Difficulty: Intermediate | Prerequisites: Chapter 11 (Monopoly and uniform pricing), basic calculus
A firm with market power can earn more profit by charging different prices to different customers (or for different quantities) instead of setting one uniform price. To pull this off, the firm needs market power, the ability to identify who will pay more, and a way to prevent resale. Perfect (first-degree) price discrimination is the theoretical extreme: the firm charges every buyer their maximum willingness to pay, captures all consumer surplus, eliminates deadweight loss, and produces the same output as a competitive market.
Uniform pricing
Charging the same price for every unit sold of a particular good. In simple terms, one price for everyone, no matter who they are or how much they buy.
Nonuniform pricing
Charging consumers different prices for the same product, or charging a single customer a price that depends on how many units they buy. Think of it as any pricing strategy where not every unit sells at the same rate.
Price discrimination
Charging consumers different prices for the same good based on individual characteristics, group membership, or quantity purchased. This is the most common form of nonuniform pricing.
Reservation price (willingness to pay)
The maximum amount a person is willing to pay for a unit of output. In simple terms, the ceiling price in a buyer's head, the absolute most they would hand over.
Deadweight loss (DWL)
The forgone value of potential sales in excess of the cost of producing the good. It represents the inefficiency when output falls below the competitive level because price exceeds marginal cost.
Perfect price discrimination (first-degree price discrimination)
The firm sells each unit at the maximum amount each customer is willing to pay. Prices differ across customers and across units for the same customer. Think of it as the theoretical ideal where the seller extracts every last penny of consumer surplus.
Consumer surplus (CS)
The difference between what a good is worth to a consumer and what the consumer actually pays. Under perfect price discrimination, consumer surplus is zero.
Producer surplus (PS)
The revenue a firm earns above its variable costs. Under perfect price discrimination, the firm captures all surplus: PS = the entire area between the demand curve and the marginal cost curve.
Two-part pricing
Charging a customer one fee (an access fee) for the right to buy the good, plus an additional per-unit fee for each unit purchased. Think of it as a membership fee plus a usage charge.
Bundling
Selling several products together as a package for a fixed price that is less than the sum of the individual prices. In simple terms, a combo deal.
Vertically integrating
Participating in more than one successive stage of the production and distribution chain for a good or service. Firms sometimes do this to prevent resale and preserve price discrimination.
A single-price monopoly faces a trade-off: charge high and lose low-valuation buyers, or charge low and leave money on the table from high-valuation buyers. Nonuniform pricing sidesteps this.
A firm earns higher profit from nonuniform pricing for two reasons:
It captures some or all of the consumer surplus that would exist under a single price.
It converts some of the single-price deadweight loss into profit by selling to consumers who would not buy at the uniform price.
All three must hold for a firm to price discriminate profitably:
Market power. The firm must be able to charge above the competitive price. Monopolies, oligopolies, monopolistically competitive firms, and cartels can potentially price discriminate. A perfectly competitive firm cannot.
Ability to identify consumers. The firm must know (or be able to infer) which consumers have higher reservation prices. This can be done through observable characteristics (age, location) or by designing mechanisms that let consumers self-select (coupons, advance-purchase discounts).
Ability to prevent or limit resale. If low-price buyers can easily resell to high-price buyers, the price discrimination scheme collapses. Resale is naturally difficult for services (you cannot resell a haircut) and when transaction costs are high. Firms also prevent resale through ID checks, contracts, vertical integration, and region-locked warranties.
The biggest practical obstacle is usually preventing resale.
Perfect (first-degree) price discrimination. The firm charges each buyer their reservation price for each unit. Prices differ across buyers and across units. The demand curve becomes the marginal revenue curve.
Group (third-degree) price discrimination. The firm charges different prices to different identifiable groups (students vs. adults, domestic vs. international) but charges a uniform price within each group. This is the most common type.
Nonlinear (second-degree) price discrimination. The price varies with the quantity purchased, but everyone who buys the same quantity pays the same price. Examples: bulk discounts, block pricing by utilities.
Under perfect price discrimination, the firm sells each unit at exactly the buyer's reservation price. This means:
The marginal revenue on the nth unit equals the price of that unit (the demand curve height at that quantity).
The firm's marginal revenue curve is identical to its demand curve.
The firm produces where the demand curve intersects the marginal cost curve, which is the same quantity as in perfect competition.
Graphical intuition (Figure 12.1 in the textbook): with a demand curve where the first buyer pays $6, the second $5, the third $4, and MC = $3, the firm sells 4 units. Revenue = $6 + $5 + $4 + $3 = $18. Cost = $3 x 4 = $12. Profit = $6.
This is a central comparison for the course. Using the areas A, B, C, D, E from Figure 12.2:
Competition | Single-Price Monopoly | Perfect Price Discrimination | |
|---|---|---|---|
Consumer Surplus | A + B + C | A | 0 |
Producer Surplus | D + E | B + D | A + B + C + D + E |
Total Welfare | A + B + C + D + E | A + B + D | A + B + C + D + E |
Deadweight Loss | 0 | C + E | 0 |
Key takeaways from this table:
Perfect price discrimination and competition produce the same total welfare and the same output level. Both are efficient.
The difference is distribution: under competition, consumers keep A + B + C. Under perfect price discrimination, the firm captures everything.
A single-price monopoly is the worst outcome for total welfare because of deadweight loss C + E.
Consumers are worst off under perfect price discrimination (CS = 0), but society is no worse off than under competition.
If the price difference reflects a cost difference, it is not price discrimination. An e-book costing less than a hardcover partly reflects lower marginal cost. A bridal suite costing more than a regular room may reflect higher costs (mementos stolen, extra cleaning). True price discrimination requires the same good sold at different prices where the cost of serving each customer is the same.
Revenue equals the area under the demand curve up to the quantity sold:
R = \int_0^Q D(z) \, dzwhere D(z) is the inverse demand function and z is a placeholder for quantity.
\max_Q \pi = \int_0^Q D(z) \, dz - C(Q)Differentiate using Leibniz's rule:
\frac{d\pi}{dQ} = D(Q) - \frac{dC(Q)}{dQ} = 0This says: produce until the reservation price on the last unit equals marginal cost. In other words, D(Q) = MC.
\frac{d^2\pi}{dQ^2} = \frac{dD(Q)}{dQ} - \frac{d^2C(Q)}{dQ^2} < 0Holds automatically when the demand curve slopes down and marginal cost is constant or rising.
Given: D(Q) = a - bQ, with a = 100, b = 1, MC = 10.
Profit function:
\pi = \int_0^Q (a - bz) \, dz - C(Q) = aQ - \frac{b}{2}Q^2 - C(Q)First-order condition: a - bQ - MC = 0, so 100 - Q - 10 = 0, giving Q = 90.
The monopoly produces 90 units, the same as the competitive quantity (where the demand curve meets MC).
\pi = \int_0^Q D(z) \, dz - C(Q)With D(Q) = 100 - Q, MC = 10, Q = 90:
Profit = area of the triangle between the demand curve and MC = (1/2)(100 - 10)(90) = $4,050.
Disneyland pricing. Disneyland offered Southern California locals 25% off multi-day tickets. Out-of-town visitors have higher willingness to pay because travel is already a large sunk cost, so the ticket price is a small fraction of total trip cost. Locals, who visit repeatedly, are more price-sensitive. Resale is prevented by checking driver's licences and requiring same-day use.
Botox. Allergan holds a patent monopoly on Botox. The estimated linear demand curve and constant MC of $25/vial yield a single-price monopoly profit of $375 million/year. If Allergan could perfectly price discriminate, profit would double to $750 million/year (equal to the competitive consumer surplus). The $187.5 million deadweight loss under single pricing would vanish.
Google ad auctions. Google allows advertisers to bid on contextual search terms, effectively charging each advertiser close to their willingness to pay. Smaller, harder-to-reach audiences attract higher bids per click. This is near-perfect price discrimination: the price varies by advertiser and by search term.
Designer bag purchase limits. Luxury retailers like Bergdorf Goodman cap purchases (one Prada bag per customer) to prevent bulk-buying and international resale. The same handbag sells for 20-40% more in Europe and Asia, and these purchase limits maintain international price discrimination.
Private university tuition. Colleges request detailed financial information from applicants and award scholarships accordingly. Epple et al. (2017) estimated tuition rises by $210-$510 for every $10,000 increase in family income. This approaches perfect price discrimination.
Auto dealerships. Salespeople bargain individually, trying to charge each customer the maximum they will pay. Even imperfect individual price discrimination increases profits significantly.
"Price discrimination is always illegal." It is generally legal in the United States unless it harms competition between firms (Robinson-Patman Act of 1936). Discrimination based on gender, nationality, race, or religion is prohibited.
"Price discrimination always harms consumers." Perfect price discrimination eliminates consumer surplus, but it also eliminates deadweight loss. Some consumers who could not buy at the single monopoly price can now buy. Society as a whole is no worse off than under competition.
"Any price difference is price discrimination." If costs differ between customers (e.g. e-book vs. hardcover), the price difference may simply reflect cost differences, not discrimination.
"A firm that could price discriminate always will." Solved Problem 12.3 shows that when two markets share the same demand-curve intercept and differ only in slope, the profit-maximising price is the same in both markets. The firm could discriminate but chooses not to because the elasticities at the optimal price turn out to be equal.
⚠️ You must be able to reproduce the welfare-comparison table (competition vs. single-price monopoly vs. perfect price discrimination) using area labels. This shows up in multiple-choice, short-answer, and graphical questions.
⚠️ Know that perfect price discrimination produces the competitive quantity but zero consumer surplus. If an exam asks "is perfect price discrimination efficient?", the answer is yes, but note it redistributes all surplus to the firm.
⚠️ Be able to state and explain the three conditions for price discrimination. Expect a question asking which condition fails in a given scenario.
⚠️ The first-order condition D(Q) = MC for perfect price discrimination is a frequent exam calculation. Make sure you can derive it from the profit function and solve for Q.
⚠️ Do not confuse cost-based price differences with price discrimination. Exam questions often test whether you can tell them apart.
True or false: A perfectly competitive firm can profitably price discriminate. (False. It has no market power.)
Fill in the blank: Under perfect price discrimination, consumer surplus equals ____. (Zero.)
True or false: Perfect price discrimination produces less output than a competitive market. (False. It produces the same output.)
Fill in the blank: The biggest practical obstacle to price discrimination is usually the firm's inability to prevent ____. (Resale.)
True or false: If a firm charges different prices that reflect different costs of serving each customer, that counts as price discrimination. (False. True price discrimination requires the same good at different prices with no cost difference.)
Q: A monopoly has inverse demand D(Q) = 80 - 2Q and constant MC = 10. If it can perfectly price discriminate, what quantity does it sell?
A: Set D(Q) = MC: 80 - 2Q = 10, so Q = 35.
Q: In the question above, what is the firm's profit under perfect price discrimination (assuming no fixed costs)?
A: Profit = area of the triangle between the demand curve and MC = (1/2)(80 - 10)(35) = (1/2)(70)(35) = $1,225.
Q: Name the three conditions a firm must satisfy to profitably price discriminate.
A: (1) Market power, (2) ability to identify which consumers have higher willingness to pay, (3) ability to prevent or limit resale.
Q: Why does Disneyland charge local Southern Californians less than out-of-town visitors?
A: Out-of-town visitors have already incurred large travel costs, making the ticket price a small share of total trip cost. Their demand is less elastic. Locals visit repeatedly and are more sensitive to admission price. Disneyland prevents resale by checking driver's licences and requiring same-day entry.
Q: Under perfect price discrimination, is there any deadweight loss? Explain why or why not.
A: No. The firm sells every unit for which the buyer's reservation price exceeds marginal cost, producing the competitive quantity. No mutually beneficial trades are left unrealised.
Q: A single-price monopoly earns producer surplus of B + D (in the textbook's Figure 12.2 labelling). What is producer surplus under perfect price discrimination?
A: A + B + C + D + E. The perfectly price-discriminating monopoly captures the entire area between the demand curve and the marginal cost curve.
This material builds directly on Chapter 11's analysis of single-price monopoly. The welfare comparison (CS, PS, DWL areas) uses the same tools introduced there. Understanding why a monopoly restricts output below the competitive level is prerequisite to seeing how price discrimination partly or fully corrects that inefficiency.
The three conditions for price discrimination reappear in Chapter 12's later sections on group price discrimination and nonlinear pricing, so mastering them here saves time.
The concept of elasticity-based pricing (the more elastic group pays less) connects to the Lerner Index from Chapter 11: p(1 + 1/e) = MC.
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