Difficulty: Intermediate | Prerequisites: Part 1 of these notes (Section 11.1), Chapter 9 (welfare and deadweight loss)
Part 2 of three covering Chapter 11 of Perloff's Microeconomics (5th Ed.). This part covers Sections 11.2 and 11.3: how market power depends on demand elasticity, why monopoly creates deadweight loss, and how specific and ad valorem taxes affect a monopoly differently from a competitive market.
A monopoly's ability to mark up price above marginal cost depends entirely on the elasticity of demand it faces, not on its size. The Lerner Index, (p - MC)/p = -1/epsilon, measures this pricing power. Monopoly pricing creates a deadweight loss (lost consumer and producer surplus) because output is restricted below the competitive level. Taxes on a monopoly can have consumer incidence above 100% (with constant-elasticity demand) and, for the same output reduction, an ad valorem tax raises more government revenue than a specific tax.
Market power
The ability of a firm to charge a price above its marginal cost and earn a positive profit. The degree of market power depends on the elasticity of demand, not the firm's size.
In simple terms: how much room the firm has to raise its price without losing all its customers.
Lerner Index
(p - MC)/p. A measure of a firm's market power, ranging from 0 (competitive firm, no pricing power) to just below 1 (near-total pricing power). Named after economist Abba Lerner. For a profit-maximising firm, the Lerner Index equals -1/epsilon.
Think of it as: the fraction of the price that is pure markup above cost.
Deadweight loss (DWL) of monopoly
The reduction in total welfare (consumer surplus + producer surplus) caused by monopoly pricing relative to the competitive outcome. It arises because the monopoly restricts output below the efficient level, so units that are worth more to consumers than they cost to produce are never made.
In simple terms: the value destroyed because the monopoly produces too little.
Specific tax
A fixed dollar amount, t, charged per unit of output. It shifts the monopoly's marginal cost curve upward by t. In a monopoly market, the consumer incidence of a specific tax can exceed 100% (with constant-elasticity demand).
Think of it as: a flat per-unit charge, like $2 per litre.
Ad valorem tax
A tax levied as a percentage (v) of the price, so the tax per unit is v times p. Unlike a specific tax, the ad valorem tax wedge is larger at higher prices. When set to produce the same output reduction as a specific tax, the ad valorem tax raises more government revenue from a monopoly.
Think of it as: a percentage sales tax, like 10% of the sticker price.
Tax incidence (on consumers)
The change in the price consumers pay divided by the change in the tax. In competitive markets, incidence on consumers is at most 100%. In a monopoly market with constant-elasticity demand, incidence can exceed 100%, meaning the price rises by more than the tax.
The ratio of price to marginal cost depends only on the elasticity of demand at the profit-maximising quantity: p/MC = 1/[1 + (1/epsilon)].
When demand is barely elastic (epsilon = -1.01), p/MC is about 101. When demand is very elastic (epsilon = -100), p/MC is about 1.01.
Three factors make demand more elastic (reducing market power): better substitutes become available, more firms enter the market selling similar goods, or rival firms locate closer to the monopolist.
Lerner Index = (p - MC)/p = -1/epsilon.
Ranges from 0 (competitive firm, epsilon approaches negative infinity) to just below 1 (barely elastic demand).
At epsilon = -2, the Lerner Index is 0.50. At epsilon = -5, it is 0.20. At epsilon = -1.01, it is 0.99.
The EpiPen example: price $630, MC $30, Lerner Index = 600/630 = 0.952, implying epsilon of about -1.05. This is only slightly elastic demand, consistent with a product that has almost no substitutes.
Under competition: price = MC, output = Qc. Consumer surplus = A + B + C, producer surplus = D + E, welfare = A + B + C + D + E.
Under monopoly: price > MC, output = Qm < Qc. Consumer surplus = A, producer surplus = B + D.
The monopoly transfers area B from consumers to itself (higher price on units still sold) and destroys areas C + E entirely.
Deadweight loss = C + E. This is welfare that neither consumers nor the monopoly captures. It exists because units between Qm and Qc are worth more to consumers than they cost to produce, but are never made.
In the textbook example (p = 24 - Q, MC = 2Q): competitive outcome is Qc = 8, pc = 16. Monopoly outcome is Qm = 6, pm = 18. DWL = C + E = 2 + 4 = 6.
A specific tax of t per unit shifts the MC curve up by t. The monopoly equates MR with the new, higher MC, producing less and charging more.
After-tax profit-maximisation condition: dR/dQ = dC/dQ + t.
Output always falls (dQ/dt < 0) and price always rises (dp/dt > 0) when a specific tax is imposed.
With constant-elasticity demand, consumer incidence = dp/dt = 1/(1 + 1/epsilon) > 1 (because epsilon < -1). The price rises by more than the tax.
With linear demand, incidence can be below 100%. In the textbook example (t = $8): price rises from $18 to $20 (change of $2), so incidence = 2/8 = 25%.
The tax increases the deadweight loss. Before tax, DWL was just the monopoly distortion (area F). After tax, DWL = C + E + F.
If the ad valorem rate v and the specific tax t are set to produce the same after-tax output (and hence the same DWL), the ad valorem tax generates more government revenue.
The ad valorem tax wedge (vp) is proportional to price, so it is larger at higher prices. The specific tax wedge (t) is constant.
Both taxes harm consumers equally (same price increase, same output reduction).
The government prefers the ad valorem tax; the monopoly prefers the specific tax.
This is why most state and local governments use ad valorem (percentage) sales taxes. Common exceptions: alcohol, tobacco, fuel.
Price-to-MC ratio (Eq. 11.10)
\frac{p}{MC} = \frac{1}{1 + (1/\varepsilon)}Lerner Index (Eq. 11.11)
\frac{p - MC}{p} = -\frac{1}{\varepsilon}Ranges from 0 (perfectly elastic demand, competitive) to just below 1 (barely elastic demand, extreme market power).
After-tax profit-maximisation with specific tax (Eq. 11.12)
\frac{dR(Q)}{dQ} - \frac{dC(Q)}{dQ} - t = 0Equivalently: MR = MC + t.
Monopoly price under constant-elasticity demand with specific tax (Eq. 11.14)
p = \frac{m + t}{1 + 1/\varepsilon}Where m is the constant marginal cost. Consumer incidence dp/dt = 1/(1 + 1/epsilon) > 1.
Deadweight loss
No single formula. DWL = lost consumer surplus (C) + lost producer surplus (E) from output restriction. In a linear example, these are triangular areas computed from the gap between price and MC over the range Qm to Qc.
EpiPen pricing. The EpiPen (epinephrine auto-injector for severe allergic reactions) sold for $630 per pair with an estimated MC of $30. The Lerner Index of 0.952 implies demand elasticity of about -1.05, meaning consumers are barely price-sensitive. This is what you would expect for a product that is literally life-saving with almost no substitutes.
Brand-name vs generic drugs. When a drug patent expires, generic versions enter at lower prices, yet the brand-name price often increases (by 2-7% on average). This is consistent with the remaining brand-loyal consumers having less elastic demand than the overall pre-patent market. The monopoly over the brand-loyal segment supports a higher price.
Botox. Allergan's Botox had an estimated price of $400 per vial, MC of $25, giving a Lerner Index of about 0.94 and implied elasticity of -1.067. The near-monopoly in cosmetic wrinkle treatment (with limited substitutes like collagen or Restylane) keeps demand very inelastic.
"The bigger the monopoly, the more it can mark up price." Firm size is irrelevant. What determines the markup is the elasticity of demand at the profit-maximising quantity. A small firm with no-substitute customers can charge a far higher markup than a large firm facing elastic demand.
"Monopoly transfers all lost consumer surplus to itself." Only part of the lost CS (area B) goes to the monopoly as extra profit. The rest (area C) is destroyed outright and goes to nobody. Plus the monopoly also loses area E from reduced sales.
"A tax on a monopoly can never raise the price by more than the tax itself." This is true for competitive markets but not for monopolies. With constant-elasticity demand, consumer incidence exceeds 100%.
"Specific and ad valorem taxes are interchangeable." In competitive markets they raise the same revenue for the same output effect. In monopoly markets they do not. The ad valorem tax raises more revenue for the government when both produce the same output reduction.
True or False: A monopoly with a Lerner Index of 0.5 faces a demand elasticity of -2. (True. Lerner = -1/epsilon, so 0.5 = -1/epsilon gives epsilon = -2.)
Fill in the blank: The deadweight loss of monopoly arises because output is ____ than the competitive level. (lower / smaller)
True or False: Under monopoly, consumer surplus falls by exactly the amount producer surplus rises. (False. Part of the lost CS is transferred to the producer (area B), but part (area C) is destroyed. The monopoly also loses area E.)
Fill in the blank: With constant-elasticity demand, the incidence of a specific tax on consumers is ____ 100%. (greater than)
True or False: For the same output reduction, an ad valorem tax raises less government revenue than a specific tax when applied to a monopoly. (False. The ad valorem tax raises more revenue.)
Q: A monopoly has MC = $20 and charges p = $50. What is its Lerner Index, and what is the implied elasticity of demand if the firm is maximising profit?
A: Lerner Index = (50 - 20)/50 = 0.6. If profit-maximising, 0.6 = -1/epsilon, so epsilon = -1/0.6 = -5/3 (approximately -1.67).
Q: Using the textbook linear example (p = 24 - Q, MC = 2Q), calculate the deadweight loss of monopoly. Show the competitive and monopoly outcomes.
A: Competitive: p = 24 - Q = 2Q = MC gives 3Q = 24, so Qc = 8, pc = 16. Monopoly: MR = 24 - 2Q = 2Q = MC gives 4Q = 24, so Qm = 6, pm = 18, MC at Qm = 12. DWL is the triangle between the demand curve and MC curve from Q = 6 to Q = 8. Base = 8 - 6 = 2. Height = (18 - 12) = 6. DWL = 0.5 x 2 x 6 = 6.
Q: A specific tax of $8 is imposed on the textbook monopoly (p = 24 - Q, MC = 2Q). Find the new quantity, price, and consumer tax incidence.
A: After-tax MC = 2Q + 8. Set MR = MC: 24 - 2Q = 2Q + 8, so 4Q = 16, Q* = 4. Price: p = 24 - 4 = 20. Price rose from 18 to 20, a change of 2. Tax is 8. Consumer incidence = 2/8 = 25%.
Q: Explain why a government collecting tax revenue from a monopoly prefers an ad valorem tax to a specific tax.
A: When both taxes are set to produce the same after-tax output (and therefore the same deadweight loss and the same consumer harm), the ad valorem tax generates more government revenue. The ad valorem tax collects vp per unit, and since the tax wedge is proportional to price, it takes more from the monopoly's profit. The government gets more; the monopoly keeps less.
The welfare analysis here builds directly on the consumer and producer surplus framework from Chapter 9. The tax incidence analysis extends the competitive-market tax analysis from Chapter 2 into the monopoly setting, showing that the competitive result (incidence at most 100%) does not carry over. The Lerner Index will reappear in oligopoly models (Chapters 13-14), where firms have partial market power. Part 3 of these notes covers why monopolies exist in the first place.
market power, Lerner Index, Abba Lerner, deadweight loss, DWL, welfare loss, consumer surplus, producer surplus, monopoly pricing, specific tax, ad valorem tax, sales tax, tax incidence, pass-through, constant elasticity demand, EpiPen, Botox, brand-name drugs, generic drugs, Perloff Chapter 11, intermediate microeconomics