Public Goods & Externalities

Negative Externalities

Looking at Public Goods and Externalities, if you use the graph's tax and subsidy controls, you'll find that deadweight loss disappears when the price actually shows the total cost to society.

With Negative Externalities, the graph has two supply curves: the lower one is the private supply, the upper one the total cost to society. The distance between them is how much the external cost is for each item. And that distance is all you need to know. For example, a coal power station creates electricity but also releases sulfur dioxide into the air. People living in the path of the wind then have more asthma, and they didn't choose to have that happen.

This unpaid damage to people who aren't involved is a negative externality. When deciding how much to make, the factory only considers its own costs - workers, fuel, equipment - and ignores the harm it does to everyone else. The factory's own costs are its marginal private cost (MPC). If you add on the damage to others, you get the marginal social cost (MSC), which is always higher when there's a negative externality.

Because the MSC is above the MPC, the market price ends up being too low and too much is made. The market creates more than is best for society. Look at the graph: where the demand line crosses the private supply line is different to where it crosses the total cost to society line. The amount of difference is how much is overproduced, and the shaded triangle between these two crossing points shows the deadweight loss. Every item made in that difference costs society more than it's worth, but the factory still makes them because it doesn't include those costs in its calculations.

Carbon from driving, noise from building late at night near apartments, smoke from other people's cigarettes, and antibiotic resistance from overusing medicine in animals...these are all negative externalities, and they all show the same pattern on the graph.

Positive Externalities

For Positive Externalities, turn to the demand side of the graph. This time there are two demand curves, with the private demand lower and the total social benefit above. The gap is the extra benefit for each item.

When you get a flu shot, it obviously protects you. But it also protects everyone you would have sneezed on. Your colleague in the next office, the older neighbour you greet each morning, the person on the bus with a weak immune system. They get a benefit they didn't pay for.

This benefit spreading to others is a positive externality. When deciding to get vaccinated, you only think about your own benefit (not being ill for a week), and don't consider the wider benefit to society. Your personal benefit is the marginal private benefit (MPB). Adding in the benefit to everyone else gives the marginal social benefit (MSB).

The MSB is more than the MPB, so the market price is too high and not enough is used. The market produces too little. On the graph, the total social benefit curve is above the private demand, and the amount actually used is less than where the MSB crosses the supply.

Education is a really common example. A better-educated worker earns more (that's the private benefit). But a better-educated workforce also means businesses that employ them are more productive, there's less crime and people are more involved in their communities. None of those benefits are on the student's bill. Research and development by tech companies create new knowledge that other companies and industries can use. And beekeepers whose bees pollinate nearby farms provide a benefit they can't get from the price of honey. Improvements to homes that increase property values for everyone on the block also follow this pattern.

Pigouvian Taxes and Subsidies

On the graph, if you change the tax amount, you'll find the supply curve for a product immediately jumps up to the line showing the total cost to society. As this happens, the inefficiency (deadweight loss) disappears. Generally, markets produce too much when an activity has a negative effect on others and too little when it has a positive effect on others. Arthur Pigou, an economist at Cambridge in 1920, suggested a solution economists still use. He said prices should make people pay the total cost or receive the total benefit of what they do.

A Pigouvian tax is a tax on each item that's equal to the cost of the damage caused by it. For example, if a factory creates $15 worth of pollution for each thing it makes, then a $15 tax is put on each item. The factory's own costs go up to equal the total cost to society and the supply curve shifts upwards, until it's on top of the MSC (Marginal Social Cost) line. After that, the market will, by itself, make the amount of the product that is best for society. There's no need to ban anything or tell people what to do.

A Pigouvian subsidy takes care of positive externalities. Because each flu shot gives $15 worth of benefit to others, each shot is subsidized by $15. The actual demand for the shots goes up to match the total benefit to society. When you change the subsidy on the graph, you'll see the demand curve for the product climb up to the line showing the total benefit.

What's so good about Pigouvian approaches is that they use the market to fix the market. You adjust prices so that people, acting in their own self-interest, end up doing what's best for everyone. No one in a central location has to decide how much to make, and nothing is prohibited. British Columbia put a carbon tax of $10 per ton of CO2 in place in 2008, and increased it gradually to $65 by 2023. The province lowered income and business taxes by the same amount, making the overall tax amount the same. This is a Pigouvian tax at work in the actual world, not just on a blackboard.

Public Goods and the Free-Rider Problem

A lighthouse shines its light over the ocean. Every ship that goes by gets the benefit, no matter if the captain paid for the lighthouse to be maintained or not. You can't stop any one ship from seeing the light and one ship using it doesn't make the light less bright for the next one.

Public goods are defined by two things: they are non-excludable, meaning you can't prevent people who haven't paid from using it, and non-rival, meaning one person's use doesn't reduce the amount available to others.

National defense is the typical example on the AP exam. The military protects everyone in the country simultaneously (non-rival) and you can't protect some citizens and leave others at risk (non-excludable). Street lights work in the same manner. Also, public fireworks on July Fourth. Linux, open-source software, is another one - anyone can download and use it without making it less available to others. And basic scientific research that the government funds also counts as one because published results are available to all.

If you get the benefit whether you pay for something or not, then why would you pay? This is the free-rider problem. Everyone wants the good, and everyone is encouraged to let someone else pay for it. If enough people take a free ride, the good won't be produced at all, or it will be produced in much smaller quantities than society really wants.

Private markets fail in this situation because there's no way to collect money. Instead, governments pay for public goods with required taxes, so your taxes pay for things like defense, parks and flood barriers, even if you didn't specifically ask for them. It's this requirement to pay that's important. It solves the free-rider problem by removing the option to avoid paying.

The Coase Theorem and Property Rights

The rancher's cows damaging a farmer's crops is a clear example of a negative externality: the rancher benefits, the farmer loses. However, Ronald Coase, in a significant 1960 paper, suggested that the government doesn't necessarily have to intervene in situations like this, provided certain conditions are met.

The Coase theorem states that if property rights are clearly defined and the costs of making an agreement are low, the people involved can bargain to reach the best possible outcome, no matter who originally has the right. For instance, if the farmer has the legal right to crops that aren't damaged, the rancher will pay for the right to have the cows graze, but only to the amount the rancher makes from the grazing. If this profit is higher than the cost of the damage to the crops, an agreement is reached and both are better off, otherwise the cows stay put. Either way, the situation is efficient.

Alternatively, if the rancher has the right to let the cattle roam, the farmer will pay the rancher to keep them contained, up to the value of the crops that would be saved. We'd have the same efficient use of resources, but the money would go to a different person.

In reality, though, Coase's ideas have very definite limits. The expense of negotiating can be huge. Think of trying to get 200,000 people who are affected by pollution from factories along an industrial area together to come to an agreement. Defining property rights can also be problematic—who owns the air above a chimney, for example? And when one party has a lot more power than the other, the negotiation is biased. Therefore, for large-scale issues like climate change (which affects billions of people in every country), economists generally prefer Pigouvian taxes and direct regulations. Coase works well in disagreements between two parties with a clear understanding of who owns what, and where it isn't too expensive to negotiate. Almost anywhere else, it falls apart.

Worked Example: Calculating the Optimal Pigouvian Tax

Let's look at an example of calculating the correct Pigouvian tax. Look at the graph. A factory making widgets has a private supply curve (MPC) of P = 10 + 0.7Q and the market demand is P = 90 - 0.8Q. Each widget creates $15 of pollution harm to the people in nearby towns.

Market equilibrium. To find the market equilibrium, we make the MPC equal to the demand:

10 + 0.7Q = 90 - 0.8Q
1.5Q = 80
Q_market = 53.3 units
P_market = 10 + 0.7(53.3) = $47.33

This point on the graph shows where the market will settle if the $15 pollution cost is ignored.

Social cost curve. The social cost curve (MSC) is calculated as MSC = MPC + the external cost:

MSC = (10 + 0.7Q) + 15 = 25 + 0.7Q

The top curve on the graph is exactly $15 higher than the bottom one at every amount produced; it's a parallel shift.

Socially optimal outcome. The best outcome for society is found by setting MSC equal to demand:

25 + 0.7Q = 90 - 0.8Q
1.5Q = 65
Q_optimal = 43.3 units
P_optimal = 90 - 0.8(43.3) = $55.33

Deadweight loss from the externality – that shaded triangle:

DWL = 0.5 x (Q_market - Q_optimal) x (external cost) = 0.5 x (53.3 - 43.3) x 15 = $75

Pigouvian tax. It should be $15 per widget (the same as the pollution cost). On the graph, activating the tax shifts the private supply curve up by $15, and it lands directly on the MSC curve. The new market equilibrium now matches the socially ideal outcome and the deadweight loss is gone.

As a check: with the $15 tax included, the new supply curve is P = 25 + 0.7Q, which is the same as MSC. The market fixes itself.