Pigouvian Tax
What is Pigouvian Tax?
A Pigouvian tax is a tax on a good with a negative externality, set equal to the external cost to restore the efficient quantity.
By raising the producer's marginal private cost up to the marginal social cost, it internalizes the externality. The tax reduces output to the socially optimal level and eliminates deadweight loss. A carbon tax is a common example.
Pigouvian Tax: a worked example
A pesticide market has demand P = 48 - 2Q and marginal private cost MPC = 12 + Q, and every gallon leaves runoff worth $6 of damage to third parties. Untaxed, 48 - 2Q = 12 + Q gives Q = 12 gallons at a price of $24. Marginal social cost is 18 + Q, so the efficient quantity solves 48 - 2Q = 18 + Q, giving Q = 10 gallons. Setting the tax at the $6 marginal external cost lifts the seller's effective cost curve to 18 + Q and moves output to exactly 10 gallons. Buyers now pay 48 - 20 = $28 while sellers keep 28 - 6 = $22, which matches marginal private cost at 10 gallons. Note the split: the buyer price rose $4 and the seller receipt fell $2. Revenue is 6 x 10 = $60.
The mistake students make with pigouvian tax
Students judge the tax by how much output disappears. They set the rate high enough to shut the polluter down, or they call the policy a failure because runoff still exists at 10 gallons. Zero pollution sounds like the obvious goal, which makes the overshoot tempting. The target is the quantity where marginal social benefit equals marginal social cost, and some external cost survives there because the last unit is still worth more than it harms. A rate above the marginal external cost overcorrects and opens a fresh deadweight loss.
Pigouvian Tax questions
How do you calculate the optimal Pigouvian tax?
Set the per unit tax equal to the marginal external cost measured at the efficient quantity, not at the market quantity. If the last socially desirable unit does $9 of harm to third parties, a $9 per unit tax raises the seller's cost curve until it coincides with marginal social cost, and the new equilibrium lands on the efficient quantity. When external cost per unit is constant, both measurements give the same number.
Does a Pigouvian tax create deadweight loss?
A Pigouvian tax removes deadweight loss rather than creating it, which is what separates it from an ordinary excise tax. In a market with no externality, a tax pushes quantity below the efficient level and destroys surplus. Here the untaxed quantity was already too high, so shrinking it moves the market toward the point where marginal social cost equals marginal social benefit. Setting the rate above the external cost would overshoot and reintroduce a loss.
Who actually pays a Pigouvian tax?
Buyers and sellers split the burden according to relative elasticity, exactly as with any per unit tax. The more inelastic side absorbs more of it, so a $6 tax on an inelastically demanded fuel might raise the pump price by $5 while cutting the seller's net receipt by $1. Legal responsibility for sending the payment to the government does not decide who bears the real cost.
Formula / Example
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