Externalities

When your choice spills onto others

An externality is a cost or benefit that falls on someone outside the transaction — pollution from a factory, noise from a neighbor. The market prices the private costs and benefits, but ignores the spillover, so it produces the wrong quantity.

Take a negative production externality. Firms set output where demand meets their marginal private cost (MPC) — the usual supply curve. But each unit also imposes a marginal external cost (MEC) on others. The true cost to society is \[ \text{MSC} = \text{MPC} + \text{MEC}. \] The market produces \(Q_m\) where Demand = MPC. The efficient quantity is \(Q^\*\) where Demand = MSC — smaller, because society’s true cost is higher. The gap produces a deadweight loss: units between \(Q^\*\) and \(Q_m\) cost society more than buyers value them.

The fix is a Pigouvian tax equal to the marginal external cost. It raises the firm’s effective cost curve up to the MSC, so the market now chooses \(Q^\*\) on its own. With linear curves and a constant external cost \(e\), the Pigouvian tax is simply \(e\).

Try it. Raise the external cost. The MSC curve lifts above private supply, the efficient quantity \(Q^\*\) falls below the market quantity \(Q_m\), and the shaded deadweight-loss triangle grows. The Pigouvian tax that fixes it equals the external cost.

Demand intercept (A): 30 Private cost intercept (c): 6 Marginal external cost (e): 8

▬ Demand▬ MPC▬ MSC

What to notice

• With e = 0 the MSC and MPC curves coincide, \(Q_m = Q^\*\), and there’s no deadweight loss — no externality, no problem.
• Raising e lifts MSC above private supply; the market keeps producing at \(Q_m\) while the efficient point \(Q^\*\) retreats. The red triangle is the welfare lost to overproduction.
• A Pigouvian tax of e per unit makes firms internalize the spillover — their effective cost becomes the MSC and the market lands on \(Q^\*\) by itself.