What you are actually watching
Externalities are the most common reason a working market still produces the wrong answer,
and the Pigouvian tax is the neatest idea in economics for fixing one. Here is why both
work the way they do.
Markets only weigh costs somebody pays
A supply curve is built from what producers give up: materials, wages, electricity. It is
an honest accounting of every cost that lands on a bill. If making a unit also puts smoke
over a neighbourhood, and nobody sends an invoice for it, that cost never enters the
calculation.
The red dashed line adds it back. This is the marginal social cost: what a
unit truly costs once you count everyone affected, sitting above private supply by exactly
the damage per unit. The market clears where demand meets the green line, but the
amount society would choose is where demand meets the red one. A working,
competitive market landing on the wrong answer like this is what economists call a
market failure.
The wasted units are the ones in the middle
Look at the shaded wedge between those two quantities. That is the deadweight
loss. Every unit inside it is worth less to the person buying it than it costs the
world to produce. They still get made, because the buyer and seller are both individually
better off and the loss lands on somebody else entirely.
This is worth being precise about. The problem is not that pollution exists, and the right
amount of pollution is almost never zero. The problem is that the last few units are
not worth what they cost, and the market has no way to notice.
Why this tax is different
Press "set the corrective tax". The tax comes in at exactly the damage per unit, the market
moves to the socially best quantity, and the wasted wedge disappears. Total welfare goes
up.
Compare that to the last preset, where there is no externality at all. The same tax now
pushes a healthy market away from the right answer and destroys surplus, which is the
familiar result from the supply and demand simulator.
Both results are true, and holding them together is the point. A tax on a market
that was already efficient causes harm. A tax on a market that was ignoring a real cost
repairs it. The tax has not changed, only what it is being applied to. This is the
whole argument behind carbon pricing, congestion charges, and tobacco duty.
It runs backwards too
Everything so far has been a negative externality. Drag the slider left,
past zero, or load the beekeeping preset, and you get a positive externality
instead.
A beekeeper gets paid for honey. The pollination their bees provide to every orchard within
flying distance is free, and nobody sends an invoice for it. So the beekeeper decides how
many hives to keep based only on what honey earns, ends up keeping fewer than the area
actually wants, and the deadweight loss reappears on the other side of the optimum.
The fix is the same formula with the sign flipped: a subsidy equal to the external benefit.
That is the reasoning behind subsidised vaccination, public education, and research funding,
and it comes from exactly the same diagram.
There is a good footnote to this one. Bees and orchards were the textbook
externality for decades, until Steven Cheung went and looked. His 1973 study of Washington
State found beekeepers and orchard owners already had contracts, with pollination fees
flowing in whichever direction the crop required. The externality had been quietly
internalised by people making deals. The diagram identifies a problem. It does not
prove that nobody has already solved it.
Why this is harder in practice
Everything here depends on knowing the damage per unit. Setting the tax correctly requires
a number for what a tonne of carbon or an hour of congestion actually costs, and those
estimates are contested, uncertain, and often political.
The model also assumes the damage is the same for every unit and falls on a tidy anonymous
public. Real pollution concentrates in particular places and on particular people. And a
tax set too high does its own harm, as the control preset shows. The principle is
solid. The number is the hard part, and most real arguments about carbon pricing
are arguments about the number rather than the diagram.
Things to try
Four settings, each making a point the formula alone will not.
1Overcorrect on purpose
Set the tax far above the damage. Welfare falls again, this time from producing too
little. The goal is matching the externality, not punishing the industry.
2Watch a tax help and hurt
On the pollution preset, set the corrective tax and note welfare rising. Now switch to
the no-externality preset with the same tax and watch it fall. Same tax, opposite verdict.
3Make demand stubborn
Drop buyer response to 1 and set the corrective tax. The quantity barely moves. Taxing
something people will buy regardless raises revenue but changes little behavior.
4Flip to a benefit
Drag the externality below zero. The market now underproduces, and the tax slider has
to go negative to fix it. Subsidies and taxes are the same tool pointed in opposite
directions.
Common questions about externalities
What is an externality?
A cost or benefit that falls on someone who is not part of the transaction. Factory emissions are a negative externality, since people downwind bear a cost they never agreed to. Beekeeping is a positive one, since the bees pollinate every orchard nearby and the beekeeper is paid only for honey. In both cases the market price fails to reflect the full effect, so the quantity traded is wrong.
What is a Pigouvian tax?
A tax set equal to the external cost of each unit, named after Arthur Pigou. It forces the person creating the cost to face it, which makes their private calculation match the social one. Unlike an ordinary tax it increases total welfare, because it corrects an error the market was already making rather than introducing one.
Should the optimal amount of pollution be zero?
Almost never, and this surprises people. Eliminating the last unit of pollution usually means giving up production worth more than the damage avoided. The socially best point is where the value of one more unit exactly equals the harm it causes. Zero is the right answer only when the damage is enormous relative to the value of the activity.
Why not just ban the harmful activity?
A ban sets the quantity to zero, which overshoots the optimum in most cases and destroys the surplus from the units that were worth making. A tax lets people who value the activity most continue while those who value it least stop, which reaches the same reduction at a lower cost. Bans make more sense when the damage is severe or when measuring it accurately is hopeless.