šŸ­ Correcting Externalities with a Pigouvian Tax

See how a tax equal to marginal external damage shifts the market to the socially optimal outcome

1
Set External Damage
2
Observe Market Failure
3
Apply Corrective Tax
šŸ’Ø External Damage
Marginal External Cost$20/unit
šŸ“ Market Parameters
Demand Intercept (a)100
Demand Slope1.0
Supply Slope1.0
P = 100 āˆ’ 1.0Q (Demand)
P = 1.0Q (PMC)
šŸ’µ Pigouvian Tax
Tax per Unit (t)$20/unit
āœ“ Tax = MEC ā€” Optimal!
šŸ“Š Equilibrium
Market Qā‚˜50
Optimal Q*40
With Tax Qā‚œ40
šŸ’° Welfare
DWL (no tax)$100
DWL (with tax)$0
Tax Revenue$800
šŸ’” Key Insight

The Pigouvian tax internalizes the externality. Without tax, firms overproduce (Qā‚˜ > Q*). Setting t = MEC aligns private and social costs.

Market with Negative Externality
Private vs. Social Cost and the Corrective Tax
Demand (MB)
PMC (Supply)
SMC = PMC + MEC
PMC + Tax
DWL
Market (No Tax)
Qā‚˜ = 50, Pā‚˜ = $50
Social Optimum
Q* = 40, P* = $60