Marginal Social Cost
What is Marginal Social Cost?
Marginal social cost is the total cost to society of producing one more unit, equal to private costs plus external costs.
It equals the marginal private cost plus the marginal external cost. With a negative externality, the marginal social cost curve lies above the supply (marginal private cost) curve. The socially efficient quantity occurs where marginal social cost equals marginal social benefit.
Marginal Social Cost: a worked example
A tannery's marginal private cost is MPC = 10 + 2Q dollars per crate, and each crate releases runoff that imposes a marginal external cost of $8 on downstream fishers. Marginal social cost is therefore MSC = 10 + 2Q + 8 = 18 + 2Q. Demand, which serves as marginal social benefit here, is P = 70 - 2Q. The tannery ignores the runoff and produces where MPC meets demand: 10 + 2Q = 70 - 2Q, so Q = 15 crates at a price of $40. The efficient quantity solves MSC = MSB: 18 + 2Q = 70 - 2Q, giving Q = 13 crates at $44. At the market quantity of 15, marginal social cost is 18 + 30 = $48 while marginal social benefit is $40, an $8 gap. Deadweight loss over the two extra crates is 0.5 x 2 x 8 = $8.
The mistake students make with marginal social cost
Students often scale the external cost by output before adding it. Seeing 15 crates that each cause $8 of harm, they add the full $120 of damage on top of the private cost of every unit and shift supply up by $120. The word social sounds like a whole society total, which is what makes the move tempting. Marginal social cost is a per unit figure, so add only the $8 marginal external cost. The $120 is total external cost, an area on the graph rather than a vertical shift.
Marginal Social Cost questions
How do you calculate marginal social cost?
Marginal social cost equals marginal private cost plus marginal external cost at the same quantity. If producing the 12th unit costs the firm $30 in labor and materials and imposes $7 of pollution damage on neighbors, marginal social cost for that unit is $37. When the external cost per unit is constant, the marginal social cost curve is the private cost curve shifted straight up by that amount, so the vertical gap between the two never changes as output grows.
What is the difference between marginal social cost and marginal private cost?
Marginal private cost counts only what the producer pays for the next unit, such as wages, materials, and energy. Marginal social cost adds whatever the rest of society absorbs from that same unit, such as smoke, noise, or contaminated water. When no external cost exists the two curves lie on top of each other, and the market quantity is already the efficient quantity.
Can marginal social cost be below marginal private cost?
Marginal social cost sits below marginal private cost when production creates an external benefit rather than external harm. A beekeeper whose hives pollinate the orchard next door hands society a marginal external benefit, so the cost to society of one more hive is smaller than the beekeeper's own cost. Output is then too low at the market quantity, and the correction is a per unit subsidy rather than a tax.
Formula / Example
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