Negative Externality Lab: Compare Tax and Social Cost
Adjust an illustrative external cost and per-unit tax. Compare market and efficient quantities, prices, tax revenue, external damage, and welfare loss.
Free, with no sign-up.
For High school students and adults reviewing the topic.
About 9 minutes.
How does it work?
- Set the external cost per unit and the tax per unit.
- Compare the market quantity with the efficient quantity and inspect the shaded welfare loss.
- Try the corrective-tax preset, then solve a challenge.
What will you get?
Find a corrective tax and see why excessive taxation can also reduce total surplus.
What does the model assume?
- All prices and quantities are illustrative and describe no real market.
- The market is competitive. Marginal private benefit is 100 − 2Q dollars per unit, and marginal private cost is 20 + 2Q dollars per unit.
- Marginal external cost is constant per unit. There is no external benefit, so marginal social cost equals marginal private cost plus external cost.
- The per-unit tax is fully enforced with no administrative cost. Revenue is a transfer within society, not an additional resource cost.
- Quantities cannot be negative. At a tax of $80 per unit or more, trade stops and transaction prices are shown as unavailable.
- Deadweight loss is the difference in total social surplus between the efficient quantity and the quantity traded with the tax.
- A tax equal to external cost reaches the efficient outcome. Excessive tax loses beneficial trades when efficient output is positive; after trade stops, increasing tax changes no quantities.
- When external cost is at least $80 per unit, the efficient quantity is zero.
Which setup would you like to try?
What can you change?
Range: 0 to 100 dollars/unit.
Range: 0 to 120 dollars/unit.
What does the model predict?
| Quantity | Value | Unit |
|---|---|---|
| Quantity traded with the tax | 20.0000 | units |
| Efficient quantity | 16.0000 | units |
| Price buyers pay | 60.00 | dollars/unit |
| Price sellers keep | 60.00 | dollars/unit |
| Tax revenue | 0.00 | dollars |
| External cost at the traded quantity | 320.00 | dollars |
| Deadweight loss | 32.00 | dollars |
- Marginal benefit: solid line
- Marginal private cost: dashed line
- Marginal social cost: dotted line
- Private cost plus tax: dash-dot line
Circle: traded quantity. Square: efficient quantity.
Can you reach these targets?
Keep external cost at $16 per unit and find the tax that removes deadweight loss.
- Target: Marginal external cost = 16 dollars/unit; tolerance 0 dollars/unit.
- Target: Deadweight loss = 0 dollars; tolerance 0.0001 dollars.
- Target: Quantity traded with the tax = 16 units; tolerance 0.001 units.
With external cost at $16 per unit, find a tax above $16 that leaves 12 units traded and $32 of deadweight loss.
- Target: Marginal external cost = 16 dollars/unit; tolerance 0 dollars/unit.
- Target: Quantity traded with the tax = 12 units; tolerance 0.001 units.
- Target: Deadweight loss = 32 dollars; tolerance 0.01 dollars.