Externalities & Public Goods
Positive/negative externalities, Pigouvian taxes, public goods, free riders, and the Lorenz curve
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Externalities, Public Goods, and Market Failure
Markets allocate resources efficiently under tight assumptions: many buyers and sellers, well-defined property rights, no spillovers, and goods that everyone can be excluded from consuming. When those assumptions fail, the market produces too much or too little of a good — a market failure. The two most important sources are externalities and public goods.
Externalities
An externality is a cost or benefit imposed on a third party who is not part of the transaction. Markets ignore these effects, so equilibrium quantity differs from the socially optimal quantity.
Negative externality (e.g., pollution): producer faces only its marginal private cost (MPC), not the full marginal social cost (MSC = MPC + external cost). Free-market output is HIGHER than the socially optimal . Result: deadweight loss equal to the triangle between MSC and demand from to .
Positive externality (e.g., vaccination, education): consumer's marginal private benefit (MPB) falls short of full marginal social benefit (MSB). Free-market output is LOWER than socially optimal. Deadweight loss equals the triangle between supply and MSB.
Internalizing Externalities
Government tools to fix externalities:
- Pigouvian tax = external cost per unit. Shifts MPC up to MSC. New equilibrium = social optimum.
- Pigouvian subsidy = external benefit per unit. Shifts MPB up to MSB. New equilibrium = social optimum.
- Tradable permits / cap-and-trade: government caps total emissions and lets firms trade rights, achieving the cap at lowest total cost.
- Coase theorem: with well-defined property rights and zero transaction costs, private parties can negotiate to the efficient outcome. In practice, transaction costs often block this.
- Direct regulation (command-and-control) — typically less cost-effective than price-based instruments.
Public Goods
A pure public good is:
- Non-excludable: cannot prevent someone who hasn't paid from consuming.
- Non-rival: one person's consumption doesn't reduce another's.
Examples: national defense, basic research, lighthouses, fireworks. Because consumers cannot be excluded, each has an incentive to free-ride — wait for others to pay and then enjoy the benefit. The market under-provides public goods, so government typically funds them through taxes.
The socially optimal quantity of a public good is where vertical sum of MBs (because everyone consumes the same unit simultaneously) equals MC.
Common-Pool Resources
Non-excludable but rival (fisheries, public grazing land, freeway lanes). Subject to the Tragedy of the Commons — overuse by individuals each pursuing self-interest. Solutions: privatization, regulation, quotas, user fees.
Why It Matters
Almost every government policy debated today — climate change, healthcare, education — turns on externality and public-goods analysis.
📚 Practice Problems
1Problem 1easy
❓ Question:
A factory produces steel and emits pollution that imposes $3 of external cost per ton on neighboring farms. Without intervention, the market produces 1,000 tons. (a) Is this a positive or negative externality? (b) Is the market quantity above or below the social optimum? (c) State the size of the per-unit Pigouvian tax that would internalize the externality.
💡 Show Solution
(a) Negative externality (pollution imposes cost on a third party).
(b) Market quantity is ABOVE the socially optimal quantity, because producers ignore the $3 external cost and over-produce.
(c) Pigouvian tax = exactly the per-unit external cost = $3 per ton. This raises MPC to MSC, making each producer face the true social cost.
2Problem 2easy
❓ Question:
Vaccinating against a contagious disease creates a positive externality of $50 per vaccination (lower spread reduces others' risk). The free market produces 1 million vaccinations; the social optimum is 1.4 million. (a) What size per-unit subsidy would push the market to the social optimum? (b) Who pays the subsidy and who receives it?
💡 Show Solution
(a) A Pigouvian subsidy equal to the per-unit external benefit = $50 per vaccination would shift MPB up to MSB, equating private and social marginal benefit.
(b) The government pays the subsidy out of tax revenue; the subsidy is typically given to consumers (lower price at point of purchase) or producers (per-shot reimbursement). The economic incidence is shared between the two depending on demand and supply elasticities.
3Problem 3medium
❓ Question:
Distinguish a public good from a common-pool resource, naming the two key properties (excludability and rivalry) and giving one example of each.
💡 Show Solution
Both are NON-EXCLUDABLE — you cannot prevent unpaying users from consuming. The difference is rivalry.
Public good: non-excludable AND non-rival — one person's consumption doesn't reduce another's. Example: national defense, basic scientific research, fireworks display.
Common-pool resource: non-excludable but rival — one person's use REDUCES what is available to others. Example: an ocean fishery, an open grazing pasture, congested freeway lanes. Subject to the Tragedy of the Commons (overuse).
4Problem 4medium
❓ Question:
Demand for a positive-externality good is . Private supply is . Each unit produces an external benefit of $10. (a) Find the free-market equilibrium . (b) Find the socially optimal . (c) Compute the deadweight loss of the market outcome.
💡 Show Solution
(a) Free market: where MPB = supply: .
(b) Social optimum: supply, where . Set .
(c) DWL is the triangle between MSB and supply, from to :
- Base = .
- Height = vertical distance between MSB and supply at = .
DWL = \tfrac{1}{2}(5)(10) = \boxed{\25}$.
5Problem 5hard
❓ Question:
Compare a Pigouvian tax with a cap-and-trade system as ways to address pollution. Under what circumstances would you prefer one over the other? Address (a) certainty over emission levels, (b) certainty over price/cost, and (c) administrative simplicity.
💡 Show Solution
Both achieve the efficient outcome IN PRINCIPLE, but they differ in what is fixed and what adjusts.
(a) Certainty over emissions: Cap-and-trade FIXES the total quantity of emissions (the cap). Tax fixes the per-unit price; total emissions adjust based on firms' responses. If we have a strict environmental target (e.g., a planetary CO₂ budget), cap-and-trade gives more certainty.
(b) Certainty over cost: Tax fixes the per-unit cost of polluting at a known level — firms know their costs, planning is easier. Permit price under cap-and-trade can spike or crash with economic conditions, creating cost uncertainty.
(c) Administrative simplicity: A tax is simpler to administer (per-unit charge) and avoids the complications of permit allocation, monitoring trades, and enforcement. Cap-and-trade requires building a working permit market, monitoring trades, and policing emissions levels per firm.
Preference:
- Tax preferred when we care more about cost certainty and the marginal-damage curve is FLAT (small uncertainty in environmental harm).
- Cap-and-trade preferred when we care more about emissions certainty and marginal damage rises STEEPLY (e.g., near a tipping point).
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