Price discrimination is how a firm turns consumer surplus into profit. Instead of charging one price to everyone, the firm charges different prices to different buyers — or for different quantities — and captures revenue that would otherwise stay in the buyer’s pocket. If you are studying MG207 Managerial Economics at LSE, this is the topic that separates a pass from a distinction. A Managerial Economics tutor at LSE works through the three degrees of price discrimination until the logic is automatic.
1 · The basic condition: market power and arbitrage
Price discrimination only works if two conditions hold. First, the firm must have market power — it sets price, not the market. In perfect competition, price equals marginal cost and there is no surplus to capture. Second, the firm must prevent arbitrage. If a buyer who pays a low price can resell to a buyer who would pay a high price, the price difference collapses.
Arbitrage is the practical constraint that determines which degree of discrimination is feasible. First-degree discrimination requires that resale is impossible — each unit is sold to a unique buyer. Second-degree works when the firm cannot observe buyer types but can design a menu of quantity-price bundles that sorts them. Third-degree requires that the firm can identify groups and prevent resale across groups.
Examiners test this distinction. The question is always: which degree fits this market? The answer depends on what the firm knows and whether resale is possible.
2 · First-degree price discrimination — perfect price discrimination
First-degree means charging each buyer their maximum willingness to pay. The firm extracts the entire consumer surplus. The demand curve becomes the marginal revenue curve, because each unit is sold at the price the buyer is just willing to pay.
The outcome is efficient in the narrow sense: the firm produces until price equals marginal cost, the same condition as perfect competition. But the distribution is extreme — all surplus goes to the firm, none to consumers. In practice, perfect price discrimination is rare. It requires that the firm knows each buyer’s reservation price and can prevent resale. Auctions, haggling and personalised pricing online are the closest real-world examples.
For a monopolist facing linear demand P = a − bQ and constant marginal cost c, the perfectly discriminating monopolist produces Q = (a − c)/b — twice the quantity of a single-price monopolist. Consumer surplus is zero. Producer surplus is the entire triangle under demand above marginal cost.
3 · Second-degree price discrimination — menu pricing
Second-degree discrimination happens when the firm cannot observe buyer types but can offer a menu of options that induces buyers to self-select. The classic case is quantity discounts: a firm offers a small package at a high per-unit price and a large package at a low per-unit price. High-value buyers choose the large package; low-value buyers choose the small one.
The constraint is incentive compatibility. The high-type buyer must prefer the large package to the small one. The low-type buyer must prefer the small package to nothing. The firm designs the menu so that each type picks the option intended for them, and the firm captures as much surplus as possible without pushing the low type out of the market.
Second-degree discrimination is everywhere: airline tickets (economy vs business), software (basic vs premium), cinema tickets (adult vs child). The firm does not need to know who you are — it just needs to design the menu so that you reveal your type through your choice.
4 · Third-degree price discrimination — group pricing
Third-degree is the most common form in exam problems. The firm observes an observable characteristic — age, location, student status — that correlates with willingness to pay. It charges a different price to each group. The key assumption is that resale across groups is impossible.
The firm sets marginal revenue equal to marginal cost in each market separately. If marginal cost is constant and identical across markets, the rule is MR₁ = MR₂ = MC. Since MR = P(1 − 1/|ε|), the price in each market depends on the elasticity of demand:
P₁ / P₂ = (1 − 1/|ε₂|) / (1 − 1/|ε₁|)
The less elastic market pays the higher price. Students with inelastic demand for textbooks pay full price; students with elastic demand get a discount. Senior citizens pay less for cinema tickets because their demand is more elastic — they have more substitutes (daytime TV, walking).
The welfare effect of third-degree discrimination is ambiguous. Output may rise or fall compared to uniform pricing. If the high-price market is small and the low-price market is large, total output can increase, which may raise total surplus even though some consumers lose. Examiners test this ambiguity directly.
5 · The welfare comparison — uniform price vs third-degree
Compare a monopolist who must charge one price to all buyers with one who can segment markets. Under uniform pricing, the monopolist sets MR = MC for the aggregate demand curve. Under third-degree discrimination, the monopolist sets MR₁ = MR₂ = MC.
The uniform-price monopolist may serve only the high-demand group if the low-demand group’s reservation price is below marginal cost. Third-degree discrimination can bring the low-demand group into the market, increasing total output and total surplus. But it can also reduce output if the high-demand group’s price rises enough that its quantity falls more than the low-demand group’s quantity rises.
The textbook result: third-degree discrimination raises total surplus if it increases total output, and lowers total surplus if it decreases total output. Consumer surplus always falls for the group that pays a higher price. The firm always gains.
Worked example — third-degree discrimination in the London cinema market
A cinema in central London faces two groups of customers. Students have demand P_S = 12 − Q_S. Adults have demand P_A = 20 − Q_A. Marginal cost is constant at MC = 4 per ticket. Fixed costs are zero.
Step 1 — Derive marginal revenue for each group. For students, MR_S = 12 − 2Q_S. For adults, MR_A = 20 − 2Q_A.
Step 2 — Set MR = MC in each market. Students: 12 − 2Q_S = 4 → 2Q_S = 8 → Q_S = 4. Price: P_S = 12 − 4 = 8. Adults: 20 − 2Q_A = 4 → 2Q_A = 16 → Q_A = 8. Price: P_A = 20 − 8 = 12.
Step 3 — Compute profit and consumer surplus. Profit from students: (8 − 4) × 4 = 16. Profit from adults: (12 − 4) × 8 = 64. Total profit = 80. Consumer surplus for students: 0.5 × 4 × (12 − 8) = 8. Consumer surplus for adults: 0.5 × 8 × (20 − 12) = 32. Total consumer surplus = 40.
Step 4 — Compare with uniform pricing. Aggregate demand: for P > 12, only adults buy: Q = 20 − P. For P ≤ 12, both groups buy: Q = (20 − P) + (12 − P) = 32 − 2P. Invert: P = 16 − 0.5Q for Q > 8 (the adult-only region), and P = 16 − 0.5Q for Q ≤ 8? Check: at Q = 8, P = 12, consistent. Aggregate MR: for Q ≤ 8, MR = 16 − Q. For Q > 8, MR = 16 − Q as well? Actually, the kink matters. The aggregate MR has a discontinuity at Q = 8. Set MR = MC = 4 in the lower segment: 16 − Q = 4 → Q = 12. But Q = 12 is in the region where both groups buy. Price: P = 16 − 0.5(12) = 10. Check: at P = 10, students buy Q_S = 12 − 10 = 2, adults buy Q_A = 20 − 10 = 10, total = 12. ✓
Step 5 — Uniform pricing outcomes. Q = 12, P = 10. Profit: (10 − 4) × 12 = 72. Consumer surplus: students: 0.5 × 2 × (12 − 10) = 2; adults: 0.5 × 10 × (20 − 10) = 50; total = 52.
Step 6 — Compare. Third-degree discrimination raises profit from 72 to 80 (+11%) but lowers consumer surplus from 52 to 40 (−23%). Total surplus falls from 124 to 120: under uniform pricing it is profit (72) + CS (52) = 124, and under discrimination it is profit (80) + CS (40) = 120. This is the ambiguous welfare result — discrimination raises profit but can lower total surplus. Total output is the same (12 units) in both cases, so the loss comes entirely from reallocating output across groups: students consume more (2 to 4) and adults fewer (10 to 8), and shifting units from the high-value adult market to the lower-value student market destroys surplus.
Step 7 — Interpretation. The cinema charges adults £12 and students £8. Elasticity at each optimum is |ε| = (P/Q) × |dQ/dP|, and dQ/dP = −1 for both demands, so |ε_S| = 8/4 = 2 for students and |ε_A| = 12/8 = 1.5 for adults. Adults have the less elastic demand, so they pay the higher price — exactly what the model predicts. That matches the intuition: adults who really want to see the film pay £12, while students with more substitutes pay £8.
Struggling with the welfare arithmetic? The uniform-vs-discrimination comparison is the most common exam question in MG207, and the sign of the welfare change depends on whether total output rises or falls. A one-on-one Managerial Economics tutor at LSE works through these calculations until the logic is second nature. Book a trial session.
Practice
Q1. A firm faces two markets. Market 1: P₁ = 100 − Q₁. Market 2: P₂ = 60 − 0.5Q₂. Marginal cost is constant at MC = 20.
(a) Find the third-degree discriminating prices and quantities.
(b) Compute total profit.
(c) Compare with uniform pricing. Does total output rise or fall?
Q2. A monopolist with MC = 10 faces demand P = 50 − Q. Compare profit, consumer surplus and total surplus under:
(a) Single-price monopoly.
(b) First-degree (perfect) price discrimination.
Q3. A firm offers two package sizes. Low-type demand: P = 10 − Q. High-type demand: P = 20 − Q. Marginal cost is 2 per unit. The firm cannot identify types. Design a menu of two quantity-price bundles that induces self-selection. (Hint: the low-type bundle must give zero surplus to the low type; the high-type bundle must give the high type at least as much surplus as the low-type bundle.)
Answers: Q1 (a) Market 1: Q₁ = 40, P₁ = 60; Market 2: Q₂ = 40, P₂ = 40; (b) Profit = 40×(60−20) + 40×(40−20) = 1600 + 800 = 2400; (c) Uniform: for P ≤ 60 both markets buy, so aggregate demand is Q = (100−P) + (120−2P) = 220 − 3P, i.e. P = (220−Q)/3 with MR = (220−2Q)/3; MR = MC gives Q = 80, P ≈ 46.67, profit ≈ 2133. Total output is 80 under discrimination (40+40) and 80 under uniform pricing — output is unchanged, so total surplus falls (the standard linear-demand result). Q2 (a) Q = 20, P = 30, π = 400, CS = 200, TS = 600; (b) Q = 40, π = 800, CS = 0, TS = 800. Q3: Low-type bundle: Q_L = 8, total price = 48 (area under low demand from 0 to 8: 0.5×8×(10−2) + 2×8 = 32+16 = 48), leaving the low type zero surplus. High-type bundle: Q_H = 18; the high type values 18 units at 0.5×18×(20−2) + 2×18 = 162+36 = 198, but would earn surplus 128 − 48 = 80 by taking the low bundle instead (it values those 8 units at 0.5×8×(20+12) = 128), so charge 198 − 80 = 118. Check: the high type earns surplus 198 − 118 = 80 from Q_H, equal to the 80 it would get from Q_L, so the menu is incentive-compatible (the tie is broken toward the intended bundle).
Key takeaways
- Price discrimination requires market power and no arbitrage. The degree depends on what the firm knows and whether resale is possible.
- First-degree discrimination extracts all consumer surplus. Output is efficient (P = MC), but consumers get zero surplus.
- Second-degree uses self-selection menus. The firm designs bundles so that each buyer type reveals their willingness to pay through their choice.
- Third-degree charges different prices to observable groups. The less elastic group pays more: P₁/P₂ = (1 − 1/|ε₂|)/(1 − 1/|ε₁|).
- The welfare effect of third-degree discrimination is ambiguous. Total surplus rises if total output rises, and falls if total output falls.
Why LSE students choose our Managerial Economics tutoring
- MG207-specific syllabus coverage: our tutors know the LSE Managerial Economics module inside out — from price discrimination through game theory to transfer pricing — and structure sessions around your lecture slides and problem sets.
- One-on-one exam technique: every session is private and focused on the question formats that appear in LSE exams, including the welfare comparison calculations that carry the heaviest marks.
- PhD-level economics tutors: your tutor holds a PhD in economics or is a current doctoral researcher at a top London university, with proven experience teaching managerial economics at the undergraduate level.
FAQ
Q: What is price discrimination in economics?
A: Charging different prices to different buyers for the same product, when the price difference is not based on cost differences. It lets the firm capture consumer surplus and turn it into profit.
Q: What is the difference between first, second and third-degree price discrimination?
A: First-degree charges each buyer their maximum willingness to pay. Second-degree offers a menu of options and lets buyers self-select. Third-degree charges different prices to observable groups like students or seniors.
Q: When is third-degree price discrimination welfare-improving?
A: When it increases total output compared to uniform pricing. If the low-price market brings in new buyers who would not have been served under uniform pricing, total surplus can rise. If output falls, total surplus falls.
Q: Why do students get discounts?
A: Students typically have more elastic demand — they have lower income and more substitutes (streaming, library copies). Third-degree discrimination charges a lower price to the more elastic group, so students pay less than adults.
Q: Is price discrimination illegal?
A: Some forms are regulated. In the US, the Robinson-Patman Act restricts price discrimination that harms competition. In the UK, competition law prohibits discriminatory pricing that abuses a dominant market position. But most everyday price discrimination — student discounts, senior prices, airline pricing — is legal.
Q: How do I calculate the optimal prices for third-degree discrimination?
A: Set marginal revenue equal to marginal cost in each market separately. Use the formula MR = P(1 − 1/|ε|) to check that the less elastic market gets the higher price. Then compare total output and welfare with the uniform-pricing benchmark.
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