Source: Demand Analysis and Optimal Pricing lecture, Texas A&M
Tags: price discrimination, first degree, second degree, third degree, consumer surplus, hurdle model, coupons, intertemporal pricing, Uber surge pricing, dynamic pricing, multinational pricing, airline yield management, pure selling problem
Price discrimination is charging different prices to different customers (or groups) for the same good. It works when the firm can distinguish customer types and prevent resale. Three degrees exist: first (extract each buyer's full willingness to pay), second (quantity discounts), and third (segment markets by observable traits). The principle behind all of them is that groups with more elastic demand should face lower prices.
Price discrimination
Charging different prices for the same good to different buyers or groups, based on differences in their willingness to pay rather than differences in cost.
Consumer surplus
The difference between what a buyer is willing to pay and what they actually pay. If you would pay $4 for a pen priced at $2, your consumer surplus is $2.
First-degree (perfect) price discrimination
Each buyer is charged exactly their maximum willingness to pay. The firm captures all consumer surplus. Rare in practice; closest examples are car negotiations and net tuition (financial aid adjusts price per student).
Second-degree price discrimination
Price varies by quantity or version purchased, but not by customer identity. Examples: quantity discounts, utility rate tiers, two-part pricing at amusement parks (entry fee + per-ride charge).
Third-degree price discrimination
The most common form. The firm divides customers into identifiable groups and charges each group a different price. Examples: student vs. adult movie tickets, business vs. tourist airline fares.
Hurdle model
A self-selection mechanism used when the firm cannot directly identify customer types. A "hurdle" (e.g. clipping a coupon, waiting for a paperback release) separates price-sensitive customers from less price-sensitive ones.
No-arbitrage condition
Resale must be prohibitively costly for price discrimination to hold. If the low-price group could easily resell to the high-price group, the price difference would collapse.
Intertemporal price discrimination
Charging a high price at launch (capturing eager, less price-sensitive buyers) and lowering the price later. The hurdle is time. Examples: hardcover vs. paperback books, new tech products.
Yield management
Revenue-optimising pricing used by airlines, hotels, and sports venues. Allocates a fixed capacity across customer segments to maximise total revenue.
Two conditions must hold:
Distinguishable customers. The firm must be able to identify or sort groups. This can be direct (student ID, age) or indirect (hurdle model).
No arbitrage. Resale between groups must be impractical. An ID check at the cinema prevents an adult from using a student ticket.
First degree: charge each individual their willingness to pay. Extracts all consumer surplus. Theoretically the most profitable but requires perfect information about every buyer.
Second degree: same menu offered to everyone, but the price per unit varies with quantity or version. Customers self-select. Quantity discounts, utility block pricing, amusement park entry-plus-ride pricing.
Third degree: segment by an observable trait (age, location, time of purchase, flexibility of travel). Set MR = MC separately in each segment. The segment with more elastic demand gets the lower price.
Used when customer types are not directly observable.
The firm creates a hurdle that price-elastic customers are willing to jump (effort, time, inconvenience) but price-inelastic customers are not.
The condition: low price + cost of the hurdle < high price. Otherwise the hurdle fails to separate the groups.
Coupons: clipping and redeeming a coupon takes effort. Price-elastic shoppers do it; inelastic shoppers do not. Pillsbury data: coupon users had Ep = –4, non-coupon users had Ep = –2.
Paperbacks vs. hardcovers: marginal production costs are surprisingly similar. The hurdle is time. Eager readers pay full price for the hardcover at launch; patient readers wait for the cheaper paperback months later. This is intertemporal price discrimination.
Rebates: same logic as coupons. The hassle of mailing in a rebate form separates elastic from inelastic buyers.
When demand surges (e.g. snowstorm), Uber multiplies its base price. During one observed surge, the multiplier was 1.2× (a 20% price increase), and quantity demanded dropped 27%.
Elasticity: |27% / 20%| = 1.35. Demand was elastic, so the price increase reduced total revenue.
This suggests Uber was maximising rides (and driver availability), not revenue. Raising the price signals dormant drivers to enter the market, increasing supply.
If Uber kept prices flat during surges, excess demand would develop. Rides would be rationed by non-price mechanisms: waiting, connections, luck. Letting the price rise reduces the queue and draws in more supply over time.
Behavioural economics note: Uber found that customers complain heavily when the multiplier jumps from 1.9× to 2.0× (the round number feels like "double"), but barely react to a jump from 2.0× to 2.1× (the same absolute increase). Round-number aversion is a real behavioural phenomenon.
Online retailers use algorithms to adjust prices frequently ("prices vibrate"), moving away from the historic one-fixed-price model.
Fixed pricing only became standard around 1860. Before that, haggling was normal.
Amazon hires economists (not just marketers) for pricing strategy. Prices are set partly by data, partly by experimentation.
"Left-digit bias" in grocery pricing: consumers focus on the rightmost digits and neglect the leftmost, so $3.99 feels meaningfully cheaper than $4.00 for small-ticket items.
Two types of value in a purchase:
Acquisition value: the perceived utility of the product itself.
Transaction value: the feeling of having won or lost the negotiation (getting a "deal").
A firm sells in two markets with different demands but the same MC = $10,000.
U.S.: Inverse demand P = 90,000 – 40Q. MR = 90,000 – 80Q.
Set MR = MC: 90,000 – 80Q = 10,000 → Q = 1,000. P = $50,000.
Japan: Inverse demand P = 60,000 – 50Q. MR = 60,000 – 100Q.
Set MR = MC: 60,000 – 100Q = 10,000 → Q = 500. P = $35,000.
Japan's price is lower because its demand is more elastic (more substitutes available).
Point elasticity confirmation:
Japan: |1/50 × (35,000/500)| = 1.4
U.S.: |1/40 × (50,000/1,000)| = 1.25
Japan's |Ep| is higher, confirming more elastic demand.
Margins: Japan = 1/1.4 = 71.4%. U.S. = 1/1.25 = 80%.
Mark-ups: Japan = (35,000 – 10,000)/10,000 = 250%. U.S. = (50,000 – 10,000)/10,000 = 400%.
This explains why the same product can cost less abroad. It is not "cut-throat pricing"; it is an outcome of different demand elasticities.
An airline has 180 seats and two segments.
Business: Q(B) = 330 – P(B)
Tourists: Q(T) = 250 – P(T)
Since MC ≈ 0 (pure selling problem), the airline maximises revenue by setting MR(B) = MR(T).
If MR(B) > MR(T), the airline should shift seats from tourists to business travellers (higher marginal revenue per seat).
Inverse demands: P(B) = 330 – Q(B), P(T) = 250 – Q(T).
MR(B) = 330 – 2Q(B), MR(T) = 250 – 2Q(T).
Setting equal: 330 – 2Q(B) = 250 – 2Q(T), plus the constraint Q(B) + Q(T) = 180.
Solving: Q(B) = 110, Q(T) = 70.
P(B) = $220, P(T) = $180.
Total revenue = 220 × 110 + 180 × 70 = $36,800.
If the airline charged a single price instead:
Combined demand: Q = 580 – 2P. With Q = 180: P = $200.
Revenue = 200 × 180 = $36,000.
Price discrimination earns $800 more.
Consumer surplus (for one buyer): CS = Willingness to pay – Price paid
Third-degree pricing rule: Set MR₁ = MR₂ = ... = MC in each market segment.
Pure selling (MC ≈ 0): Set MR₁ = MR₂ (equalise marginal revenues across segments).
Capacity constraint: Q₁ + Q₂ = Total capacity
⚠️ The segment with more elastic demand always gets the lower price under third-degree discrimination. If you get the opposite in a calculation, check your algebra.
⚠️ The airline problem has two equations and two unknowns: the equal-MR condition and the capacity constraint. Know how to solve this system.
⚠️ Do not confuse the three degrees. First = individual pricing, second = quantity/version menus, third = group segmentation. Third degree is the most commonly tested.
⚠️ The hurdle model is a self-selection variant of third-degree discrimination. The firm does not observe type directly; customers sort themselves.
⚠️ Uber's surge pricing example shows elastic demand (|Ep| = 1.35 > 1), meaning the price increase reduced revenue. This demonstrates that Uber's goal is maximising rides and driver supply, not revenue per ride.
Q: A cinema charges $8 for students and $12 for adults. State the two conditions that make this price discrimination possible.
A: (1) Distinguishable customers: student ID verifies group membership. (2) No arbitrage: tickets are checked with ID, so adults cannot use student tickets.
Q: An airline has 200 seats. Business demand: Q(B) = 400 – P(B). Tourist demand: Q(T) = 300 – P(T). MC ≈ 0. Find the revenue-maximising allocation and prices.
A: MR(B) = 400 – 2Q(B). MR(T) = 300 – 2Q(T). Set equal: 400 – 2Q(B) = 300 – 2Q(T), so Q(B) – Q(T) = 50. Combined with Q(B) + Q(T) = 200: Q(B) = 125, Q(T) = 75. P(B) = 400 – 125 = $275. P(T) = 300 – 75 = $225. Revenue = 275 × 125 + 225 × 75 = $51,250.
Q: A publisher releases a hardcover for $30 and a paperback six months later for $12. The marginal cost of each is about $3. What type of price discrimination is this, and what is the hurdle?
A: Intertemporal price discrimination (a form of the hurdle model). The hurdle is time. Eager, less price-sensitive readers pay $30 at launch. Patient, more price-sensitive readers wait and pay $12.
Q: In the multinational pricing example, why is the price lower in Japan than in the U.S.?
A: Japanese consumers have more substitutes available, making their demand more elastic (|Ep| = 1.4 vs. 1.25 for the U.S.). The margin formula (P – MC)/P = 1/|Ep| produces a thinner margin for the more elastic market, so the price is lower.
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