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Microeconomics guide, Unit 4, step 17 of 28Previous stepNext step

Step 17: Price Discrimination

By the EconTutorials team. 10-minute read with 6 practice questions.
SyllabusAP Micro 4.3 · Cambridge 7.6 · IB 2.11 (HL)
In 30 seconds
  • Price discrimination means charging different buyers different prices for the same good, when the difference is not caused by a difference in cost.
  • It needs three conditions: market power, groups of buyers with different price elasticities of demand, and no resale between groups.
  • Perfect (first-degree) price discrimination: \( MR = D \), output rises to the competitive level, there is no deadweight loss, and all consumer surplus becomes profit.
  • Third-degree: set \( MR = MC \) in each market and charge the higher price to the group with less elastic demand.
Video lesson coming soonA short animated lesson for this step will appear here.

What price discrimination means

Think about a cinema. An adult ticket for the Saturday evening show costs more than a student ticket for the same seat at the same show. A Tuesday afternoon ticket costs less again. The film, the seat and the cost of showing it are identical. The cinema simply knows that some people will pay more than others.

Key termPrice discrimination: charging different prices to different consumers for the same good or service, where the price difference is not due to a difference in the cost of supplying them.

Why do it? A single-price monopolist must cut its price on every unit to sell one more, which is why its marginal revenue (MR) is below price. If it could cut the price only for the extra buyers, while keeping a high price for those willing to pay it, it would earn more from the same customers. Price discrimination does exactly that.

The three conditions

All three must hold:

  1. Market power. The firm must be a price maker with a downward-sloping demand curve. A perfectly competitive firm that charged some buyers more would lose them to rivals.
  2. Separate groups with different elasticities. The firm must be able to identify groups whose price elasticities of demand (PED) differ. If every group reacted to price in the same way, different prices would gain nothing.
  3. No resale (no arbitrage). Low-price buyers must not be able to resell to high-price buyers. If students could resell cheap tickets to adults, nobody would pay the adult price.

That is why price discrimination is common for services consumed on the spot (haircuts, train journeys, cinema seats) and for tickets tied to a named person, such as airline tickets.

First-degree (perfect) price discrimination

Imagine a tutor who could read every parent’s mind and charge each one the most they would pay: $40 to one family, $35 to the next, $22 to the next. This is first-degree, or perfect, price discrimination. Every buyer pays their reservation price, the highest price they are willing to pay.

  • \( MR = D \). Selling one more unit no longer means cutting the price on earlier units, so the extra revenue from the next unit is simply the price that buyer pays. The demand curve is the MR curve.
  • Output equals the competitive level. The firm produces where \( MR = MC \), which is now where demand meets MC: the same quantity as perfect competition. So \( P = MC \) for the last unit and the outcome is allocatively efficient.
  • No deadweight loss, but no consumer surplus. Every trade worth making happens, but every buyer pays their maximum, so all consumer surplus becomes profit.
Worked example

A firm faces demand \( P = 20 – Q \) and a constant MC of $4 (no fixed costs). Compare a single price with perfect price discrimination.

Step 1Single price: \( MR = 20 – 2Q = 4 \Rightarrow Q = 8,\ P = 12 \).
Step 2Profit \( = (12 – 4)(8) = 64 \); consumer surplus \( = \tfrac{1}{2}(20 – 12)(8) = 32 \); DWL \( = \tfrac{1}{2}(12 – 4)(16 – 8) = 32 \).
Step 3Perfect price discrimination: \( MR = D \), so \( 20 – Q = 4 \Rightarrow Q = 16 \).
Step 4Profit \( = \tfrac{1}{2}(20 – 4)(16) = 128 \); consumer surplus \( = 0 \); DWL \( = 0 \).

Output doubles from 8 to 16, the competitive level. Total surplus rises from 96 to 128 because the deadweight loss of 32 disappears, but all of it now goes to the firm.

DiagramPrice on the vertical axis, quantity on the horizontal. Draw a downward-sloping demand curve labelled \( D = MR \) and a horizontal MC line. Output is where \( D = MR \) meets MC; label it \( Q_{PD} \). Shade the whole triangle between demand and MC up to \( Q_{PD} \) as profit. There is no consumer-surplus area and no deadweight-loss triangle.
Common mistakeWriting that perfect price discrimination “creates a deadweight loss”. It removes the deadweight loss and is allocatively efficient. The concern is equity: consumers lose all their surplus.

Third-degree price discrimination

This is the type you see every day. The firm splits buyers into groups by a visible feature (age, student status, time of purchase, location) and charges each group one price. The rule: charge the higher price to the group whose demand is less elastic.

A group with inelastic demand has few alternatives and keeps buying at a high price. A group with elastic demand is very price-sensitive, so a lower price wins many extra sales. Students usually have lower incomes and flexible time, so their demand is more elastic. Business travellers must fly on set days and their employer pays, so their demand is inelastic.

To maximise profit, the firm equalises marginal revenue across markets:

\[ MR_A = MR_B = MC \]

If MR were higher in A than in B, moving one sale from B to A would raise revenue at no extra cost. Using \( MR = P\left(1 – \frac{1}{|PED|}\right) \), equal MRs mean the market with the lower \( |PED| \) must have the higher price.

Worked example

For example, a cinema has a constant MC of $4 per seat (no fixed costs). Adult demand is \( P_A = 20 – Q_A \); student demand is \( P_S = 12 – Q_S \). Find each price.

Step 1Adults: \( MR_A = 20 – 2Q_A = 4 \Rightarrow Q_A = 8,\ P_A = 12 \).
Step 2Students: \( MR_S = 12 – 2Q_S = 4 \Rightarrow Q_S = 4,\ P_S = 8 \).
Step 3Profit \( = (12 – 4)(8) + (8 – 4)(4) = 64 + 16 = 80 \).
Step 4Elasticities: adults \( |PED| = \frac{12}{8} = 1.5 \); students \( |PED| = \frac{8}{4} = 2 \) (both slopes are 1).

Adults, the less elastic group, pay $12; students pay $8. Check: \( 12(1 – \tfrac{1}{1.5}) = 4 \) and \( 8(1 – \tfrac{1}{2}) = 4 \), so both MRs equal MC.

With one price for everyone, combined demand (for prices up to $12) is \( Q = 32 – 2P \), so \( P = 16 – \tfrac{Q}{2} \) and \( MR = 16 – Q \). Setting \( MR = 4 \) gives \( Q = 12,\ P = 10 \) and profit \( = 6 \times 12 = 72 \). Discrimination raises profit from 72 to 80. Total output stays at 12, but students now buy 4 instead of 2 and adults 8 instead of 10.

DiagramDraw two panels side by side with price on each vertical axis and the same horizontal MC line in both. Left: the less elastic market (adults) with a steep demand curve and its MR. Right: the more elastic market (students) with a flatter demand curve and its MR. In each panel find where MR meets MC, drop down for quantity and go up to demand for price. The left-hand price is clearly higher.
Real exampleHow groups are separatedWho pays more
Student and senior discountsID cardWorking adults: higher incomes, less elastic demand
Airline faresBooking date, flexibility; named ticketsLast-minute business travellers: must travel, employer pays
Cinema timesTime and day of the showEvening and weekend viewers: when most people are free
Exam tipAP Micro FRQs often ask what happens when a monopolist moves to perfect price discrimination. Full marks: output increases to where demand meets MC, consumer surplus falls to zero, deadweight loss is eliminated, profit rises. For Cambridge 9708 and IB HL, state the three conditions, draw two markets with MR = MC in each and the higher price in the less elastic one, then evaluate the effects on each group.

Welfare effects and evaluation

Against: consumer surplus is transferred to the firm, so the high-price group is worse off; many see paying different amounts for the same thing as unfair; extra profit for a firm with market power can widen inequality; and separating markets (checking IDs, complex fares) uses up resources.

For: output may rise, and under perfect price discrimination it reaches the efficient level, removing the deadweight loss. Low-income groups such as students may buy at prices they could not afford under a single price. Some services, such as a rural rail line, may only cover their costs if different groups pay different prices, so they exist only because of discrimination.

A balanced conclusion: the firm always gains and the high-price group always loses. Overall efficiency improves only if total output rises. If output stays the same, as in the cinema example, the main effect is a transfer of surplus from consumers to the firm.

Practise: 6 questions

Try each one on paper first, then check the worked answer.

EasyQ1. State the three conditions needed for price discrimination. Show worked answer
1. Market power (a downward-sloping demand curve).
2. Buyers can be separated into groups with different price elasticities of demand.
3. No resale between groups (no arbitrage).
EasyQ2. Group X has a PED of −0.5 and group Y a PED of −2.0. Which group should pay the higher fare? Show worked answer
Group X. Its demand is inelastic (\( |PED| = 0.5 < 1 \)), so a higher fare loses few sales. Group Y’s demand is elastic, so it should get the lower fare.
MediumQ3. A monopolist faces \( P = 30 – Q \) and a constant MC of $6 (no fixed costs). Find output and profit (a) with a single price and (b) with perfect price discrimination. (c) What happens to deadweight loss? Show worked answer
(a) \( 30 – 2Q = 6 \Rightarrow Q = 12,\ P = 18 \). Profit \( = (18 – 6)(12) = 144 \).
(b) \( 30 – Q = 6 \Rightarrow Q = 24 \). Profit \( = \tfrac{1}{2}(30 – 6)(24) = 288 \).
(c) Single-price DWL \( = \tfrac{1}{2}(18 – 6)(24 – 12) = 72 \), consumer surplus \( = \tfrac{1}{2}(12)(12) = 72 \). Check: \( 144 + 72 + 72 = 288 \). With perfect discrimination DWL and consumer surplus both fall to 0.
MediumQ4. MC is a constant $10. Market A: \( P_A = 50 – 2Q_A \). Market B: \( P_B = 30 – Q_B \). Find each price and quantity and total profit (no fixed costs). Show worked answer
A: \( MR_A = 50 – 4Q_A = 10 \Rightarrow Q_A = 10,\ P_A = 30 \).
B: \( MR_B = 30 – 2Q_B = 10 \Rightarrow Q_B = 10,\ P_B = 20 \).
Profit \( = (20)(10) + (10)(10) = 300 \).
At these points \( |PED_A| = \frac{30}{10} \times \frac{1}{2} = 1.5 \) and \( |PED_B| = \frac{20}{10} \times 1 = 2 \): A is less elastic and pays more.
MediumQ5. At current prices, MR in market A is $8 and MR in market B is $5. Is the firm maximising profit? What should it do? Show worked answer
No: profit needs \( MR_A = MR_B = MC \). Moving one sale from B to A gains $8 and loses $5, a net $3 gain. So lower the price in A to sell more there, and raise it in B, until the MRs are equal (and equal to MC).
ExamQ6. An airline charges business travellers more than leisure travellers on the same flight. Using a diagram, explain how it sets these fares and evaluate whether society benefits. [8 marks] Show worked answer
Indicative mark scheme
Conditions [1]: market power; passengers separable by booking time and flexibility; named tickets cannot be resold.
Diagram [2]: two markets with a common MC; steeper demand for business, flatter for leisure; MR = MC in each; higher business fare read from its demand curve.
Explanation [2]: business demand is inelastic (fixed dates, employer pays), so its profit-maximising fare is higher; leisure demand is elastic, so a lower fare fills extra seats.
Evaluation [3]: business travellers lose consumer surplus and the airline gains; leisure travellers may gain seats they could not otherwise afford; if total passengers rise, deadweight loss falls; profit may keep thin routes running. But if output does not rise, it is mainly a transfer to the airline. A justified conclusion is needed for full marks.

Check yourself

1. Under perfect price discrimination, which is true?

MR = D, so output is where D = MC, the efficient level. Consumer surplus is zero but there is no deadweight loss.

2. In third-degree price discrimination, the higher price goes to the group whose demand is:

Inelastic buyers cut purchases only a little when the price rises.

3. Which makes price discrimination impossible?

With resale, low-price buyers sell to high-price buyers and the higher price collapses.

Your score: 0 out of 3

The short version

  • Price discrimination is charging different prices for the same good to different buyers, for reasons not linked to cost.
  • It needs market power, separable groups with different elasticities, and no resale.
  • Perfect price discrimination: \( MR = D \), competitive output, no deadweight loss, all consumer surplus becomes profit.
  • Third-degree: \( MR = MC \) in each market; the less elastic group pays more.
  • The firm always gains and high-price buyers lose; society gains only if total output rises.

Further reading on EconTutorials

Older in-depth articles on this topic from our blog:

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