In human language:
"Tyrion enjoys smoking cigar at home. His wife, Sansa, was diagnosed with lung cancer. The doctor says it was partly due to her exposure to second-hand smoking.
A complete and competitive market leads to a Pareto efficient allocation of resources.
This requires that:
If an agent making a decision that does not bear all of the consequences of his or her action, then there exists an externality.
"Tyrion enjoys smoking cigar at home. His wife, Sansa, was diagnosed with lung cancer. The doctor says it was partly due to her exposure to second-hand smoking.
“Tormund is a bike-rider, and he recently attended the 80th annual motorcycle rally held in Sturgis, South Dakota, despite warning signs from health experts and local officials. Tormund was tested positive for COVID-19 days after he returned to his home in Midland, Texas, as do his wife and his 80 year-old mother. His mother passed away a week later.”
“Economists have estimated that the Sturgis event is linked to an estimated COVID-19 case count of over 200,000, and over $12 billion in public health expenses (Dave et al. 2020).”
Red Keep LLC is a small mining company located near Riverrun. They extract heavy metals such as iron, copper, and uranium. Along the process, they discharge wastewater containing highly toxic metals and organics into the nearby Red Fork River.
Several years later, doctors find that children born in the town of Maidenpool, located at the downstream of the plant, suffers from leukemia at a much higher odds than children elsewhere.
Red Keep LLC can mine the uranium with a total cost of: \[P = 0.5Q^2\]
Thus the marginal cost of production is: P = Q
The market demand for uranium is: P = 30 - Q
For a private market, the equilibrium price and quantity will be determined by setting the supply equal to the demand:
Q = 30 - Q
which yields:
Q’ = 15, and P’ = 15
The production of uranium generates toxic wastewaters, which causes damage of $10 per unit of uranium mined.
The marginal social cost of uranium mining is thus determined by:
Marginal Social Cost(MSC) = Marginal Private Cost(MPC) + Marginal External Cost(MEC)
Or, numerically:
MSC = Q + 10
A socially optimal level of uranium production requires that marginal social cost (the supply) equals to marginal benefits (the demand):
Q + 10 = 30 - Q
which yields:
\(Q^*\) = 10, and \(P^*\) = 20
Externalities can be positive, negative, or pecuniary:
A new cinema opens at the Winterfell Shopping Center. The opening of the cinema increases revenue for nearby restaurants, coffee shops, and department stores because movie fans will often visit those stores before and after the movie.
Question: when will this positive externality disappear?
Planted forestry provides the landowner with timber revenue, but at the same time generates:
Property rights: a bundle of entitlements defining the owner’s rights, privileges, and limitations for the use of the resource
A property can be owned by:
Another important concept related to the nature of the good is called rivalry:
A good is rival if one person’s consumption of that good diminishes (or impairs) other people to consume that good.
If I start from the moral position, that we have no choice but to do everything that we can, with countries all over the world, to save this planet for our children and future generations, that will mean change.
- Senator Bernie Sanders
If you believe that God is watching (as humanity spews pollutants), what do you think God thinks of that? This is less and less about the planet as an abstract thing and more about specific people suffering specific harm because of what we’re doing right now. At least one way of talking about this is that it’s a kind of sin.
- Mayor Pete Buttigieg
What is the ultimate cause of the tragedy of the commons, and specifically, should the tragedy be attributed to moral impetus embedded in human nature?
What do you think are some of the ways that can avoid the tragedy of the commons from happening?
Now we turn to another class of property right regime, public good (or bad). Public goods are characterized by:
Typical public goods include:
Suppose there are two homeowners, each with a demand curve of:
Demand for A: 50 - Q
Demand for B: 30 - 2Q
The marginal cost for providing abatements is MC = 45
The aggregate demand is given as the vertical sum of the two individual demands, because all consumers will consume the same amount of public good:
Aggregate demand:
80-3Q when Q \(\leq\) 15, and
50-Q when Q > 15
This is DIFFERENT from what the aggregate demand for a private good, which is a horizontal sum of the individual demands.
The socially optimal provision of abatement will be:
Aggregate Demand = Marginal Cost
80 - 3Q = 45
Q* = 11.67
If abatement is provided privately though, only homeowner A will be willing to chip in. This leads to:
Demand for A = Marginal Cost
50 - Q = 45
\(Q_P\) = 5
Open-access resources, or common-pool resources, are characterized by:
Typical open-access resources include:
In his 1968 book, Garrett Harding coined the term “tragedy of the commmons”, that self-interested humans will enter and over-exploit the common-pool resources, even though collectively this diminishes the resource pool.
The only sensible course for him to pursue is to add another animal to his herd. And another, and another… Therein is the tragedy. Each man is locked into a system that compels him to increase his herd without limit — in a world that is limited. Ruin is the destination toward which all men rush, each pursuing his own best interest in a society that believes in the freedom of the commons.
Harding believed that the problem lies within human nature: the selfishness, the rationality, decisions that make sense as an individual but do not as a society when dealing with the commons:
It is a mistake to think that we can control the breeding of mankind in the long run by an appeal to conscience … The argument is straightforward and Darwinian.
But temperance also can be created by coersion… Who enjoys taxes? We all grumble about them. But we accept that voluntary taxes would favor the conscienceless. We institute and support taxes and other coercive devices to escape the horror of the commons.
Rather than rely on propaganda, we follow Frankel’s lead and insist that a bank is not a commons; we seek the definite social arrangements that will keep it from becoming a commons.
I like the idea of coercion into social responsibility without really explicitly creating a dialogue about it because often times when these issues are talked about, they are only talked about in extremes from opposite parties but the sweet gray spot is often not recognized, so the right way might just be manipulation!
Hardin presents a powerful argument for progressive political action, arguing against laissez-faire politics and observing that we do not complain as much about supposed infringements upon our liberty that we are accustomed to.
By advocating for coercion and limiting “breeding rights”, (Hardin) infringes on personal freedom and also deprives less privileged people in the world of such rights while only marginally affecting the rich, furthering the wealth gap. He also does not consider how humanity as a whole has constructed and built the elaborated society we have today, and such contributions could potentially balance out some vices coming from us humans.
When pollution of common waterways and air was limited, people’s freedom to dispose of their pollutants anywhere was limited. However, this benefited far more people than it hurt. We live in a limited world and it is time we acknowledge that. Similarly if we were to limit the commons of breeding, many people would cry out about the (impingement on their freedom. But as Hegel said“Freedom is the recognition of necessity.” If people continue to breed unchecked, eventually there will not be enough food and space to go around.
Is the following listed issue a problem? Why or why not?
Which of the following do you think is the best way to address the issue: (1) moral persuasion (2) mutual coercion (3) Other (please specify)
Choose one to answer:
We (Bill Nordhaus and I) both believe that only new discoveries can protect the environment and sustain material progress. We both believe that such discoveries are possible. I am perhaps a bit more optimistic than Bill that the discovery and adoption of new low-carbon energy technologies will be less costly and less disruptive than everyone seems to think. Once people get serious about adopting some policy measure which foster discoveries that truly add social value, discoveries will follow.
- Paul Romer, on the possibility of progress
Blackwater Bay is an area known for its commercial fishery for high-quality salmons.
The growth of the fish stock in the Blackwater Bay fishery follows a logistic growth function:
In the long-run, fishing efforts and the total sustainable catches also have a inverted-U shaped relationship:
\[TVC = 100B - 2B^2\]
\[MC = 10\]
For the fishery to have the highest net benefit, we need to solve:
Marginal Benefit = Marginal Cost
where MB is the slope of the total benefit, or \[MB = 100 - 4B\] (differentiate the total benefit function gets you the marginal benefit).
This yields:
\[100 - 4B = 10\]
\[B^* = 22.5\]
Under the socially optimal outcome, there are economic rents generated from the fishery. To see this, calculate the net benefit from the fishery:
Net Benefit = Total Benefit - Total Cost
At B=22.5, the net benefit from the fishery is:
NB = 100 * 22.5 - 2 * 22.5 * 22.5 - 10 * 22.5
= 1012.5
In other words, each boat will get a rent equal to 1012.5 / 22.5 = 45 from the fishery.
The open-access nature of the fishery dictates that additional boats will enter the fishery as long as there are economic rents to be extracted from the resource.
An open-access outcome is characterized by:
Total Benefit = Total Cost
where at such point each and every boat just breaks even from the fishery. Notice that the total cost is just TC=10B, we have:
\[100B - 2B^2 = 10B\]
\[B^{OA}=45\]
This phenomenon under the open-access outcome is called rent dissipation:
To quote Hardin again:
The only sensible course for him to pursue is to add another animal to his herd. And another, and another… Therein is the tragedy. Each man is locked into a system that compels him to increase his herd without limit — in a world that is limited.
To address rent dissipation (and the externality problem overall), there are generally two quantitative instruments:
Both should arrive at the same equilibrium point - the homework problem will ask you to derive the tax instrument
For the fishery to have the highest positive benefit, we need to solve:
Marginal Benefit = Marginal Cost
where MB is the slope of the total benefit, or \[10 = 100 - 4B\] \[B^*=22.5\]
At the socially optimal point, each boat can earn an economic rent equals to:
\[\text{Rent = Average Benefit - Average Cost}\] or
\[Rent = \frac{100B - 2B^2}{B} - 10\] at B*=22.5
which gives rent=$45
Rights-based approach works better:
Permits (quota) assigned to vessel sizes:
What’s gonna happen?