How to Calculate Marginal Social Cost
Marginal social cost equals marginal private cost plus marginal external cost: MSC = MPC + marginal external cost.
The Marginal Social Cost formula
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Add marginal private cost and marginal external cost to get the full cost to society of one more unit.
What the producer pays for one more unit. This is the supply curve.
Spillover cost borne by third parties, such as pollution damage.
Society gives up $110 for that unit: $80 borne by the producer plus $30 borne by everyone else.
- External cost as a share of MSC
- 27.3%
- Efficient per-unit tax
- $30
- Market outcome
- Overproduction
How much of the true cost of the last unit the producer never pays.
A Pigouvian tax equal to the marginal external cost lifts private cost up to marginal social cost.
Buyers weigh only the $80 private cost, so the market makes more than the efficient quantity and the last unit costs society $30 more than it is worth.
How to calculate Marginal Social Cost, step by step
- 1Start with marginal private cost. MPC is the cost the producer bears to make one more unit, and it is what the market supply curve shows.
- 2Measure the marginal external cost. This is the spillover cost imposed on third parties per unit, such as pollution damage to nearby residents.
- 3Add the two costs. MSC = MPC + marginal external cost, the full cost to society of producing one more unit.
- 4Place MSC on the graph. With a negative production externality, MSC sits above supply by the external cost, so the efficient quantity is smaller than the market quantity.
Worked example: Marginal Social Cost
Producing a ton of steel costs the mill $80 in labor, ore, and energy, so MPC = $80. Each ton also releases pollution that costs nearby residents $30 in health and cleanup, which is the marginal external cost. MSC = 80 + 30 = $110 per ton. At the market quantity buyers value the last ton at the $80 they pay, which is 110 − 80 = $30 less than what that ton costs society, so the market produces too much steel.
Marginal Social Cost questions
What is the difference between marginal social cost and marginal private cost?
Marginal private cost is what the producer pays for one more unit, while marginal social cost adds the cost imposed on everyone else. The two are equal only when there is no negative externality.
Does a positive externality change marginal social cost?
Usually not. A positive consumption externality raises marginal social benefit instead, leaving MSC equal to MPC; only a spillover on the cost side separates the two.
How does a Pigouvian tax use MSC?
The tax is set equal to the marginal external cost at the efficient quantity, which lifts the firm's private cost up to MSC and shrinks output to the efficient level.
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