Price Discrimination: Study Guide (Microeconomics 4.3)

What price discrimination is

In Topic 4.2 the monopolist charged one price to every buyer. That leaves money on the table in two ways. Some buyers would have paid more than the price; their extra value is consumer surplus. Other buyers would have paid more than the marginal cost but less than the price, so they do not buy at all; that is the deadweight loss.

Price discrimination is the practice of selling the same product to different buyers at different prices, where the price difference is not caused by a difference in the cost of supplying them. A firm does this to turn some consumer surplus into profit and to sell extra units it would otherwise lose.

Familiar forms include cheaper tickets for students or older people, lower fares for travellers who book weeks ahead, and discount coupons that only price-sensitive shoppers bother to collect.

A price difference that matches a cost difference is not price discrimination. Charging more to deliver a sofa to a distant village than to a house next to the warehouse simply passes on a higher cost.

The three conditions

A firm can only price discriminate when all three of these hold:

1. Market power. The firm faces a downward-sloping demand curve and sets its own price. A perfectly competitive firm is a price taker: if it charged anyone more than the market price, that buyer would go to a rival.
2. Buyers can be told apart. The firm must be able to identify buyers, or groups of buyers, with different willingness to pay (different price elasticities of demand). It might use age, student status, booking date, location or time of use.
3. Resale can be stopped. If low-price buyers could resell to high-price buyers, the high price would collapse. This is called arbitrage. Named tickets, ID checks and services that cannot be passed on (a haircut, a medical appointment, a seat on a specific train) all block resale.

Who pays more: the role of elasticity

When a firm can split its buyers into groups, it treats each group as a separate market and uses MR = MC in each one. The group with less elastic demand cares less about price, so the firm can raise the price to that group without losing many sales. The group with more elastic demand would buy much less at a high price, so it gets the lower price.

This is why business travellers who must travel on a fixed day pay more than holiday travellers who can choose any day, and why adults often pay more than students for the same seat.

Perfect price discrimination

Perfect price discrimination is the extreme case. The firm knows each buyer’s maximum willingness to pay and charges every buyer exactly that amount. It is a model, not a common real-world practice, because firms rarely know each buyer’s maximum price. It is useful because it shows the limit of what price discrimination can do.

The key change is to marginal revenue. A single-price monopolist must cut the price on all units to sell one more, so its MR lies below demand. A perfectly price-discriminating firm cuts the price only for the extra buyer; everyone else still pays their own maximum. So the extra revenue from one more unit is simply the price that buyer pays:

Under perfect price discrimination, MR = P, so the MR curve is the demand curve.

The firm still produces where MR = MC. Because MR is the demand curve, that means producing where demand (price) = MC. This gives four results:

Measure	Single-price monopoly	Perfect price discrimination
Output	where MR = MC; less than the competitive quantity	where P = MC; equal to the competitive quantity
Price	one price, above MC	a different price for each buyer; the last buyer pays MC
Consumer surplus	positive	zero: every buyer pays their maximum
Profit / producer surplus	the rectangle between price and MC (constant MC, no fixed costs)	all of the surplus under demand and above MC
Deadweight loss	positive	zero
Allocative efficiency	no (P > MC)	yes: the last unit has P = MC

Notice the trade-off. Perfect price discrimination is efficient: total surplus is as large as it can be. But the distribution is very one-sided: consumers keep none of it.

Worked example 1: a single price versus perfect price discrimination

Question. Skylark Balloons is the only hot-air balloon company in a fictional valley. Demand for rides is P = 120 − 2Q, where P is the price in dollars per ride and Q is rides per week. The marginal cost of a ride is constant at $20, and there are no fixed costs, so ATC = MC = $20.

(a) As a single-price monopolist, find Skylark’s output, price and profit. (b) Calculate consumer surplus and deadweight loss. (c) Skylark finds a way to charge each rider their maximum price. Find the new output, profit, consumer surplus and deadweight loss.

(a)

1. For a straight-line demand curve, MR has the same price intercept and twice the slope: MR = 120 − 4Q.
2. Set MR = MC: 120 − 4Q = 20, so 4Q = 100 and Q = 25 rides per week.
3. Read the price from demand, not MR: P = 120 − 2(25) = $70 per ride.
4. Profit = (P − ATC) × Q = (70 − 20) × 25 = $1,250 per week.

(b)

1. Consumer surplus is the triangle above the price and below demand: ½ × 25 × (120 − 70) = $625.
2. The efficient quantity is where demand meets MC: 120 − 2Q = 20, so Q = 50.
3. Deadweight loss is the triangle between demand and MC from 25 to 50 rides: ½ × (50 − 25) × (70 − 20) = $625.

(c)

1. With perfect price discrimination MR is the demand curve, so Skylark produces where P = MC: Q = 50 rides per week, the same as a competitive market.
2. The first rider pays almost $120, the next a little less, and the 50th pays $20.
3. Profit equals the whole triangle under demand and above MC: ½ × 50 × (120 − 20) = $2,500 per week.
4. Consumer surplus = $0. Deadweight loss = $0.

Check and interpretation. Under a single price, total surplus was 1,250 + 625 = $1,875, and $625 was lost. Under perfect price discrimination total surplus is $2,500: the full amount, with nothing lost. So the $2,500 profit is made of three parts: the old profit ($1,250), the old consumer surplus ($625) and the old deadweight loss ($625), which is now created and kept by the firm. Riders 26 to 50 now get a ride they would not have bought at $70, but because each pays their maximum, they gain no consumer surplus from it.

Worked example 2: two groups, two prices

Question. Calder Coaches is the only coach company on a fictional route between Arnmouth and Kelby. It sells tickets to two groups who cannot swap tickets, because a student ticket needs a student card at boarding. The marginal cost per passenger is constant at $10, with no fixed costs.

• Standard (adult) demand: P = 90 − Q
• Student demand: P = 50 − Q

(P in dollars per ticket, Q in tickets per day.)

(a) Find the profit-maximising price and quantity for each group, and the total profit. (b) Calculate the price elasticity of demand at each chosen point and explain which group pays more. (c) If Calder had to charge one price to everyone, it would charge $40 and sell 60 tickets. Compare its profit with part (a).

(a) Treat each group as its own market and set MR = MC in each.

	Standard	Student
MR	90 − 2Q	50 − 2Q
MR = MC	90 − 2Q = 10, so Q = 40	50 − 2Q = 10, so Q = 20
Price (from demand)	90 − 40 = $50	50 − 20 = $30
Profit	(50 − 10) × 40 = $1,600	(30 − 10) × 20 = $400

Total profit = 1,600 + 400 = $2,000 per day.

(b) For a straight line, the size of the elasticity at a point is (change in Q ÷ change in P) × (P ÷ Q). Both lines have ΔQ ÷ ΔP = 1 (ignoring the minus sign).

• Standard: 1 × (50 ÷ 40) = 1.25
• Student: 1 × (30 ÷ 20) = 1.5

Students have the more elastic demand at the chosen prices, so a high price would cost Calder many student sales. They get the lower price. Standard passengers are less price-sensitive, so they pay more.

(c) At a single price of $40, standard passengers buy 90 − 40 = 50 tickets and students buy 50 − 40 = 10, so 60 in total. Profit = (40 − 10) × 60 = $1,800 per day. Price discrimination raises profit by 2,000 − 1,800 = $200 per day.

Interpretation. Standard passengers pay more ($50 instead of $40), so the firm captures some of their consumer surplus. Students pay less ($30 instead of $40) and more of them travel (20 instead of 10). Unlike perfect price discrimination, this group pricing still leaves P > MC in each group, so some deadweight loss remains.

Common misconceptions

• “Any difference in price is price discrimination.” Only if the cost of supplying the buyers is the same. A higher delivery charge for a distant address reflects a higher cost.
• “The group with the higher demand pays the higher price.” What matters is elasticity. The group that is less sensitive to price pays more.
• “A perfectly competitive firm could price discriminate if it wanted to.” It has no market power. Any buyer charged more than the market price would buy from a rival.
• “Under perfect price discrimination, MR is still below demand.” The firm does not cut the price on earlier units to sell one more, so MR equals demand.
• “Perfect price discrimination is inefficient because the monopolist takes everything.” It is allocatively efficient (P = MC for the last unit, no deadweight loss). Who gets the surplus is a question of distribution, not efficiency.
• “Perfect price discrimination raises the price for everyone.” Buyers with the highest willingness to pay pay more than the single price, but buyers who value the good between MC and the single price now pay less than the old single price and are served.
• “Price discrimination always reduces output.” Perfect price discrimination raises output to the competitive level. Group pricing can raise, keep or lower total output, depending on the demand curves.

Where this leads

Perfect price discrimination shows that the deadweight loss of a single-price monopoly comes from having to charge every buyer the same price: remove that limit and the lost units are produced. Next, Topic 4.4: Monopolistic Competition looks at many firms that each have a little market power. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate.