact the world would be as simple as teach environmental economics well. And so I really care about this. This doesn’t get reported to anybody but me, and it’s anonymous, but I would really love it if you could fill this out.
And just so that there’s no pressure on you, I’m going to head out of the room for about 5 minutes so you have a chance to do that. Just a simple Google form, and I’ll be back.
Looks like most of you are done. I’ll let you keep typing in if you’re not, but thank you for that. I really want to do as good of a job as I can with this.
For now, we’re going to spend the last 10 minutes of class jumping over to the next set of slides, corresponding to Lecture 8 on externalities.
So hopefully all of you have been introduced to externalities in your principles class. But I’m still going to give a brief reminder, and then we’re going to dive a little deeper into the mathematics that we use to answer how do we solve these.
So what is an externality? The long definition that’s fully precise is an externality is whenever the production or consumption of a good has a positive or negative effect on the value obtained by a firm or household that was external to the decision of how much to produce or consume.
That’s a mouthful, and so I tend to prefer the second one. Externality is simply when value goes to someone external. External here just means they weren’t the decision maker. And so frankly, the better definition is that there are spillovers.
And I almost think environmental economists did themselves a huge disservice in using the word externality. It sounds nerdy, wonky, hard to understand, and weird, whereas we have this real word, spillover, that I think is just as accurate, and it gets the idea across in a much better way.
Maybe in future years, I’ll actually call it spillovers everywhere, but I’ll use these two interchangeably. Basically, a spillover just means that there is value, positive or negative, that spills over to somebody who wasn’t the one who made that decision, to those external people.
The classic definition of an externality is a certain type of externality called a negative production externality. So I’ve added two words, and that will take our long, long definition and simplify it somewhat. It’s just now when production, because we’re talking about a producer, of a good inflicts spillover costs, it’s negative, on someone else.
And so the simpler definition even collapses as well to just a negative production externality is a cost of production incurred on someone external.
So the problem with this, and this is going to be the recurrent thread throughout all of our externalities, is when you have externalities, the market’s marginal costs, which in this case would be represented by the supply curve because we’re having a production externality, doesn’t match the true marginal cost.
And so in other words, when the firm who is polluting, a classic externality example, they do have costs, like how much coal did they buy, and how much labor wages did they pay their coal workers. Those are real costs, but it leaves out a whole big category of costs. All of the things that the smoky air will lower value to people living nearby, as well as damages from greater climate change thereafter.
And that means, in this case of a negative production externality, their costs are less than the true costs. And the implications for social welfare, and we’ll draw this in a minute, is that the market left to its own devices will over-allocate and generate deadweight loss. So pretty similar to that.
But we’re going to add some different terminology to make this more specific to externalities.
Okay, so the first one is MPC. You can see the marginal cost, right, so we can kind of see where this is going, but we’re going to add some letters to say that this is marginal private cost.
So if we’re thinking back to the ordinary supply curve, or the cost curves faced by the firm under perfect competition, this is just marginal cost. But now we’re giving it an extra letter to denote that it’s only the set of costs felt directly by the production firm. So that’s MPC.
And the P is in contrast to MEC, marginal external costs. I started to rewrite this lecture with the word spillover everywhere, but then I’m like, man, now I got to make all my graphs change, because it would be no longer MEC, but MSC, I don’t know, so I’m probably not going to do it.
But regardless, these are the portion of the costs imposed by the last unit of good, but on the external people who didn’t make the choice to produce it. And the easiest one, then, is just we’re going to sum those together.
The MSC is the marginal social cost. And the MSC just equals MPC plus MEC.
And graphically, what this is going to do is exactly what I just said, is it’s going to result in a divergence between the costs felt by the individual, in this case the producer, and the true ones. And so if we were to chart the production decision, this is an ordinary supply and demand curve, so let’s talk about, I suppose, cars.
The ordinary supply curve would look a little bit like this, and the supply curve equals the marginal cost curve. We showed that way back when, but we’re going to label this one the marginal private costs.
And the challenge is that that’s not the true costs. The marginal social costs are going to be up there. And so in this particular case, I guess for each unit of car produced, there’s this unit of additional MEC, marginal external cost. And we can see that adding those two up is what gives us the MSC.
So I’ve already told you this is going to be bad because of deadweight loss. But to be able to see that, we need to add one more bit of information, which is marginal willingness to pay.
And so let’s see if I can draw this right. Tighten this up a little bit. When we’re thinking about it in terms of just the MPC, the private things, this is a demand curve, in this case for cars. But what’s going to happen is that the marginal willingness to pay isn’t reflecting the fact that the consumers of cars are also getting a different sort of value, a negative value in this case, of all of the downsides of having more cars. And that could be more congestion on the highways, it could be more pollution up in the skies.
But they would like to be able to have this lower level. They’d like to be able to reduce the number from the quantity, the equilibrium, Q star, in a market solution, to the socially optimal Q star S.
But here we’re not saying how, and all we would note here is that this point would be optimal. The area ABC here is going to be representing deadweight loss, because it’s areas that were not provided that could have been provided at positive value. But the punchline to this is that we are going to have overproduction in a negative externality.
So cars, or pollution, or whatever might be a good example of negative externalities, but there’s also the flip side of this. Remember that long definition I had, all the different possibilities included increases in value to somebody external.
And so suppose I have a nice wild backyard in my yard, and I have 10 acres. I’m fantasizing now. And it has wetlands that provide clean water services to people living downstream from me. It might be nice and magnanimous of me to provide that for people, but the value that I get from it is going to be less than the value all of society gets from it, because I don’t see those values that the downstream clean water recipients get.
And so, I guess if I was a really good person, I wouldn’t do this, but I would be tempted to maybe replace it with an indoor playground or something, to unnecessarily tie back to something else. But the point is that when I am choosing what’s optimal for me, I’m going to be ignoring the benefits that wetland has to other people.
And this will result in under-provision.
What I’ll leave you with is the thought that it turns out public goods are basically just positive externalities. And so we could use this exact graph to talk about everything we were talking about before. It’s a little different because with private versus public goods, we added a different shaped curve because you can kind of rotate it up. Here we’re going to talk about the case where it’s a per unit, but nonetheless, I’ll pick up next class talking about the similarities between public good provision and positive externalities.
And then talk about the ultimate externality of carbon emissions.
Great. Any questions?
Cool. Have a good rest of your day.