Non-rival, non-excludable goods that markets under-provide, from lighthouses to national defense.
Warming up the engine…
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
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.
For public goods you sum demand curves VERTICALLY (everyone consumes the same quantity), not horizontally.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at Q 50, P 25.
Equilibrium: Q* = 50.0, P* = 25.0
Current equations
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.