Externalities
The market settles where PMC = PMB; the optimum is where SMC = SMB. Negative externality ⇒ overproduction, tax it. Positive ⇒ underproduction, subsidize it.
Formula
The two cases
| Type | Curve that moves | Result | Fix |
|---|---|---|---|
| Negative pollution | SMC above PMC | Q* < Q₁ — overproduces | Tax = external MC |
| Positive vaccines, education | SMB above PMB | Q* > Q₁ — underproduces | Subsidy = external MB |
The deadweight loss triangle always points toward the social optimum.
Optimal pollution is not zero
A past midterm asked this. If the activity raises social marginal cost by a quantifiable amount, the optimal quantity sits where SMC meets SMB — typically nonzero and finite. It could land at zero; nothing says it must. Preposterous to a biologist, and it is the economist's answer.
The policy toolkit
- Pigouvian tax / subsidy
- Named for Arthur Pigou. Per-unit charge equal to the external harm, or payment equal to the external benefit, sized at the efficient point. Cases: gas taxes earmarked for road maintenance (wear and tear, not global warming), London's congestion charge — £5 in 2003, now £15 — New York's $9 Manhattan charge below 61st Street from 2025, R&D tax credits.
- Coase (Nobel 1991)
- Clearly defined property rights let private parties negotiate to the efficient outcome without government. Negotiation is costly, so rights must be assigned well.
- Ostrom (Nobel 2009)
- Communities manage common resources sustainably without privatization or central control. Ingredients: long-term interest, monitoring, trust. People are not mindlessly trapped in the tragedy of the commons.
- Regulation
- Bans, emission limits, smog checks — what usually happens. A fine is economically a tax. But abatement costs vary enormously: electric cars exist, electric planes do not, so a uniform CO₂ rule could wipe out aviation.
- Cap and trade
- Tradable permits, so every emitter faces the same price and cuts happen where they are cheapest. Set the cap so the permit price equals SMC. Worked for SO₂ (acid rain) and CFCs (ozone), where bans were infeasible and allowances shrank over years.
Climate change
Costs: extreme weather making places less livable and potentially driving mass migration; agricultural disruption, which bites because food demand is inelastic in the short run, so shortfalls become price spikes and famines in low-income countries; biodiversity loss. The pace of change makes adaptation hard.
The fix is a carbon tax equal to the marginal damage of CO₂. The unsettled part is the discount rate, since most damage lies ahead: discount heavily and the tax is small, lightly and it is large and politically unpopular. Economics cannot settle it — ethics must. Hence the 2019 economists' carbon tax letter agreed on the instrument, not the number.
Rules that earn points
- Draw the private equilibrium first — PMC and PMB crossing at Q₁.
- Add the social curve above the private one on the correct side.
- Mark Q* where SMC = SMB, and say over- or underproduces.
- Put the triangle between Q* and Q₁, point at Q*.
- Prescribe a tax or subsidy sized to the external effect at Q*.
- Shifting the wrong curve. Pollution is a cost, so it moves the cost curve.
- Saying the optimal level of pollution is zero.
- Forgetting Coase needs property rights and low negotiation costs.
- Treating the carbon tax as a settled number. The discount rate is the whole argument.
Burning gasoline imposes pollution costs on people outside the market. Relative to the social optimum, the unregulated market:
- AProduces too much, because SMC lies above PMC
- BProduces too little, because SMB lies above PMB
- CProduces too much, because demand shifts down
- DProduces the efficient quantity, since buyers and sellers are both better off
Answer
A — too much, because SMC lies above PMC.
The market equates PMC and PMB at Q₁; the optimum is where SMC meets SMB at Q* < Q₁. The gap between Q* and Q₁ is the deadweight loss triangle.
C is the trap: it reaches the right conclusion through the wrong curve. Pollution is a cost, so it moves the cost curve. Willingness to pay for gasoline is unchanged.
A Pigouvian tax that corrects a negative externality should equal:
- AThe total external cost imposed by the industry
- BThe external marginal cost at the socially efficient quantity Q*
- CThe external marginal cost at the unregulated quantity Q₁
- DThe full vertical gap between SMC and SMB at Q₁
Answer
B — the marginal external effect at Q*.
A per-unit tax of that size shifts private supply up until it coincides with SMC, so the market delivers Q* on its own.
A is the trap: it confuses a total with a marginal. Firms respond to per-unit incentives, and total external cost would be an enormous, quantity-independent number.
Economists prefer cap and trade to a uniform emissions regulation mainly because:
- AIt eliminates emissions entirely, while regulation only limits them
- BAbatement costs differ across emitters, and trading equalizes the price every emitter faces so cuts happen where they are cheapest
- CIt raises more government revenue than a tax
- DIt avoids the need to decide how much pollution is acceptable
Answer
B — it puts one price on emissions and lets cheap cuts happen first.
Electric cars exist, electric planes do not, so a flat CO₂ requirement could destroy high-value aviation. It worked for SO₂ under acid-rain rules and for ozone-depleting CFCs.
D is the trap: choosing the cap is deciding how much pollution is acceptable. Cap and trade fixes the quantity and lets the market find the price.
Economists disagree sharply about the size of the optimal carbon tax mainly because they disagree about:
- AWhether climate change is happening
- BThe discount rate applied to damages that occur far in the future
- CWhether a tax or a subsidy is the right instrument
- DThe price elasticity of demand for gasoline
Answer
B — the discount rate.
The tax should equal the marginal damage of CO₂, but almost all damage lands in the future. Discount heavily and the present value is small; discount lightly and it is enormous. The economics cannot settle it — it is a question about how much weight to give future generations.
C is the trap: there is broad agreement on the instrument. The 2019 economists' carbon tax letter united signatories on the tax and not on the number.
Draw the market for gasoline with a pollution externality. Show the market equilibrium, the social optimum, the deadweight loss, and the corrective policy.
Model answer
Demand is PMB = SMB, since the externality is on the cost side. Supply is PMC. They cross at Q₁, the market equilibrium.
Draw SMC above PMC, separated vertically by the external marginal cost. SMC crosses demand at Q* < Q₁ — the market overproduces.
The deadweight loss triangle sits between Q* and Q₁, bounded by SMC above and demand below, with its point at Q*. At Q₁, social marginal cost exceeds social marginal benefit.
The fix: a Pigouvian tax equal to the external marginal cost at Q*, which shifts supply up until it coincides with SMC and the market delivers Q* on its own.
- Stating that demand is unaffected — PMB = SMB — before drawing anything.
- SMC drawn above PMC, separated by the external marginal cost, not an arbitrary gap.
- Q* to the left of Q₁, with the word overproduces.
- The triangle bounded correctly and pointing at Q*.
- The tax sized to the external MC at Q*, with the mechanism (supply shifts onto SMC).
Can there be an "optimal" level of polluting, or is the optimal level always zero? Refer to social marginal cost and social marginal benefit.
Model answer
It may sound preposterous to biologists, but economists hold that if a polluting activity raises social marginal cost by some quantifiable amount, then the socially optimal quantity and price in that market are typically nonzero and finite.
They are found at the intersection of social marginal cost and social marginal benefit — the latter being demand, or willingness to pay. That intersection could occur at zero quantity and therefore zero pollution, but there is no reason to expect that it must.
- Answering the question directly: no, not always zero.
- Locating the optimum at SMC = SMB, naming both curves.
- Identifying SMB with demand / willingness to pay.
- Conceding that zero is possible but not to be expected — the nuance is worth a point.
- Treating the external cost as quantifiable and marginal, not infinite.