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AP® Microeconomics · Unit 6 · Topic 6.2

Externalities: Study Guide (Microeconomics 6.2)

Learn what positive and negative externalities are, why markets over- or under-produce, how to graph and calculate the deadweight loss, and how taxes, subsidies, regulation and property rights correct it.

What an externality is

In Topic 6.1 you saw that a competitive market is efficient only when buyers and sellers bear all the benefits and costs of their choices. An externality is what happens when they do not.

An externality is a cost or benefit of producing or consuming a good that falls on a third party: someone who is not the buyer or the seller and who is not paid or charged for it through the market.

  • A negative externality imposes a cost on third parties. Its size per unit is the marginal external cost (MEC).
  • A positive externality gives a benefit to third parties. Its size per unit is the marginal external benefit (MEB).

Social values add the external part to the private part:

  • MSC = MPC + MEC (marginal social cost = marginal private cost + marginal external cost)
  • MSB = MPB + MEB (marginal social benefit = marginal private benefit + marginal external benefit)

The efficient quantity is still where MSB = MSC, because that is where total economic surplus, including third parties, is greatest. Externalities can arise from production or from consumption:

Type Example Which curve differs Market result
Negative, in production a factory’s smoke damages nearby crops MSC is above MPC too much
Negative, in consumption loud music at a late party disturbs neighbours MSB is below MPB too much
Positive, in production a beekeeper’s bees pollinate a neighbour’s orchard MSC is below MPC too little
Positive, in consumption a vaccinated person makes others less likely to catch a disease MSB is above MPB too little

A useful rule: for a production externality the cost curves split; for a consumption externality the benefit curves split.

Why markets ignore external effects

Rational agents respond to private costs and benefits, not external ones. A paper mill compares the price of paper with its own marginal cost. The damage its waste does to fishing downstream is not on its bill, so it does not affect its output decision. A person deciding whether to get a vaccination weighs their own protection against the price, not the protection it gives to others.

Why are these effects left out? There are two main reasons:

  1. Property rights are not well defined. Nobody owns the river, the air or the quiet of a street. If no one owns them, no one can charge for their use, so damaging them is free to the person doing it.
  2. Transaction costs are high. Even when rights exist, the people affected may be too many, or too hard to identify, to bargain with. Two neighbours can talk; ten thousand people downwind of a factory cannot easily organise.

Positive externalities have an extra problem: free riding. If a benefit spills over to people who cannot be excluded from it (it is non-excludable), each of them has an incentive to let someone else pay. Suppose one farm in a valley restores a wetland that holds back floodwater for every farm. The other farms gain whether or not they contribute, so it is rational for each to pay nothing. Too little of the good is provided. You will see this again with public goods in Topic 6.3.

Negative externalities on a graph

Paper mills on the Rennick River, a fictional river, form a competitive market. Q is in thousand tonnes per year and P is in dollars per tonne.

  • Demand: MPB = MSB = 100 − Q (no external benefit)
  • Supply: MPC = 20 + Q
  • Waste harms fishing downstream: MEC = $20 per tonne, so MSC = 40 + Q
Overproduction of paper on the Rennick River: a negative production externality Graph with quantity of paper in thousand tonnes per year on the horizontal axis, 0 to 90, and price or cost in dollars per tonne on the vertical axis, 0 to 120. Downward-sloping demand, labelled D = MPB = MSB, starts at $100. Upward-sloping supply, labelled S = MPC, starts at $20. A second upward-sloping line, dashed and labelled MSC = MPC + $20, lies $20 above S at every quantity and starts at $40. S meets D at the market point M, 40 thousand tonnes and $60, shown as an open circle. MSC meets D at the socially optimal point O, 30 thousand tonnes and $70, shown as a filled circle. A hatched triangle with corners at O, at M, and at the point on MSC above M (40 thousand tonnes and $80) is labelled deadweight loss $100 thousand. A double arrow between S and MSC at 66 thousand tonnes is labelled MEC = $20. M O MEC = $20 deadweight loss $100 thousand D = MPB = MSB S = MPC MSC (dashed) 0 $20 $40 $60 $80 $100 $120 10 20 30 40 50 60 70 80 90 Quantity of paper (thousand tonnes per year) Price or cost ($ per tonne)
Figure 1. Paper mills on the Rennick River (fictional data). The market (open circle M) ignores the $20 external cost per tonne and produces 40 thousand tonnes. The socially optimal point (filled circle O) is 30 thousand tonnes. The hatched triangle is the deadweight loss from the 10 thousand tonnes whose MSC is above their MSB.

What the graph shows:

  • The market finds where MPB = MPC (point M). It ignores the $20 external cost.
  • The socially optimal point is where MSB = MSC (point O).
  • The market produces too much, at too low a price. The price does not include the damage to fishing.
  • For each unit between Qs and Qm, MSC is above MSB. Making those units loses surplus. The deadweight loss is the triangle between MSC and MSB, from Qs to Qm, pointing to O.

Be careful: the whole band between MPC and MSC up to Qm is the total external cost, not the DWL. Most of that cost comes with units that are still worth producing. Only the triangle is lost surplus.

Positive externalities on a graph

For a positive consumption externality, MSB lies above MPB (demand). Buyers ignore the benefit to others, so the market stops at Qm, where MPB = MPC. The socially optimal quantity Qs, where MSB = MSC, is larger. The market produces too little. The DWL is the triangle between MSB and MSC from Qm to Qs, again pointing to where MSB = MSC. Figure 2, in Worked example 2, shows this case with numbers.

Policies that correct externalities

Policy How it works Notes
Per-unit tax (on a negative externality) set the tax equal to the MEC at the optimal quantity; MPC + tax = MSC there, so the market moves to Qs raises revenue; the price buyers pay rises
Per-unit subsidy (on a positive externality) set the subsidy equal to the MEB at the optimal quantity; the market expands to Qs costs the government money
Environmental regulation limits on output or emissions, required equipment, bans on harmful methods can reach the target directly, but raises no revenue and needs the regulator to know the right limit
Public provision the government supplies the good itself, often free or cheap (e.g. vaccinations, parks) used when the benefit spills over widely
Assignment of property rights give someone a legal right (e.g. to clean water), so damage must be paid for or bargained over needs rights that can be enforced
Reassignment of rights through private transactions rights are bought and sold: one side pays the other to stop, or firms trade pollution permits works best when transaction costs are low

When the MEC or MEB is the same for every unit, the right tax or subsidy is just that amount. If the MEC rises with output, use its value at the optimal quantity, not at the market quantity.

Worked example 1: a tax on paper

Question. Use the Rennick River paper market above. (a) Find the market quantity and price. (b) Find the socially optimal quantity and price. (c) Calculate the DWL. (d) The government sets a per-unit tax of $20 on paper. Find the new quantity, the price buyers pay, the price sellers keep and the tax revenue. (e) Compare the total external cost before and after the tax.

(a) MPB = MPC: 100 − Q = 20 + Q, so 2Q = 80, Qm = 40 thousand tonnes and P = $60 per tonne.

(b) MSB = MSC: 100 − Q = 40 + Q, so 2Q = 60, Qs = 30 thousand tonnes and P = $70 per tonne.

(c) At Qm = 40: MSC = 40 + 40 = $80 and MSB = 100 − 40 = $60. DWL = ½ × (40 − 30) × (80 − 60) = ½ × 10 × 20 = $100 thousand per year.

(d) The tax adds $20 to every unit, so sellers now face 20 + Q + 20 = 40 + Q, which is the MSC line.

  1. 100 − Q = 40 + Q gives Q = 30 thousand tonnes: the optimal quantity.
  2. Buyers pay $70; sellers keep 70 − 20 = $50 per tonne.
  3. Tax revenue = 20 × 30 = $600 thousand per year.

(e) Before: 20 × 40 = $800 thousand. After: 20 × 30 = $600 thousand. The tax cuts the damage, but not to zero. Each of the remaining 30 thousand tonnes is worth at least its full social cost to buyers, so producing them is efficient.

Check. The tax works because it makes sellers pay the external cost: it internalises the externality.

Worked example 2: a subsidy for vaccinations

Question. In Ostley, a fictional city, flu vaccinations are sold in a competitive market. Q is in thousands of doses per year and P is in dollars per dose.

  • MPB = 60 − 0.5Q MPC = MSC = 10 + 0.5Q
  • Each dose also protects other people: MEB = $10 per dose, so MSB = 70 − 0.5Q.

(a) Find the market and optimal quantities. (b) Calculate the DWL. (c) Find the subsidy per dose that gives the optimal quantity, the prices that result and the cost to the government.

Underconsumption of flu vaccinations in Ostley: a positive consumption externality Graph with quantity of vaccinations in thousands per year on the horizontal axis, 0 to 120, and price, benefit or cost in dollars per dose on the vertical axis, 0 to 80. Upward-sloping supply, labelled S = MPC = MSC, starts at $10. Downward-sloping demand, labelled D = MPB, starts at $60. A second downward-sloping line, dashed and labelled MSB = MPB + $10, lies $10 above D at every quantity and starts at $70. D meets S at the market point M, 50 thousand doses and $35, shown as an open circle. MSB meets S at the socially optimal point O, 60 thousand doses and $40, shown as a filled circle. A hatched triangle with corners at the point on MSB above M (50 thousand and $45), at M, and at O is labelled deadweight loss $50 thousand. M O deadweight loss $50 thousand D = MPB MSB (dashed) S = MPC = MSC 0 $10 $20 $30 $40 $50 $60 $70 $80 20 40 60 80 100 120 Quantity of vaccinations (thousands per year) Price, benefit or cost ($ per dose)
Figure 2. Flu vaccinations in Ostley (fictional data). Buyers ignore the $10 benefit each dose gives to other people, so the market (open circle M) stops at 50 thousand doses. The socially optimal point (filled circle O) is 60 thousand doses. The hatched triangle is the deadweight loss from the doses whose MSB is above their MSC but which are not bought.

(a) Market: 60 − 0.5Q = 10 + 0.5Q, so Qm = 50 thousand doses at $35. Optimum: 70 − 0.5Q = 10 + 0.5Q, so Qs = 60 thousand doses, where MSB = MSC = $40.

(b) At Qm = 50: MSB = 70 − 25 = $45 and MSC = 10 + 25 = $35. DWL = ½ × (60 − 50) × (45 − 35) = ½ × 10 × 10 = $50 thousand per year.

(c) A subsidy of $10 per dose (the MEB). Paid to buyers, it raises what they are willing to pay by $10, so their demand becomes the MSB line.

  1. 70 − 0.5Q = 10 + 0.5Q gives Q = 60 thousand.
  2. Sellers receive $40; buyers pay 40 − 10 = $30 after the subsidy.
  3. Cost to the government = 10 × 60 = $600 thousand per year.

If the $10 were paid to sellers instead, their marginal cost line would shift down by $10, to 0.5Q, and the result would be the same: 60 thousand doses, buyers paying $30 and sellers receiving $40. The government could also reach Qs through public provision, for example by offering free doses at clinics.

Worked example 3: bargaining over property rights

Question. Brackenhill Quarry (fictional) wants to start blasting at night. This would add $30 thousand a year to its profit. The noise would cost the only nearby hotel $50 thousand a year in lost bookings. Assume the two can bargain at no cost. (a) What is the efficient outcome? (b) What happens if the hotel has the legal right to quiet nights? (c) What happens if the quarry has the legal right to blast? (d) Why might bargaining fail if 2,000 households were affected instead of one hotel?

(a) The blasting gains $30 thousand but costs $50 thousand. Society is $20 thousand worse off with it, so the efficient outcome is no night blasting.

(b) The quarry would need to pay the hotel at least $50 thousand for permission. Blasting is worth only $30 thousand to the quarry, so it does not buy the right. No blasting.

(c) The hotel can offer the quarry a payment between $30 thousand and $50 thousand to stop. Any amount in that range leaves both better off. No blasting.

(d) Each household would have to be found and included, and the cost of organising them would be large: high transaction costs. Each household would also hope that others pay, because it gains from quiet nights either way: free riding. The bargain probably never happens, so a government policy (a ban on night blasting, or a charge for it) may be needed.

Interpretation. With well-defined rights and low transaction costs, private bargaining reaches the efficient outcome whichever side holds the right. The right only decides who pays whom. Economists call this result the Coase theorem.

Common misconceptions

  • “Any cost of making a good is an externality.” Only costs that fall on third parties count. Wages and materials are private costs.
  • “With a negative externality, the market price is too high.” It is too low: it leaves out the external cost, so too much is bought.
  • “The socially optimal level of pollution is zero.” It is where MSB = MSC, which usually involves some pollution.
  • “The DWL of a negative externality is the area between MPC and MSC.” That band is the total external cost. The DWL is only the triangle beyond Qs.
  • “The tax should equal the MEC at the market quantity.” It should equal the MEC at the optimal quantity. With a constant MEC the two are the same; with a rising MEC they are not.
  • “Free riders are behaving irrationally.” Free riding is a rational response to a benefit you cannot be excluded from.
  • “A positive externality shifts the demand curve.” Demand stays as the MPB curve; the MSB curve is a separate line. A subsidy is what changes the market outcome.

Where this leads

Free riding returns in Topic 6.3, where it explains why markets rarely supply public goods: Public and Private Goods study guide. To review the MSB = MSC rule, see the Topic 6.1 study guide. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate.

Quick questions

Is the socially optimal amount of pollution zero?

Usually not. Cutting pollution to zero would mean giving up goods whose benefit is greater than their full social cost. The optimal quantity is where MSB = MSC, which normally still involves some pollution.

Does it matter whether a corrective subsidy is paid to buyers or to sellers?

Not for the quantity. Either way the gap between what buyers pay and what sellers receive equals the subsidy, so the market reaches the same quantity. The prices quoted differ, but the outcome is the same.

Is a rise in the price of a good caused by other buyers an externality?

No. Price changes are passed through the market and are part of how markets work. An externality is an effect on a third party that no market price records, such as noise, pollution or a health benefit.

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