Price discrimination
Learning goals
After this page, you can:
- State the three conditions for price discrimination, say which one fails in a given case, and tell it apart from a price difference that comes from a cost difference.
- Name the three types — perfect, group, and nonlinear — with one example each.
- Set the best price for each group with MR = MC on that group’s own demand line, and use the Lerner rule to show that the less elastic group pays more.
The idea
For years, U.S. airlines sold a much cheaper round trip if the trip included a Saturday night away. Same seat. Same plane. Same fuel. Why the rule? Business travelers want to be home for the weekend, and they will pay to be home. Vacationers do not mind staying over. The rule let the airline charge two prices without ever asking anyone who they were.
Price discrimination means charging different prices for the same product when the cost of serving each buyer is the same. The test is short: same cost, different price. If a delivery to a far-away town costs more and the price is higher, that is a cost-based price difference, not price discrimination. The word “discrimination” here is a technical word. It does not mean the practice is illegal or unfair. Student tickets and senior discounts are price discrimination.
Three conditions. Price discrimination only works when all three hold.
- Market power. The seller must be able to set its own price. A farm selling wheat into a national market cannot. Buyers would simply go to another farm.
- Customers who value the good differently, and can be sorted. The seller needs a way to tell the groups apart, or to let them sort themselves. That way is called a fence: an ID check, a Saturday-night stay, a booking date, a student email address.
- No resale. If low-price buyers can resell to high-price buyers, the low price leaks to everyone. Airlines print names on tickets for this reason.
When a plan fails, ask which condition broke. Usually it is the fence or resale.
Three types.
- Perfect price discrimination: each customer pays their own maximum. Nobody keeps any consumer surplus. Real firms never get all the way there. It is the benchmark: the most a seller could ever collect.
- Group price discrimination: each group pays its own price. Student, senior, and military prices. Business fares and leisure fares. The seller has to sort people into groups.
- Nonlinear price discrimination: the price per unit depends on how many units you buy. A 10-ride pass costs less per ride than single tickets. Nobody shows an ID. Heavy users pick the pass themselves, so the menu does the sorting.
Setting each group’s price. Treat each group as its own market. Each group has its own demand line, P = a − b·Q. For a straight line, marginal revenue is MR = a − 2b·Q: it starts at the same top price and falls twice as fast. The marginal cost c is the same for both groups, because the seat is the same. Set MR = c for each group. Then read the price off that group’s demand line. On a straight line this gives a neat shortcut: the best price is halfway between the top price and the cost, P* = (a + c) ÷ 2.
Who pays more? The Lerner index is the markup as a share of price: (P − c) ÷ P. At the best price, the Lerner index equals 1 ÷ |ε|, where |ε| is the price elasticity of demand at that price. So a big markup means a small elasticity. The group that is less sensitive to price pays more. The group that is more sensitive to price — the more elastic group — gets the lower price. Business travelers have few other choices and need to fly on a set day, so they pay more. Vacationers can drive, wait, or pick a different place, so they pay less.
Why the fence is worth money. Charging two prices earns more than the best single price, because each group gets a price that fits it. But if the fence breaks, the low price leaks to everyone. Then the seller can end up worse off than if it had set one price from the start. That is why firms spend real effort on fences — names on tickets, student verification, rules that make one plan unattractive to the other group.
Your company. Look for the fences. Who gets a lower price, and what stops everyone else from paying it? That is Playbook P6, prompt 3.
For each group: P = a − b·Q · MR = a − 2b·Q · set MR = c → Q* = (a − c) ÷ (2b), P* = (a + c) ÷ 2
Lerner: (P − c) ÷ P = 1 ÷ |ε| → lower markup = more elastic group = lower price. Perfect benchmark: profit = (a − c)² ÷ (2b), twice the single-price profit on a straight line.
Try it
The tool shows two groups flying the same route. Each panel has the group’s demand line, its MR line, and the same marginal cost. The shaded rectangle is the markup times the seats: the profit from that group.
- Read the two fares. Which group has the lower markup (Lerner)? Is that the group with the lower fare?
- Turn on One fare for everyone. How much profit does the airline lose compared with two fares?
- Turn it off and turn on Resale allowed. Compare this profit with the one-fare profit. What does the fence protect?
- Raise marginal cost from $50 to $150. How many dollars does each fare rise? (Hint: P* = (a + c) ÷ 2.)
Worked example
Problem. Lakeshore Air (a fictional airline) flies one route. Marginal cost is $50 per passenger. Names are printed on tickets, so there is no resale. Business demand is P = 450 − 2·Q. Leisure demand is P = 210 − 0.5·Q (seats per week, dollars per seat). What fare should each group pay?
Step 1. Business. MR = 450 − 4·Q. Set it equal to 50: Q = (450 − 50) ÷ 4 = 100 seats. Fare = 450 − 2 × 100 = $250. Shortcut check: (450 + 50) ÷ 2 = 250.
Step 2. Leisure. MR = 210 − 1·Q. Set it equal to 50: Q = (210 − 50) ÷ 1 = 160 seats. Fare = 210 − 0.5 × 160 = $130.
Step 3. Profit. Business: (250 − 50) × 100 = $20,000. Leisure: (130 − 50) × 160 = $12,800. Total $32,800 a week.
Step 4. Who is more elastic? Business Lerner = 200 ÷ 250 = 0.80, so |ε| = 1.25. Leisure Lerner = 80 ÷ 130 = 0.62, so |ε| ≈ 1.63. Leisure is more elastic, and it gets the lower fare.
Step 5. Compare with one fare. The best single fare is $154. Business buys 148 seats and leisure buys 112, so 260 seats in all. Profit = (154 − 50) × 260 = $27,040. Two fares earn $5,760 more, about 21% more.
Step 6. If the fence breaks. With resale, everyone pays $130. Business now buys 160 seats and leisure 160. Profit = 80 × 320 = $25,600 — less than the single fare.
Step 7. The perfect benchmark. If every business traveler paid their own maximum, the airline would keep selling until the price reached $50: 200 seats. It would keep the whole triangle above cost: ½ × 400 × 200 = $40,000, twice the $20,000 from one business fare.
One more type. A 10-flight pass at a lower price per flight than single tickets is nonlinear pricing. Frequent flyers choose the pass themselves. Nobody has to show an ID.
Check yourself
A farm sells wheat into a national grain market. It wants to charge food companies more than animal-feed buyers for the same wheat. Why will this plan fail?
Price discrimination needs market power, customers who can be sorted, and no resale; a price taker fails the first test.
A coffee chain’s app sells single drinks at $5 or a 10-drink card for $40. Anyone may choose either option. Which type of pricing is this?
When the price per unit falls with the amount bought and customers pick their own option, the pricing is nonlinear.
A regional airline’s leisure travelers have demand P = 220 − 0.5·Q (seats per week, dollars per seat). Marginal cost is $60 per passenger. What fare maximizes profit from this group?
For each group, set MR = MC on that group’s own demand line, then read the price off the demand line.
A software firm sells the same license to corporate customers for $250 and to nonprofits for $100. Marginal cost is $50. If both prices are profit-maximizing, what elasticities do they imply?
Lerner = (P − MC) ÷ P = 1 ÷ |ε|; the group with the lower markup share is the more elastic group.
Business travelers’ demand is P = 450 − 2·Q and marginal cost is $50. With one business fare, the airline flies 100 seats at $250 and earns $20,000. If it could charge every traveler exactly their own maximum, what would happen?
Perfect price discrimination is the benchmark: the seller serves everyone who values the good above cost and keeps all of the surplus.
Video
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