A College Board–style free-response question on Market Failure and the Role of Government, broken into parts with a model answer showing exactly how each point is earned.
The market for industrial solvent is perfectly competitive. Production releases fumes that impose costs on nearby residents who are not part of the transaction. The relevant curves are given below, where Q is measured in thousands of gallons and all values are in dollars.
| Curve | Equation | What it represents |
|---|---|---|
| Demand (MPB = MSB) | P = 40 − Q | What buyers are willing to pay; no consumption spillover |
| Supply (MPC) | P = 10 + Q | The private cost borne by producers |
| MSC | P = 16 + Q | Private cost plus the cost imposed on residents |
The unregulated market equilibrium occurs where demand equals private supply, because producers respond only to their own costs:
40 − Q = 10 + Q → 30 = 2Q → Q = 15 thousand gallons
Substituting back: P = 40 − 15 = $25.
The socially optimal quantity occurs where MSB = MSC:
40 − Q = 16 + Q → 24 = 2Q → Q = 12 thousand gallons
This is less than the market quantity of 15. Because production imposes a cost on third parties, marginal social cost exceeds marginal private cost at every quantity. Producers ignore that spillover, so the free market overproduces by 3 thousand gallons.
The per-unit external cost is the vertical distance between MSC and MPC: (16 + Q) − (10 + Q) = $6 per unit, constant at every quantity.
The corrective (Pigouvian) tax should be $6 per unit — exactly equal to the per-unit external cost.
The tax shifts the supply curve upward by $6, so private cost becomes P = 10 + Q + 6 = 16 + Q, which is precisely the MSC curve. Producers now internalize the cost their fumes impose on residents, and the new market equilibrium occurs where 40 − Q = 16 + Q, giving Q = 12 — the socially optimal quantity.
Consumers pay 40 − 12 = $28, while producers keep $28 − $6 = $22 per unit.
Deadweight loss in the unregulated market. At the market quantity of 15, marginal social cost is 16 + 15 = $31 while marginal social benefit is 40 − 15 = $25. Every unit between 12 and 15 costs society more than it is worth, by a gap widening from $0 to $6:
DWL = ½ × base × height = ½ × (15 − 12) × ($31 − $25) = ½ × 3 × $6 = $9 thousand.
A $10 tax overshoots. It would raise private cost to P = 20 + Q, above true MSC of 16 + Q. The new equilibrium would be 40 − Q = 20 + Q, giving Q = 10 — now below the socially optimal 12. The market would underproduce, and deadweight loss would reappear on the other side of the optimum. Intervention larger than the actual externality creates its own inefficiency rather than removing it.