10. Monopoly + Negative Externalities

Based on Dr. Said's Figures 10, 10-a, 10-b (slides pp. 46-63) & Buchanan (1969)

Note: This topic is NOT expected in the exam.

This section is for deeper understanding only. Past exams have never included monopoly + externality questions, and Dr. Galal's notes do not cover this topic. Focus your exam preparation on the other sections.

The Problem: Two Opposing Distortions

What happens when a market has both a monopoly and a negative externality? This is one of the trickiest topics in welfare economics because the two distortions pull output in opposite directions:

Monopoly restricts output — the monopolist sets MR = MPC and produces less than the competitive level to raise price and earn profit
Negative externality causes overproduction — ignoring external costs means the market produces more than the socially efficient level

Why this matters: In a competitive market with a negative externality, the answer is always "impose a Pigouvian tax = MEC." But with a monopoly, a tax might make things worse! The monopolist is already restricting output, and a tax restricts it further. Sometimes the right policy is a subsidy to a polluting monopolist.

First-Best vs Second-Best Solutions

First-best: Break up the monopoly (restore competition) AND impose a corrective tax = MEC. This fixes both distortions simultaneously.
Second-best: If breaking up the monopoly is infeasible, we must find the optimal policy given that monopoly power exists. The answer depends on the size of MEC relative to the monopoly markup.

This is an application of the Lipsey-Lancaster (1956) Theory of Second Best: when one condition for efficiency is violated (monopoly), correcting another distortion (externality) does not necessarily improve welfare.

Interactive Chart: Monopoly + Externality

Equations: $\text{AR} = 100 - Q$, $\text{MR} = 100 - 2Q$, $\text{MPC} = 10 + Q$, $\text{MSC} = \text{MPC} + \text{MEC}$

DWL Area Competitive Point E2 Price Lines Monopoly Markup

MEC Level: $30

Step-by-Step Analysis

Step 1: The Monopolist's Decision (No Externality)

The monopolist maximizes profit by setting MR = MPC:

\[100 - 2Q = 10 + Q \implies 90 = 3Q \implies Q_{\text{mono}} = 30\]

At $Q = 30$:

Price (from AR): $P = 100 - 30 = 70$
MPC: $10 + 30 = 40$
Monopoly markup: $P - MPC = 70 - 40 = 30$

This gives us point E1 = (30, 40) — the monopolist's equilibrium on the MPC curve.

Key number: The monopoly markup is $30. This is the gap between what consumers pay ($70) and what it costs to produce ($40). This number will be crucial for determining when the externality perfectly offsets monopoly power.

Step 2: The Competitive Equilibrium (No Externality)

Under perfect competition, firms produce where AR = MPC (price = marginal cost):

\[100 - Q = 10 + Q \implies 90 = 2Q \implies Q_{\text{comp}} = 45\]

At $Q = 45$:

Price: $P = 100 - 45 = 55$
MPC: $10 + 45 = 55$ (price = cost, as expected)

This gives us point E2 = (45, 55) — the competitive equilibrium.

Without any externality, E2 is the efficient outcome and the monopolist underproduces by $45 - 30 = 15$ units.

Step 3: Monopoly DWL (No Externality)

The deadweight loss from monopoly (without any externality) is the triangle between E1 and E2:

Base: $Q_{\text{comp}} - Q_{\text{mono}} = 45 - 30 = 15$ units
Height: $\text{AR}(30) - \text{MPC}(30) = 70 - 40 = 30$ (the markup)

\[\text{DWL}_{\text{monopoly}} = \frac{1}{2} \times 15 \times 30 = 225\]

For each unit between 30 and 45, consumers value it more than it costs to produce (AR > MPC), but the monopolist refuses to produce it because MR < MPC for those units.

Step 4: Adding the Externality — MSC Shifts Up

Now introduce a negative externality with marginal external cost MEC. The social cost becomes:

\[\text{MSC} = \text{MPC} + \text{MEC} = (10 + Q) + \text{MEC}\]

The socially efficient output is where $\text{AR} = \text{MSC}$:

\[100 - Q = 10 + Q + \text{MEC} \implies Q_{\text{eff}} = \frac{90 - \text{MEC}}{2}\]

Notice what happens to the competitive equilibrium at E2 ($Q = 45$): it is now inefficient because MSC > AR at that quantity. Competition overproduces when there's a negative externality.

Critical observation: The monopolist's quantity ($Q = 30$) doesn't change when we add the externality — the monopolist still sets MR = MPC and ignores external costs. But the efficient quantity shifts down from 45 (with no externality) toward the monopolist's output.

Step 5: The Key Insight — Two Wrongs Can Make a Right

Set $Q_{\text{eff}} = Q_{\text{mono}}$ to find when the two distortions perfectly cancel:

\[\frac{90 - \text{MEC}}{2} = 30 \implies \text{MEC} = 30\]

When MEC = 30, the efficient output exactly equals the monopolist's output. No government intervention is needed!

Buchanan's Insight (1969): Perfect offset occurs when MEC equals the monopoly markup. The monopoly markup is $\text{AR}(Q_{\text{mono}}) - \text{MPC}(Q_{\text{mono}}) = 70 - 40 = 30$. At this point, the monopolist's output restriction (which normally causes DWL) coincidentally produces exactly the right amount. "The monopolist simultaneously imposes two external diseconomies on the economy: pollution AND output restriction. These work in opposite directions."

At MEC = 30: point E3 = (30, 70) — where MSC intersects AR at the monopolist's quantity. Since AR(30) = MSC(30) = 70, this confirms the efficient output is 30.

Step 6: Three Scenarios Depend on MEC Size

Scenario A: Perfect Offset (MEC = 30 = Markup)

$Q_{\text{eff}} = 30 = Q_{\text{mono}}$
The two distortions exactly cancel
Policy: No intervention needed (second-best optimum)

Scenario B: Overproduction (MEC > 30)

Example: MEC = 45 → $Q_{\text{eff}} = (90-45)/2 = 22.5 < 30$
The externality is so large that even the monopolist produces too much
Policy: Tax needed, but smaller than under competition (monopoly already restricts some output)

Scenario C: Underproduction (MEC < 30)

Example: MEC = 15 → $Q_{\text{eff}} = (90-15)/2 = 37.5 > 30$
The externality is small; monopoly restriction is the dominant problem
Policy: A subsidy (not a tax!) to encourage the monopolist to increase output toward $Q_{\text{eff}}$

The surprising result: It may be optimal to subsidize a polluting monopolist! This seems counterintuitive, but the welfare loss from underproduction (monopoly restricting output) outweighs the welfare loss from pollution when MEC is small.

Competition vs Monopoly: Side-by-Side

Aspect	Perfect Competition	Monopoly
Output rule	AR = MPC	MR = MPC
Output level	Q = 45	Q = 30
Without externality	Efficient (Q* = 45)	DWL = 225 (underproduces)
With MEC = 30	Overproduces (Q* = 30), need tax = 30	Perfect offset! No intervention
With MEC = 45	Overproduces (Q* = 22.5), need tax = 45	Overproduces (Q* = 22.5), need smaller tax
With MEC = 15	Overproduces (Q* = 37.5), need tax = 15	Underproduces (Q* = 37.5), need SUBSIDY

Buchanan's Key Contribution (1969)

Core idea: "The monopolist simultaneously imposes two external diseconomies on the economy: pollution AND output restriction. These work in opposite directions." When MEC exactly equals the monopoly markup (AR − MPC at the monopolist's quantity), the two distortions perfectly offset, and the monopolist's output is socially efficient without any government intervention.

This result has profound policy implications:

A blanket "tax all polluters" policy is wrong when the polluter has market power
The optimal tax/subsidy depends on the relative size of MEC vs the monopoly markup
When MEC < markup: the monopoly restriction dominates → subsidize
When MEC > markup: the pollution dominates → tax (but less than under competition)
When MEC = markup: do nothing → perfect second-best offset