Source: ECN 312, Lecture 16 (Arizona State University)
Difficulty: Intermediate | Prerequisites: Basic monopoly theory (profit maximisation under monopoly, MR = MC rule, demand curves, consumer and producer surplus). You should be comfortable with simple calculus (derivatives, integrals) and the concept of price elasticity of demand.
This lecture extends basic monopoly theory into the strategies a monopolist uses to increase profit beyond the simple "set MR = MC" result. If you already know that a monopolist restricts output and charges above marginal cost, the next question is: can they do even better by charging different prices to different buyers, or for different quantities? That is the central thread here. The material connects directly to welfare analysis (deadweight loss, consumer surplus, producer surplus) and to real market structures you encounter constantly, from airline tickets to software bundles. You will also need this for the monopolistic competition material that closes the lecture.
A monopolist can boost profits by charging different prices for different units, to different customers, or in different markets. First-degree discrimination captures all consumer surplus; second-degree uses quantity discounts to let buyers self-select; third-degree segments the market by group and charges each according to its price elasticity. The more elastic group always gets the lower price.
Price discrimination
A seller charges different prices for different units of output. In simple terms, this means the firm does not offer one flat price to everyone for every unit.
First-degree price discrimination (perfect price discrimination)
The seller sells each unit of a good for exactly the consumer's maximum willingness to pay. Think of it as the ideal extraction scenario: every last pound of consumer surplus goes to the producer.
Second-degree price discrimination (non-linear pricing)
The price per unit depends on how much you buy. In simple terms, this means quantity discounts or tiered pricing, where the firm lets buyers self-select into different price brackets.
Third-degree price discrimination (market segmentation pricing)
The seller charges different prices to different identifiable groups of buyers. Think of it as student discounts, senior discounts, or regional pricing: the firm can tell which group you belong to and prices accordingly.
Price elasticity of demand (|ε|)
Measures how sensitive quantity demanded is to a change in price. A higher absolute value means the group is more price-sensitive and will receive the lower price under third-degree discrimination.
Deadweight loss (DWL)
The loss of total surplus that occurs when the market outcome is not efficient. In simple terms, this is the value of trades that would benefit both buyer and seller but do not happen because the monopolist restricts output.
Consumer surplus
The difference between what consumers are willing to pay and what they actually pay. Under perfect price discrimination, this falls to zero because the monopolist captures it all.
Producer surplus
The difference between the price received and the cost of production. Under perfect price discrimination, this equals the entire social surplus (no deadweight loss remains).
The monopolist sells each unit at exactly the buyer's willingness to pay.
Output expands until the price on the last unit equals marginal cost, the same quantity as the competitive equilibrium.
All consumer surplus is transferred to the producer. Deadweight loss is eliminated.
Worked example
Demand: D(p) = 100 – p. Cost: c(y) = ½y².
Because the monopolist charges each buyer's willingness to pay, it produces until price equals marginal cost:
MC = y, and the demand curve gives p = 100 – y, so set y = 100 – y, giving y = 50 units.
Producer surplus is total willingness to pay minus total cost:
∫₀⁵⁰ (100 – y) dy – ∫₀⁵⁰ y dy = 100(50) – ½(50²) – ½(50²) = $2,500.
If there are fixed costs, subtract them from this figure to get profit.
The price per unit depends on the quantity purchased. Buyers self-select into different pricing tiers.
The budget constraint becomes discontinuous: at a certain quantity, the per-unit price drops, creating a kink.
Two types of consumer respond differently:
Low-willingness-to-pay consumers ignore the quantity discount and buy at the standard price.
High-willingness-to-pay consumers adjust their consumption bundle to take advantage of the lower per-unit rate.
Welfare consequences
The outcome sits between the standard monopoly result and the perfectly competitive one. The monopolist is trying to let buyers who would otherwise fall in the deadweight-loss region self-select into purchasing at a different quantity and price.
Real-world examples
Apple's iPhone storage tiers: jumping from 16 GB to 64 GB cost the consumer an extra $100, while Apple's actual cost increase was marginal. Buyers who value the phone more tend to need more storage, so the pricing extracts their higher willingness to pay.
Pizza sizing: a 12" pizza at $8.30 costs $0.07 per square inch; a 24" pizza at $23.00 costs $0.05 per square inch. The per-unit price falls as you buy more, which is the signature of non-linear pricing.
The monopolist identifies distinct groups of buyers and charges each group a different price.
The firm is effectively selling in two (or more) separate markets with separate demand curves.
Profit-maximisation condition
The monopolist's profit across two markets is: π = p₁(y₁)·y₁ + p₂(y₂)·y₂ – c(y₁ + y₂).
Optimality requires MR₁(y₁) = MC(y₁ + y₂) and MR₂(y₂) = MC(y₁ + y₂). In other words, equate marginal revenue across both markets and set each equal to marginal cost.
Which group gets the higher price?
Recall MR(y) = p(y)[1 – 1/|ε|]. Setting the two marginal revenues equal gives p₁[1 – 1/|ε₁|] = p₂[1 – 1/|ε₂|]. If p₁ > p₂, then |ε₂| > |ε₁|: the market with the lower price must have the more elastic demand. The more price-sensitive group receives the discount.
Worked example
Two demand curves: D₁(p₁) = 100 – p₁ and D₂(p₂) = 100 – 2p₂. Cost: c(y₁ + y₂) = 20(y₁ + y₂).
Inverting the demand curves and writing profit:
π = (100 – y₁)y₁ + (50 – ½y₂)y₂ – 20(y₁ + y₂)
First-order conditions:
∂π/∂y₁ = 100 – 2y₁ – 20 = 0, so y₁ = 40, p₁ = 60.
∂π/∂y₂ = 50 – y₂ – 20 = 0, so y₂ = 30, p₂ = 35.
Elasticities at these prices: |ε₁| = 1.5 and |ε₂| = 2.33. Group 2 has the higher elasticity and the lower price, exactly as the theory predicts.
What if the monopolist cannot segment?
Market demand is y = (100 – p) + (100 – 2p) = 200 – 3p. Inverting: p = 200/3 – y/3.
π = (200/3 – y/3)y – 20y. First-order condition: 200/3 – 2y/3 = 20, so y = 70, p ≈ 43.33.
Compared with discrimination, the elastic group (Group 2) now pays more (43.33 vs 35), and the inelastic group (Group 1) pays less (43.33 vs 60). The price-sensitive group loses when the monopolist cannot price-discriminate.
Marginal revenue with elasticity: MR(y) = p(y)[1 – 1/|ε|]
First-degree output rule: Produce until p = MC (same as competitive output).
First-degree surplus: Producer surplus = ∫₀ʸ* [p(y) – MC(y)] dy (the entire area between demand and MC).
Third-degree optimality (two markets): MR₁(y₁) = MR₂(y₂) = MC(y₁ + y₂).
Elasticity–price link (third-degree): If p₁ > p₂, then |ε₂| > |ε₁|. The lower-price market is always the more elastic one.
Apple Watch variants at launch ranged from $349 to $17,000 with roughly the same production cost, approximating first-degree discrimination through minor product differentiation.
iPhone storage tiers (16 GB, 64 GB, 128 GB) use second-degree discrimination: the cost difference to Apple is negligible, but consumers who value the phone more self-select into higher tiers.
Student and senior discounts at cinemas are textbook third-degree discrimination: students and seniors have more elastic demand for entertainment, so they get the lower price.
Pizza sizing is non-linear pricing in everyday life: the per-square-inch cost falls as the pizza gets larger.
Students often think first-degree price discrimination reduces output below the competitive level. It does not. Output under perfect discrimination equals the competitive quantity; the difference is that the monopolist captures all the surplus.
Students sometimes confuse second-degree and third-degree discrimination. The distinction: second-degree lets the buyer choose (self-selection through quantity tiers), while third-degree requires the seller to identify and separate groups before setting prices.
A common error is believing that price discrimination always harms consumers. Under third-degree discrimination, the more elastic group may pay less than it would under a single monopoly price.
Students often forget that price discrimination requires two conditions: monopoly power and the ability to prevent resale (enforcement). Without both, the strategy collapses.
⚠️ Be able to compute output and price under first-degree discrimination given a demand function and cost function. The key step: set p = MC, not MR = MC.
⚠️ For third-degree discrimination, you will likely be asked to solve for optimal prices in two markets and show which group gets the lower price. Know how to invert demand, write the profit function, and take first-order conditions.
⚠️ The elasticity–price relationship is a favourite exam question: explain why |ε₂| > |ε₁| when p₂ < p₁. Derive it from the MR formula.
⚠️ Expect a comparison question: what happens to each group's price when the monopolist can vs cannot discriminate? The elastic group benefits from discrimination; the inelastic group pays more.
⚠️ Know the two requirements for price discrimination to work: monopoly power and enforcement (preventing resale).
True or false: Under first-degree price discrimination, the monopolist produces the same quantity as a perfectly competitive market. (True)
Fill in the blank: Second-degree price discrimination is also known as _______ pricing. (Non-linear)
True or false: Under third-degree price discrimination, the group with the more inelastic demand receives the lower price. (False, the more elastic group gets the lower price)
True or false: Price discrimination eliminates deadweight loss only under first-degree discrimination. (True)
Fill in the blank: The two requirements for price discrimination are monopoly power and _______. (Enforcement / prevention of resale)
Q: A monopolist faces demand D(p) = 200 – 2p and has cost c(y) = ¼y². If the monopolist can perfectly price-discriminate, what is the profit-maximising output?
A: Set p = MC. The demand curve gives p = 100 – y/2, and MC = y/2. So 100 – y/2 = y/2, giving y = 100 units.
Q: Why does the market with more elastic demand receive the lower price under third-degree price discrimination?
A: Because MR must be equal across markets. MR = p[1 – 1/|ε|]. If a market has high elasticity, the bracketed term [1 – 1/|ε|] is closer to 1, so a lower p is needed to produce the same MR as a market with low elasticity and a larger discount from p to MR.
Q: A monopolist sells to two groups. Group A has demand D_A = 80 – p_A and Group B has demand D_B = 80 – 4p_B. Marginal cost is constant at 10. Find the optimal price for each group.
A: For Group A: π_A = (80 – y_A)y_A – 10y_A. FOC: 80 – 2y_A – 10 = 0, so y_A = 35, p_A = 45. For Group B: Inverse demand is p_B = 20 – y_B/4. π_B = (20 – y_B/4)y_B – 10y_B. FOC: 20 – y_B/2 – 10 = 0, so y_B = 20, p_B = 15. Group B (more elastic) gets the lower price.
Q: Explain why perfect price discrimination eliminates deadweight loss.
A: Under perfect price discrimination, every consumer who values the good above marginal cost buys it, because each is charged exactly their willingness to pay. Output equals the competitive quantity. No mutually beneficial trades go unmade, so there is no deadweight loss. The difference from competition is distributional: all surplus goes to the producer rather than being shared.
This material builds directly on the basic monopoly model (Lecture 15 / earlier chapters): you need the MR = MC framework and the concept of deadweight loss before any of this makes sense. Price discrimination also connects to welfare economics and efficiency, because first-degree discrimination is one of the few cases where a monopoly produces the efficient output. The elasticity logic here reappears in international trade (dumping) and in public economics (Ramsey pricing for regulated utilities).
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