Enter Values

$
P = a - bQ; price when Q = 0
$/unit; b = 0 means perfectly elastic demand
$
P = c + dQ; price when Q = 0
$/unit; d = 0 means perfectly elastic supply
$ /unit
Constant external cost per unit produced
Curve Equations
Demand: P = a - bQ
Supply (Private MC): P = c + dQ
Market Eq: Qmkt = (a - c) / (b + d)
Social MC: P = (c + MEC) + dQ
Model Assumptions
  • Linear demand and supply curves (inverse form)
  • Constant marginal external cost/benefit (not quantity-dependent)
  • No pre-existing taxes, subsidies, or regulations
  • Competitive market (no market power)
  • Interior solutions only — corner solutions flagged, not computed

For educational purposes. Not financial advice. Market conventions simplified.

Ryan O'Connell, CFA
Calculator by Ryan O'Connell, CFA

Externality Analysis Results

Market Equilibrium (Unadjusted)
Quantity (Qmkt) 45.00
Price (Pmkt) $55.00
Externality-Adjusted Equilibrium
Quantity (Qsoc) 35.00
Buyer Price $65.00
Seller Price $45.00
Price Wedge (Tax) $20.00
Overproduction 10.00 units
Welfare Effects
DWL from Externality $100.00
Model Tax $20.00/unit
Change in Total Surplus $100.00
Tax Revenue $700.00

Supply & Demand Diagram

Supply and demand diagram with externality correction visualization
Demand (D) Supply (Private MC) Social MC DWL

Formula Breakdown

DWL = ½ × MEC × (Qmkt − Qsoc)
Model Tax = MEC per unit  |  Total Surplus Change = DWL removed in this model

Understanding Pigouvian Taxes & Externalities

What Are Externalities?

An externality is an uncompensated impact of one person’s actions on a bystander. Negative externalities (e.g., factory emissions affecting nearby households) add costs outside the buyer-seller transaction, which in the textbook model leads to output above Qsoc. Positive externalities (e.g., education or basic research) create spillover benefits outside the transaction, which in the model leads to output below Qsoc.

Key Formulas (Mankiw Ch. 10)
Market Eq: Qmkt = (a - c) / (b + d)
Social Opt (neg): Qsoc = (a - c - MEC) / (b + d)
DWL: ½ × MEC × (Qmkt - Qsoc)
Source: Mankiw, Principles of Microeconomics, Ch. 10

How Pigouvian Taxes Work

A Pigouvian tax is a tax set equal to the marginal external cost per unit in the textbook model. Adding MEC to private marginal cost aligns the private and social cost schedules, moving the model from Qmkt to Qsoc.

For positive externalities, the analogous textbook instrument is a Pigouvian subsidy equal to the marginal external benefit per unit, which aligns private and social marginal benefit in the same framework.

Understanding the Diagram

The diagram shows three key curves:

  • Demand (blue): Private willingness to pay (P = a - bQ)
  • Supply / Private MC (orange): Private marginal cost (P = c + dQ)
  • Social MC or Social MB (green dashed): The full social cost or benefit curve, shifted by the externality amount

The shaded DWL triangle represents the welfare loss from the externality — the net social cost of units produced between Qsoc and Qmkt (or vice versa for positive externalities).

Verification Example (Mankiw Ch. 10 style): P = 100 - Q, P = 10 + Q, MEC = $20.
Qmkt = 45, Pmkt = $55. Qsoc = 35, Buyer pays $65, Seller gets $45.
Overproduction = 10 units. DWL = $100. Model tax = $20/unit. Revenue = $700.

Frequently Asked Questions

A Pigouvian tax is a tax applied to an activity with a negative externality. Named after economist Arthur Pigou, it is set equal to the marginal external cost (MEC) per unit in the textbook model. Adding MEC to private marginal cost shifts the model from Qmkt to Qsoc, aligning private and social cost schedules.

A negative externality occurs when an economic activity imposes costs on third parties outside the transaction (for example, factory emissions affecting nearby households). In the textbook model, social cost exceeds private cost, which leads to output above Qsoc. A positive externality occurs when an activity generates spillover benefits for third parties (for example, education or basic research). In that case, social benefit exceeds private benefit, which leads to output below Qsoc.

For a negative externality with linear supply and demand, DWL = 0.5 × MEC × (Qmkt - Qsoc), representing the area of the triangle between the demand curve and social marginal cost curve over the range of overproduction. For a positive externality, DWL = 0.5 × MEB × (Qsoc - Qmkt), the triangle between the social marginal benefit curve and supply curve over the range of underproduction. These formulas apply to interior solutions with constant marginal externality values.

In this calculator’s linear model, the implied Pigouvian tax equals the marginal external cost (MEC) per unit, and the implied Pigouvian subsidy equals the marginal external benefit (MEB) per unit. When that adjustment is applied, the model’s private and social marginal schedules coincide at Qsoc.

A regular (non-corrective) tax creates a wedge between what buyers pay and sellers receive, reducing quantity traded below the no-tax benchmark. In the textbook externality model, a Pigouvian tax or subsidy is designed to align private and social marginal conditions. Which tool, if any, is used in practice depends on measurement, monitoring, administration, and institutional context.

The Coase theorem (Ronald Coase, 1960) states that if property rights are well-defined and transaction costs are negligible, private bargaining between affected parties can resolve externalities regardless of who initially holds the rights. In many real-world settings, transaction costs, information limits, or the number of affected parties can make bargaining difficult. Textbook treatments therefore compare bargaining, taxes/subsidies, and regulatory approaches as alternative ways to analyze the same problem.

Related Articles & Calculators

Related Articles
Sibling Calculators

Related Calculators

Professional finance illustration representing Game Theory Payoff Matrix Calculator

Game Theory Payoff Matrix Calculator

Find Nash equilibria and dominant strategies in a 2-player, 2-strategy game. Identifies Prisoner's Dilemma and...

Try Calculator →
Professional finance illustration representing Monopoly Profit & Deadweight Loss Calculator

Monopoly Profit & Deadweight Loss Calculator

An economics calculator from the microeconomics series.

Try Calculator →
Professional finance illustration representing Consumer & Producer Surplus Calculator

Consumer & Producer Surplus Calculator

An economics calculator from the microeconomics series.

Try Calculator →
Disclaimer

This calculator is for educational purposes only. Results are based on linear supply and demand curves with constant marginal externality values (interior solutions only). Real-world externalities involve nonlinear relationships, measurement uncertainty, administrative costs, and general-equilibrium effects not captured here. This tool should not be used for business, investment, or policy decisions.