Price Discrimination: Resale, Elasticity and Welfare
Price discrimination depends on more than charging two prices. Check cost differences, buyer separation and resale, then follow the effect on profit and welfare. Compare the pricing methods and test a two-group example with three original interactive questions.
Group markups depend on demand at the chosen prices.
Check Three Group-Pricing Cases
The first three cases concern group, or third-degree, price discrimination with comparable costs. Observable group membership is not a requirement for every form of discrimination: a second-degree menu can let buyers sort themselves. Treat the examples as economic models, not conclusions about any real group’s demand.
Successful price discrimination requires market power, identifiable buyer groups, and
- constant marginal cost
- government ownership
- a perfectly elastic demand curve
- free entry
- limits on resale between groups
limits on resale between groups Profitable, easy resale lets low-price purchases compete with the seller’s high-price offer. The group-pricing model therefore needs effective separation; resale need not be physically impossible if transaction costs or restrictions sufficiently limit arbitrage.
A movie theater charges lower prices to students when resale is impossible. This is most directly an example of
- first-degree price discrimination
- third-degree price discrimination
- peak-load pricing only
- average-cost regulation
- two-part tariff pricing
third-degree price discrimination For the comparable service and costs specified here, student status identifies a group offered a distinct price. That is third-degree discrimination; student status alone does not measure how elastic its demand is.
A cinema can verify student status, prevent ticket resale, and observes that students are more price sensitive than other adults. Which pricing plan can increase profit through separation?
- Charge students more than adults
- Offer a lower verified student price
- Set one price equal to marginal cost for everyone
- Allow unrestricted resale
- Charge each group its average cost
Offer a lower verified student price A lower price for the more elastic student group can expand sales without forcing the same discount for less elastic buyers. Verification separates the groups, and resale control prevents low-price tickets from being transferred to the high-price market.
Video Lesson: Price Discrimination
A focused video lesson from Alvin Chiang.
Separate Price Differences from Cost Differences
In economic analysis, discriminatory price differences are not explained by relevant cost differences. A seller needs pricing power and a way to sustain different offers, using identified groups or self-selection. Group markup comparisons also require demand and cost assumptions; a discount label alone is not enough.
Cost-based price differences are not discrimination in the economic definition. Charging more to deliver a heavy package farther may reflect added cost. Charging two otherwise similar buyers different markups because one group has fewer alternatives is discrimination. The question normally states that cost differences do not explain the prices.
Distinguish Identification and Self-Selection
Market separation prevents low-price buyers from reselling to high-price buyers. Identification can use age, purchase timing, location, coupons, or self-selection through product versions. Without separation, arbitrage undermines the price difference by moving units from the low-price group to the high-price group.
State the Markup Rule’s Conditions
With smooth interior profit-maximizing choices, a served group’s marginal revenue equals the common marginal cost. If that cost is positive, (price − MC) / price equals 1 / |demand elasticity| at the chosen price. The less elastic served group then has the larger proportional markup, with both absolute elasticities above one. Costs, capacity constraints or boundary choices can change the comparison.
Identify the Ideal First-Degree Benchmark
Perfect first-degree discrimination prices individual units at willingness to pay. Under the ideal information and resale assumptions, it serves units whose benefit covers marginal cost. Imperfect schemes need not reproduce that allocation; evaluate actual buyers, output and costs rather than treating different prices as proof of efficiency.
In the perfect first-degree model, no uniform price must be cut on earlier units to sell the next one. Conditional on operation being feasible, output reaches Q_e, where marginal willingness to pay meets marginal cost. The seller receives the gains above variable cost as producer surplus; fixed cost still has to be subtracted to find economic profit.
Compare Four Pricing Methods
| Pricing method | Output tendency | Surplus implication |
|---|---|---|
| Single price | Q_m<Q_e |
Can leave beneficial trades unmade; profit also depends on costs |
| Perfect first degree | Q_e |
Ideal seller captures all gains above variable cost; no static DWL under stated assumptions |
| Third degree | Separate group prices | Conditional markup rule; welfare depends on allocation as well as total output |
| Second degree | Price varies with quantity or version | Buyers self-select. Outcome depends on schedule |
Check the Actual Resale Constraint
An airline charges business travelers more than vacation travelers for the same seat when cost is equal. Advance-purchase and change restrictions help separate the groups. If vacation travelers could freely resell tickets to business travelers, the low fare would undermine the high-fare market.
Check Allocation as Well as Total Output
A group discount can expand purchases in one segment while purchases contract elsewhere. Total output, allocation across buyers, real costs and any externalities all matter for welfare. Higher profit does not establish higher total surplus, and unchanged total quantity does not establish unchanged welfare.
Match the condition to the question. Group pricing needs distinguishable markets and sufficiently limited arbitrage; second-degree menus rely on self-selection; perfect first-degree pricing requires much more information about willingness to pay. Use elasticity at the relevant prices, not a stereotype about the buyers.
Read the Menu That Sorts Buyers
Self-selection can separate buyers without asking their identity. Refund restrictions, versions, coupons, and quantity blocks induce people with different values or flexibility to choose different offers. The price difference is discriminatory only to the extent it exceeds relevant cost differences.
If resale is cheap and unrestricted, arbitrage can undermine the high-price offer. Check the actual transfer rule and transaction costs before assuming separation succeeds. A price-taking seller also cannot simply sustain different markups for identical purchases against otherwise identical competing offers.
Read the Pricing Models
The author’s Oregon State pricing-strategies chapter distinguishes perfect, group and self-selected pricing. OpenStax’s monopoly output lesson explains the marginal revenue and cost comparison. The two-group numbers and questions below are original, not copied textbook exercises.
Compare Two Groups with a Uniform Price
Use fictional inverse demands P_A = 30 − Q_A and P_B = 18 − 0.5Q_B. Both groups have the same $6 marginal cost, with no fixed cost, capacity limit, externality or separation expense. Quantity is continuous. Assume the seller can keep the two groups separate without profitable resale. Producer surplus equals profit here because fixed cost is zero.
With separate prices, marginal revenues are 30 − 2Q_A and 18 − Q_B. Equating each to $6 gives Q_A = 12 at P_A = $18 and Q_B = 12 at P_B = $12. Total output is 24 and profit is ($18 − $6) × 12 + ($12 − $6) × 12 = $216. At those prices, absolute demand elasticities are 1.5 in A and 2 in B, consistent with A’s larger proportional markup.
At a common price no higher than $18, quantities add to Q = (30 − P) + (36 − 2P) = 66 − 3P. The inverse combined demand is P = 22 − Q/3 and marginal revenue is 22 − 2Q/3. Setting MR to $6 gives Q = 24 and P = $14. A buys 16 units and B buys 8; profit is ($14 − $6) × 24 = $192. This is also better than serving only A: the best A-only price in the $18-and-above range is $18, with $144 profit.
Does the Same Quantity Mean the Same Welfare?
Both regimes sell 24 units, and separate prices increase profit by $24. Check the consumer-surplus triangles before concluding that total welfare is unchanged or higher.
Check your reasoning
At the uniform $14 price, A’s consumer surplus is ½ × 16 × ($30 − $14) = $128. B’s is ½ × 8 × ($18 − $14) = $16. Total consumer surplus is $144; adding $192 profit gives $336 total surplus.
With separate prices, A’s consumer surplus is ½ × 12 × ($30 − $18) = $72 and B’s is ½ × 12 × ($18 − $12) = $36. Total consumer surplus is $108. Adding $216 profit gives $324 total surplus: $12 less, despite the identical total quantity of 24.
Allocation explains the difference. Relative to uniform pricing, four units shift from A to B. At the final separate allocation, A’s marginal willingness to pay is $18 while B’s is $12; with the same marginal production cost, total benefit could increase by reallocating units toward A. Equal total output does not remove this allocation issue. This example establishes a possibility, not a claim that group pricing always reduces welfare.
Try Three Price-Discrimination Questions
Choose one answer, then check your reasoning. These are short learning checks, not an exam score. If the controls are unavailable, the explanations remain readable below each question.
Answer B. For A, 30 − 2Q_A = 6 gives Q_A = 12 and its demand gives P_A = $18. For B, 18 − Q_B = 6 gives Q_B = 12 and P_B = $12. These choices assume the stated common cost, interior solution and effective separation.
Answer C. Consumer surplus falls from $144 to $108, while profit rises from $192 to $216. Adding them gives a $12 reduction. The same total output can be allocated differently across buyers; the result is specific to this model.
Answer A. Cheap resale creates competition for the seller’s high-price offer and weakens effective separation. Transaction costs and actual transfer restrictions matter; a group label alone does not prevent arbitrage or establish the optimal markup.
Connect Pricing, Surplus and Regulation
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