Public Goods & the Free-Rider Problem

Non-rival, non-excludable goods that markets under-provide, from lighthouses to national defense.

Equilibrium: Q* = 50.0, P* = 25.0

Current equations

Private MB: P = 50 − 0.5·QSocial MB: P = 80 − 0.8·QMC: P = 10 + 0.3·Q

Some goods, once provided, serve everyone: streetlights, defence, clean air. Because nobody can be excluded, everyone waits for someone else to pay. The market only sees the private benefit curve, so it stops far short of what the good is really worth to society.

Shift the curves

Free-riding (people hide their true willingness to pay)0

The more people free-ride, the less private willingness to pay is revealed.

Social value of the good0

Summing everyone's benefit vertically: the true social demand for the good.

The Public Goods & the Free-Rider Problem model, in writing

Definition

Goods that are non-excludable (can't keep non-payers out) and non-rival (my use doesn't reduce yours), so private markets under-provide them.

Efficient provision: ΣMB (sum of everyone's marginal benefits) = MC

The intuition

If the lighthouse shines for everyone, why would you pay for it? Everyone reasons the same way, everyone free-rides, and the lighthouse never gets built, which is why defense, streetlights, and basic research are publicly funded.

Exam tip

For public goods you sum demand curves VERTICALLY (everyone consumes the same quantity), not horizontally.

Related models in Micro Foundations

Production Possibility Frontier →Absolute vs. Comparative Advantage →Supply & Demand →Price Elasticity of Demand & Supply →