Difficulty: Intermediate | Prerequisites: Supply and demand basics, consumer and producer surplus, market equilibrium (Chapters 1–5)
This material sits at the intersection of supply-and-demand analysis and welfare economics, two pillars of intermediate micro. You need to be comfortable computing equilibrium, calculating surplus areas, and understanding what externalities do to efficiency before any of this will land. The overarching question: when private markets generate costs that fall on third parties, what happens to welfare, and what can policy do about it?
A competitive gasoline market with a negative externality overproduces relative to the social optimum. A Pigouvian tax equal to the marginal external cost corrects the distortion and maximises total social welfare. A monopoly restricts output, which can accidentally move quantity closer to the social optimum when externalities are present, but that is not a reliable policy tool.
Competitive equilibrium
The price and quantity where quantity demanded equals quantity supplied, with no individual buyer or seller able to influence the price. In simple terms, it is the "natural" resting point of a market with many small participants.
Consumer surplus (CS)
The area below the demand curve and above the market price, measuring how much more consumers were willing to pay than they actually paid. Think of it as the collective "bonus" buyers get from trading.
Producer surplus (PS)
The area above the supply curve and below the market price, measuring the difference between what producers receive and the minimum they would accept. In simple terms, the collective gain sellers earn beyond their costs.
Negative externality
A cost imposed on third parties who are not involved in the transaction. Pollution from burning petrol is the textbook example: the driver and the petrol station agree on a price, but bystanders bear health and environmental costs they never consented to.
Marginal external cost (MEC)
The additional cost imposed on third parties by each extra unit consumed or produced. In this problem, MEC = $8 per gallon.
Social marginal cost (SMC)
Private marginal cost plus the marginal external cost: SMC = MC + MEC. This is the true cost to society of producing one more unit.
Pigouvian tax
A per-unit tax set equal to the marginal external cost, designed to make private decision-makers internalise the externality. Think of it as a price correction that forces the market to "see" the damage it causes.
Deadweight loss (DWL)
The reduction in total surplus that results from a quantity above or below the social optimum. It is the welfare that simply evaporates because the wrong amount is being produced.
Total social welfare
Consumer surplus plus producer surplus plus any government revenue, minus the total external cost. It captures the net benefit to everyone in society, not just the people in the transaction.
Monopoly
A single seller in a market. The monopolist sets MR = MC to maximise profit, producing less than the competitive quantity and charging a higher price.
Demand: Qd = 24,000 - 2,000P, which inverts to P = 24 - (1/2,000)Q
Supply: Qs = 2,000P, which inverts to P = (1/2,000)Q
Every gallon consumed imposes $8 of external harm (greenhouse gases, car crashes)
Set Qd = Qs: 24,000 - 2,000P = 2,000P, so 4,000P = 24,000, giving P* = $12 and Q* = 24,000 gallons (24k)
CS = 0.5 x (24 - 12) x 24,000 = $144,000 (144k)
PS = 0.5 x 12 x 24,000 = $144,000 (144k)
Negative externality = $8 x 24,000 = $192,000 (192k)
Total social welfare = CS + PS - externality = 144k + 144k - 192k = $96,000 (96k)
If gasoline is banned, Q = 0, so CS = 0, PS = 0, and the externality = 0
Total social welfare = $0
Since $0 < $96k, a complete ban reduces total welfare. The market, even with its externality, still generates positive net value
The policy takeaway: banning a good with a negative externality is rarely optimal. The gains from trade typically outweigh the external costs, at least up to some quantity
The social optimum sets the demand curve (marginal benefit) equal to the social marginal cost (private MC + $8 externality)
Demand: P = 24 - Q/2,000
Social MC: P = Q/2,000 + 8
Setting them equal: 24 - Q/2,000 = Q/2,000 + 8, so 16 = Q/1,000, giving Q_optimal = 16,000 (16k)
P at optimal Q: plug back into demand, P = 24 - 16/2 = $16 (consumers pay $16)
The supply price at Q = 16k is P = 16,000/2,000 = $8 (producers receive $8)
The $8 gap between consumer price ($16) and producer price ($8) is exactly the Pigouvian tax
CS = 0.5 x (24 - 16) x 16,000 = $64,000 (64k)
PS = 0.5 x 8 x 16,000 = $64,000 (64k)
Tax revenue = $8 x 16,000 = $128,000 (128k)
Negative externality = $8 x 16,000 = $128,000 (128k)
Total social welfare = CS + PS + tax revenue - externality = 64k + 64k + 128k - 128k = $128,000 (128k)
This is higher than the $96k from the unregulated competitive equilibrium, confirming the tax improves welfare
MC = (1/2,000)Q (same as the supply curve)
Demand: P = 24 - (1/2,000)Q
MR = 24 - (1/1,000)Q (twice the slope of the inverse demand curve)
Set MR = MC: 24 - Q/1,000 = Q/2,000
Solving: 48,000 - 2Q = Q, so 3Q = 48,000, giving Q_monopoly = 16,000 (16k)
P_monopoly = 24 - 16,000/2,000 = 24 - 8 = $16
CS = 0.5 x (24 - 16) x 16,000 = $64,000 (64k)
PS = 0.5 x (16 + 8) x 16,000 - that is, the area of the trapezoid above MC and below $16, which equals 0.5 x 16 x (8 + 16) = $192,000 (192k). More precisely: PS = total revenue - total variable cost = 16 x 16,000 - 0.5 x 8 x 16,000 = 256k - 64k = 192k
Private welfare (CS + PS) = 64k + 192k = $256,000 (256k)
Negative externality = $8 x 16,000 = $128,000 (128k)
Total social welfare = 256k - 128k = $128,000 (128k)
Without externalities, a competitive market always yields higher total welfare than a monopoly, because the monopoly restricts output below the efficient level
With negative externalities, the competitive market overproduces. A monopoly restricts output, which may coincidentally bring quantity closer to (or even exactly to) the social optimum
In this specific problem, the monopoly quantity (16k) happens to equal the socially optimal quantity (16k), so total social welfare under monopoly ($128k) equals the welfare under the optimal Pigouvian tax
This is a coincidence of the numbers, not a general result. Monopolies are not a policy substitute for corrective taxes, because there is no guarantee the monopoly output restriction will match the externality correction needed
Competitive equilibrium
Set Qd = Qs, solve for P*, then plug back for Q*.
Consumer surplus
CS = 0.5 x (P_max - P*) x Q*, where P_max is the y-intercept of the demand curve.
Producer surplus
PS = 0.5 x P* x Q* (when supply starts at the origin).
Total social welfare with externality
TSW = CS + PS + government revenue - total external cost.
Socially optimal quantity
Set demand = social marginal cost (i.e. private MC + MEC). Solve for Q.
Pigouvian tax rate
Tax = MEC = the gap between the consumer price and the producer price at the optimal quantity.
Monopoly output
Derive MR from the inverse demand curve (double the slope coefficient), set MR = MC, solve for Q.
Monopoly price
Plug Q_monopoly back into the inverse demand curve.
Pigouvian taxes on gasoline are not hypothetical. Many countries levy fuel excise duties that function as partial externality corrections, covering costs like road maintenance, air pollution, and carbon emissions. The UK fuel duty, for instance, is explicitly framed as pricing in environmental and congestion costs.
The monopoly-externality intersection appears in debates about pharmaceutical patents: a patent holder restricts output (raising price), which can reduce overconsumption of antibiotics, though the restriction is driven by profit, not public health.
Students often think banning a harmful good maximises welfare. It does not. A ban destroys all gains from trade, which usually outweigh the externality at low quantities. The optimal policy reduces quantity, not eliminates it.
Students sometimes forget to subtract the externality when computing total social welfare. CS + PS alone is private welfare, not social welfare.
A common error is setting the Pigouvian tax equal to the total externality cost rather than the per-unit marginal external cost. The tax is $8 per gallon, not $192,000.
Students may assume that because a monopoly produces less, it always makes welfare worse. With negative externalities, lower output can be welfare-improving, and in some cases (as in this problem) the monopoly quantity coincidentally equals the social optimum.
⚠️ You will almost certainly be asked to compute social welfare (CS + PS + gov revenue - externality). Make sure you include all four components.
⚠️ Expect a question asking whether a ban improves welfare. The answer is nearly always no, because $0 < the welfare from any positive quantity up to the social optimum.
⚠️ The Pigouvian tax rate equals the marginal external cost, not the total external cost. This distinction is tested frequently.
⚠️ Know how to show that monopoly output can match the socially optimal quantity when externalities are present. This is a favourite "explain the intuition" prompt.
⚠️ Be ready to draw the diagram: demand, private supply, social MC (shifted up by MEC), competitive equilibrium, and socially optimal equilibrium. Label CS, PS, DWL, and the tax wedge.
True or false: A Pigouvian tax always reduces total quantity traded in the market. (True)
Fill in the blank: Total social welfare = CS + PS + ______ - total external cost. (Government revenue)
True or false: Banning a good with a negative externality always increases social welfare. (False)
Fill in the blank: The socially optimal quantity is found by setting demand equal to ______. (Social marginal cost)
True or false: A monopoly always produces less than the socially optimal quantity when externalities are present. (False, it depends on the size of the externality relative to the monopoly restriction)
Q: Given demand Qd = 24,000 - 2,000P and supply Qs = 2,000P, with a $8/unit negative externality, what is the competitive equilibrium price and quantity, and what is total social welfare?
A: P* = $12, Q* = 24,000. CS = $144k, PS = $144k, externality = $192k. Total social welfare = 144k + 144k - 192k = $96,000.
Q: Would banning gasoline increase social welfare in this market?
A: No. A ban yields zero social welfare ($0), which is less than the $96k from the competitive equilibrium. Some trade is better than none, even with the externality.
Q: What Pigouvian tax achieves the socially optimal quantity, and what is welfare at that quantity?
A: A tax of $8/gallon (equal to MEC). Optimal Q = 16,000. Social welfare = CS ($64k) + PS ($64k) + tax revenue ($128k) - externality ($128k) = $128,000.
Q: If the market is served by a monopolist with MC = Q/2,000 and no government intervention, what is the monopoly price, quantity, and total social welfare?
A: Q_m = 16,000, P_m = $16. CS = $64k, PS = $192k, externality = $128k. Total social welfare = 64k + 192k - 128k = $128,000.
Q: Why might a monopoly yield higher social welfare than a competitive market when negative externalities are present?
A: The competitive market overproduces relative to the social optimum because it ignores external costs. A monopoly restricts output to maximise profit, which can coincidentally move quantity toward or to the social optimum. The monopoly "accidentally" corrects the externality by producing less.
This material connects directly to the theory of market failure: externalities are one of the four classic causes (along with public goods, market power, and information asymmetry). The Pigouvian tax concept reappears in environmental economics and public finance.
The monopoly-vs-competition welfare comparison ties back to earlier chapters on market structure. The twist here is that the standard "monopoly is always worse" result breaks down when externalities are in the picture, which is a useful bridge to second-best theory.
The welfare arithmetic (CS + PS + government revenue - externality) is the same framework used for analysing tariffs, quotas, and price controls later in the course.
Gasoline market, petrol market, fuel tax, externality, negative externality, Pigouvian tax, corrective tax, carbon tax, social marginal cost, marginal external cost, competitive equilibrium, consumer surplus, producer surplus, deadweight loss, total social welfare, market failure, monopoly welfare, monopoly vs competition, second-best theory, welfare economics, ECON 300, intermediate microeconomics