ECON5001 · Microeconomic Theory
Monopoly & Price Discrimination
This is the first market structure where the firm sets the price. A monopolist is the single seller of a product with no close substitutes and blocked entry, so it faces the whole downward-sloping market demand — to sell one more unit it must cut the price on every unit. That single fact drives the chapter: marginal revenue falls below price (for linear inverse demand p = a − bQ, MR = a − 2bQ, twice the slope), the firm produces where MR = MC and reads the price up to demand, and the gap shows up as the Lerner markup (P − MC)/P = −1/ε. Restricting output creates a deadweight loss, which motivates regulation and price discrimination (first, second and third degree, plus the two-part tariff). The exam rewards solving the standard monopoly problem cleanly and not confusing the look-alike cases — MR vs demand, profit tax vs quantity tax, second-degree vs third-degree.
What this chapter covers
- 011. What makes a monopoly — single seller, no close substitutes, blocked entry (resource/legal/natural)
- 022. Inverse demand IS average revenue — the monopolist faces the entire market demand curve
- 033. Marginal revenue MR = P + Q·P′(Q) < P — and MR = a − 2bQ for linear inverse demand
- 044. The monopoly rule MR = MC → find Qᵐ, then read Pᵐ UP to demand
- 055. Lerner index / markup (P − MC)/P = −1/ε — power rises as demand gets less elastic
- 066. Deadweight loss ½(Pᵐ − MC)(Qc − Qᵐ) — output restricted below the efficient level
- 077. Taxes & regulation — profit tax is price-neutral; quantity tax raises MC; P=ATC for natural monopoly
- 088. Price discrimination — first (perfect), second (self-selecting menu), third (MR₁=MR₂=MC), two-part tariff
Monopoly output, markup, profit and deadweight loss
- +1(a) Marginal revenue. TR = pQ = (200 − 5Q)Q = 200Q − 5Q², so MR = 200 − 10Q — same intercept as demand but TWICE the slope.
- +1Set MR = MC. 200 − 10Q = 20 ⇒ 10Q = 180 ⇒ Qᵐ = 18.
- +1Price off DEMAND. Pᵐ = 200 − 5(18) = 110 (read up to demand at Qᵐ, never off MR).
- +1(b) Lerner index. (P − MC)/P = (110 − 20)/110 = 90/110 ≈ 0.82.
- +2Profit. π = (Pᵐ − MC)·Qᵐ = (110 − 20)(18) = 90 × 18 = 1,620.
- +1(c) Competitive benchmark. Set P = MC = 20: 20 = 200 − 5Q ⇒ Qc = 36 (double the monopoly output).
- +2Deadweight loss. DWL = ½(Pᵐ − MC)(Qc − Qᵐ) = ½(110 − 20)(36 − 18) = ½(90)(18) = 810.
Key terms
- Marginal revenue (MR)
- The change in total revenue from selling one more unit, MR = d(TR)/dQ = P + Q·P′(Q). Because a monopolist must lower the price on every unit to sell more, the second term is negative and MR lies BELOW demand. For linear inverse demand p = a − bQ, MR = a − 2bQ: same intercept, twice the slope, hitting zero at half the output where demand hits zero.
- Monopoly pricing rule (MR = MC)
- The profit-maximising condition: produce the output where marginal revenue equals marginal cost, find Qᵐ, then set the price by reading UP to the demand (average-revenue) curve at Qᵐ. The resulting price always exceeds marginal cost, P > MC.
- Lerner index / markup
- A measure of market power, (P − MC)/P = −1/ε, where ε is the price elasticity of demand. It runs from 0 (price-taking, P = MC) toward 1 as demand becomes less elastic. Equivalently P = MC / (1 + 1/ε). It also forces the monopolist onto the elastic part of demand, since MR < 0 when |ε| < 1.
- Deadweight loss of monopoly
- The surplus destroyed because the monopolist restricts output to Qᵐ below the efficient level Qc (where P = MC). It is the triangle between the demand and MC curves over the unmade units, ½(Pᵐ − MC)(Qc − Qᵐ). Unlike the profit rectangle (a transfer), this surplus genuinely disappears.
- Natural monopoly
- A market where large fixed/sunk costs mean one firm can serve the whole market at lower cost than several could (average cost keeps falling). Marginal-cost pricing (P = MC) is efficient but makes the firm a loss since ATC > MC, so regulators often impose average-cost pricing (P = ATC) for break-even at the cost of some remaining deadweight loss.
- Profit tax vs quantity tax
- A profit (lump-sum) tax scales profit by (1 − t); since this does not move the MR = MC margin, output and price are UNCHANGED and only after-tax profit falls — it is price-neutral. A per-unit (quantity) tax raises marginal cost to MC + t, so the new rule MR = MC + t cuts output and raises price (by less than t on linear demand).
- Price discrimination (three degrees)
- Charging different prices to capture consumer surplus. First-degree (perfect): each buyer pays their exact willingness to pay — efficient output but zero consumer surplus. Second-degree: hidden types choose from a menu of versions/quantities and self-select (incentive compatibility). Third-degree: observable groups are charged separate prices via MR₁ = MR₂ = MC. All require market power, the ability to sort buyers, and no resale.
- Two-part tariff
- A pricing scheme with a fixed entry fee plus a per-unit price. Setting the per-unit price equal to MC (so the buyer consumes the efficient quantity) and the fixed fee equal to the buyer's consumer surplus replicates first-degree price discrimination when one price schedule per buyer is allowed (e.g. membership fee plus marginal-cost usage charges).
Monopoly & Price Discrimination FAQ
Why is marginal revenue below the demand curve for a monopoly?
Because the monopolist faces the whole downward-sloping demand, so to sell one extra unit it must cut the price on EVERY unit, not just the last one. The gain from the extra unit (+P) is partly offset by the lost revenue on existing units (Q·P′(Q), a negative term), so MR = P + Q·P′(Q) < P. For linear inverse demand p = a − bQ this gives MR = a − 2bQ — the same intercept as demand but twice the slope. Writing MR with the same slope as demand is the most common and most expensive mistake in this topic.
After I find Qᵐ from MR = MC, how do I get the monopoly price?
Read it UP to the DEMAND curve at Qᵐ, never off MR. The MR = MC condition only locates the profit-maximising quantity; the price buyers will actually pay for that quantity sits on the demand (average-revenue) curve. If you plug Qᵐ back into MR you just recover MC, which is below the true price. Order: MR = MC → quantity; demand at that quantity → price.
Does a tax on a monopoly always raise the price?
No — it depends on the kind of tax. A profit (lump-sum) tax scales profit by (1 − t) but leaves the MR = MC margin untouched, so output and price do not change and only after-tax profit falls — it is price-neutral. A per-unit (quantity) tax raises marginal cost to MC + t, shifting the optimum: output falls and price rises (by less than the full tax on linear demand). Swapping these two is a classic exam trap.
What is the difference between second-degree and third-degree price discrimination?
Third-degree splits buyers into OBSERVABLE groups (students, seniors, regions) and charges each group its own price by setting MR₁ = MR₂ = MC — the less elastic group pays more. Second-degree applies when types are HIDDEN: the firm offers a menu of versions or quantity blocks and lets buyers reveal themselves by what they choose, so the design must satisfy self-selection / incentive compatibility (think economy vs business class, or Standard vs Deluxe software).
Is first-degree price discrimination good or bad for efficiency?
It is efficient — perfect discrimination prices each unit at its demand height, so the firm produces all the way to the competitive (P = MC) quantity and there is no deadweight loss. But it is terrible for consumers: the seller extracts ALL the surplus and buyers are left with zero. This is the cleanest example of efficiency ≠ consumer welfare, and a popular short-answer point.
Why does a monopolist never produce where demand is inelastic?
Because in the inelastic range (|ε| < 1) marginal revenue is negative, so reducing output would raise revenue AND cut cost — production there can never be optimal. The MR = MC optimum always lands on the elastic part of demand (|ε| > 1), which is also why the Lerner index −1/ε stays between 0 and 1.
Exam move
Treat monopoly as one fixed routine you can run on autopilot, because the exam tests clean execution under time pressure. (1) Write MR with twice the slope of linear inverse demand: p = a − bQ ⇒ MR = a − 2bQ. (2) Set MR = MC to get the quantity Qᵐ. (3) Read the price UP to demand at Qᵐ — never off MR. (4) Compute the markup and profit: Lerner = (P − MC)/P = −1/ε and π = (P − MC)Qᵐ. (5) For deadweight loss, find the competitive quantity from P = MC, then take ½(Pᵐ − MC)(Qc − Qᵐ). Then drill the look-alike extensions until they are automatic: profit tax (no change to output or price) versus quantity tax (MR = MC + t), and the three degrees of price discrimination — first-degree/two-part tariff (efficient, zero consumer surplus), second-degree (hidden types, self-selecting menu), and third-degree (observable groups, MR₁ = MR₂ = MC, higher price to the less elastic market). Practise each on a numerical problem and always sanity-check that |ε| > 1 at your optimum and that the less elastic market gets the higher price.
