How to Calculate Marginal Social Benefit
Marginal social benefit equals marginal private benefit plus marginal external benefit: MSB = MPB + marginal external benefit.
The Marginal Social Benefit formula
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Add marginal private benefit and marginal external benefit to get the full value society gets from a unit.
What the buyer alone gets from one more unit. This is the demand curve.
Spillover value to third parties, such as the illness a vaccination prevents in others.
What it takes to provide one more unit, which is also the price the buyer faces.
That unit is worth $65 to society: $40 to the buyer plus $25 spilling onto everyone else.
- Net social gain from one more unit
- $15
- Private buyer's decision
- Skips
- Efficient per-unit subsidy
- $25
- Market outcome
- Underproduction
Society gains $15 on that unit, and loses that much every time it goes unprovided.
The buyer values it at $40 against a $50 price, so they walk away even though others would have gained.
A subsidy equal to the marginal external benefit lowers the buyer's price until private choice matches social value.
Society wants the unit but the buyer does not, which is exactly why a positive externality leaves the market short of the efficient quantity.
How to calculate Marginal Social Benefit, step by step
- 1Start with marginal private benefit. MPB is the value the buyer places on one more unit, and it is what the market demand curve shows.
- 2Measure the marginal external benefit. This is the spillover benefit others receive per unit, such as the lower disease transmission from one more vaccination.
- 3Add the two benefits. MSB = MPB + marginal external benefit, the full value society gets from one more unit.
- 4Compare MSB with MSC. With a positive externality MSB sits above demand, so the efficient quantity where MSB = MSC lies to the right of the market quantity.
Worked example: Marginal Social Benefit
A flu shot is worth $40 to the person who gets it, so MPB = $40. It also spares coworkers and classmates roughly $25 of avoided illness, the marginal external benefit. MSB = 40 + 25 = $65 per shot. If a shot costs $50 to provide, the buyer skips it because $40 falls short of the $50 price, yet society loses out: $65 of benefit exceeds the $50 cost by 65 − 50 = $15 per shot, and that $15 is the value destroyed each time the market underproduces.
Marginal Social Benefit questions
What is the difference between marginal social benefit and marginal private benefit?
Marginal private benefit is the value to the buyer alone, while marginal social benefit adds the benefit spilling onto third parties. They are equal when no positive externality exists.
Why does the market underproduce a good with a positive externality?
Buyers weigh only their own benefit against the price, so they stop where MPB meets marginal cost. Because MSB is higher than MPB, the efficient quantity where MSB = MSC sits further to the right.
How does a subsidy fix a positive externality?
A per-unit subsidy equal to the marginal external benefit lowers the price buyers pay so their private choice reflects MSB, expanding output to the efficient quantity.
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