Marginal Social Benefit, Marginal Social Cost & the Optimum

You’ll be able to

Distinguish private from social marginal benefit and cost
Locate the socially optimal quantity and compare it with the market quantity
Identify the deadweight loss caused by an externality

Four curves, two of which the market ignores

Private decisions rest on marginal private benefit (MPB) and marginal private cost (MPC), which are the ordinary demand and supply curves. Society cares about marginal social benefit (MSB) and marginal social cost (MSC), which add in the effects on third parties. When there is no externality the private and social curves coincide and the market gets it right. An externality separates them, and that separation is the entire content of market failure.

The relationships

MSB = MPB + external benefit · MSC = MPC + external cost · socially optimal quantity: MSB = MSC

The market produces where MPB = MPC. The optimum is where MSB = MSC. The gap between those two quantities is the market failure.

Negative externality: the market overproduces

A negative externality in production — pollution — means MSC lies above MPC. The market ignores the external cost, so it produces where MPB = MPC, which is more than the optimum where MSB = MSC. Every unit between the optimum and the market quantity costs society more than it is worth, and the surplus destroyed is the deadweight loss. Note the direction carefully: overproduction, and the socially optimal quantity is not zero.

Positive externality: the market underproduces

A positive externality in consumption — vaccination, education — means MSB lies above MPB. Buyers only count their own benefit, so the market produces less than the optimum. Units between the market quantity and the optimum would have been worth more to society than they cost, and are not made. So positive externalities also produce deadweight loss, and the correction is a subsidy rather than a tax.

Worked example

A factory's production imposes $8 per unit of pollution damage on nearby residents. The market equilibrium is 500 units; the socially optimal quantity is 380 units. Describe the graph and estimate the deadweight loss.

1.MSC lies $8 above MPC at every quantity — a vertical gap equal to the external cost.
2.The market produces where MPB = MPC, at 500 units, ignoring the $8.
3.The optimum is where MSB = MSC, at 380 units.
4.The deadweight loss triangle has base 500 − 380 = 120 units and height $8 at the market quantity.
5.Area ≈ ½ × 120 × 8 = $480.

Answer: The market overproduces by 120 units, with a deadweight loss of about $480. The optimum is 380 units, not zero — some production is worth its pollution cost, which is why the policy goal is to correct the quantity rather than eliminate the activity.

Watch out

The socially optimal quantity of a polluting good is almost never zero. It is where marginal social benefit meets marginal social cost. An answer claiming the optimum is no production at all has confused an externality with a prohibition.

Checkpoint

When a good generates a negative externality in production, the market:

Checkpoint

Vaccination generates a positive externality. Compared with the socially optimal quantity, the free market provides:

Checkpoint

The socially optimal quantity occurs where:

On the exam

Draw and label all four relevant curves and mark both quantities — market and socially optimal. Rubrics award identifying the two quantities separately from computing the deadweight loss between them.

Answer the 3 checkpoints as you read.