Public Goods & Externalities

Negative Externalities

Look at the two supply curves on the graph. The lower one is private supply. The upper one is social cost. The vertical gap between them — that's the external cost per unit.

A coal plant generates electricity for its customers and dumps sulfur dioxide into the air, causing asthma in communities downwind. Those people never agreed to bear that cost. They bear it anyway.

That uncompensated cost imposed on third parties is a negative externality. The factory considers its own production costs (labor, fuel, machinery) when choosing output levels but ignores the health damage it inflicts on others. The factory's own costs are the marginal private cost (MPC). The full cost to society — private costs plus external damage — is the marginal social cost (MSC).

Because MSC > MPC, the market price ends up too low and the quantity produced too high. The market overproduces relative to the socially optimal level. On the graph, notice where the demand curve crosses the private supply curve versus where it crosses the social cost curve. That gap in quantity is the overproduction. The shaded triangle between the two intersections is the deadweight loss.

Carbon emissions from driving, noise from late-night construction near apartment buildings, secondhand smoke, antibiotic resistance from overuse in livestock — all negative externalities producing that same gap on the graph.

Positive Externalities

Now look at the demand side of the graph. Two demand curves. The lower one is private demand. The upper one is social benefit. The gap between them is the external benefit per unit.

When you get a flu vaccine, you protect yourself. You also protect the coworker sitting next to you, the elderly neighbor you pass on the sidewalk, and the immunocompromised stranger on the bus. They benefit from your decision without paying a cent.

That spillover benefit to third parties is a positive externality. The buyer considers only their own benefit — avoiding a week of misery — and ignores the broader social gain. The buyer's benefit is the marginal private benefit (MPB). Add the benefit to others and you get the marginal social benefit (MSB).

Because MSB > MPB, the market price lands too high and the quantity consumed too low. The market underproduces relative to the socially optimal level. On the graph, the social benefit curve sits above private demand, and the equilibrium quantity falls short of where the social benefit curve intersects supply.

Education is the classic example. A more educated person earns more (private benefit) and also contributes to a more productive workforce, lower crime rates, and stronger civic engagement (social benefits that don't show up in anyone's tuition bill). R&D spending, pollination by beekeepers, and home renovations that lift a whole neighborhood's property values also qualify.

Pigouvian Taxes and Subsidies

Toggle the tax control on the graph. Watch the private supply curve jump up to meet the social cost curve. The deadweight loss triangle vanishes.

Markets overproduce goods with negative externalities and underproduce goods with positive externalities. Arthur Pigou, a Cambridge economist writing in 1920, proposed a fix that's still the standard policy tool: make people face the full social cost or benefit of their actions through the price system.

A Pigouvian tax is a per-unit tax set equal to the external cost. If a factory imposes $15 of pollution damage per unit of output, tax each unit $15. The firm's private cost rises to match social cost, the supply curve shifts up until it overlaps with the MSC curve, and the market produces the socially optimal quantity. No banning required.

A Pigouvian subsidy works in reverse for positive externalities. If flu vaccines generate $15 of external benefit per dose, subsidize each dose by $15. Effective demand rises to match social benefit. Toggle the subsidy control and watch the private demand curve climb up to meet the social benefit curve.

The elegance is that Pigouvian corrections use the market itself to fix the market. No outright prohibition, no mandates. Just adjust prices so that self-interested decisions lead to the socially optimal outcome. The British Columbia carbon tax, introduced at $10 per ton of CO2 in 2008 and gradually raised to $65 by 2023, is a real-world Pigouvian tax in action.

Public Goods and the Free-Rider Problem

A lighthouse beams light across the ocean. Every ship benefits whether or not the captain paid for it. You can't block a passing vessel from seeing the light. One ship using it doesn't dim it for others.

Public goods have two defining properties:

Non-excludable — you can't prevent non-payers from consuming the good. Non-rival — one person's consumption doesn't reduce what's available for anyone else.

National defense is the textbook example. The military protects every person in the country simultaneously (non-rival), and there's no way to defend some citizens while leaving others exposed (non-excludable). Street lighting, public fireworks on the Fourth of July, open-source software like Linux, and basic scientific research also qualify.

If you can't be excluded from the benefit, why would you voluntarily pay? That's the free-rider problem. Everyone wants the good, but everyone has an incentive to let someone else foot the bill. If everyone free-rides, the good never gets produced — even though society collectively values it far more than it costs.

Private markets fail here. Governments typically fund public goods through compulsory taxation instead. Your tax dollars pay for national defense, public parks, and flood levees whether you asked for them or not. That compulsion is the whole point — it solves the free-rider problem by removing the option to opt out.

The Coase Theorem and Property Rights

A rancher's cattle trample a neighboring farmer's crops. The rancher profits, the farmer suffers. Clear negative externality. Ronald Coase, in a famous 1960 paper, argued that under the right conditions the government doesn't need to intervene at all.

The Coase theorem states that if property rights are well-defined and transaction costs are low, private parties can negotiate their way to the efficient outcome regardless of who initially holds the rights.

Suppose the farmer has the legal right to untrammeled crops. The rancher will offer to pay for grazing permission, but only up to the amount the rancher gains. If the rancher's profit from grazing exceeds the farmer's crop damage, a deal gets struck and both parties end up better off. If not, the cattle stay penned. Efficient either way.

Reverse the assignment: the rancher has the right to let cattle roam freely. Now the farmer offers to pay the rancher to pen them, up to the value of crop damage avoided. Same efficient result. Different distribution of money, but identical resource allocation.

In practice, the Coase theorem hits hard limits. Transaction costs are often enormous. Imagine trying to negotiate individually with 200,000 pollution sources across an industrial region. Property rights are sometimes murky — who owns the air above a factory? Power imbalances distort bargaining. So Pigouvian taxes and direct regulation remain essential tools for large-scale externalities. Climate change, for instance, involves billions of affected parties across every country. Coasian bargaining is a nonstarter at that scale.

Worked Example: Calculating the Optimal Pigouvian Tax

Follow the math on the graph. A factory produces widgets. Private supply (MPC) is P = 10 + 0.7Q and market demand is P = 90 - 0.8Q. Each widget generates $15 of pollution damage to surrounding communities.

Market equilibrium. Set MPC = Demand:

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

Look at that intersection on the graph. The market ignores the $15 external cost entirely.

Social cost curve. MSC = private supply plus external cost per unit:

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

Notice the upper curve on the graph sits exactly $15 above the lower one at every quantity.

Socially optimal outcome. Set MSC = 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. The shaded triangle between the two intersections:

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

Pigouvian tax. Set it equal to the external cost per unit: $15 per widget. Toggle the tax on the graph and watch the private supply curve jump up by $15, landing exactly on top of the MSC curve. The new market equilibrium matches the socially optimal point. Deadweight loss gone.

Verification: with the $15 tax, new supply is P = 25 + 0.7Q — identical to MSC. The market self-corrects.