Price Discrimination and Perfect Price Discrimination

Two people float down the same lazy river at the same water park. One paid $25 to get in. The other paid $50. Nobody got scammed; the park planned it. Why charge one person half price for the same thing? This is Module 4.3, Price Discrimination. Stay for the one version of this trick that makes a market efficient.

So far, every monopoly charged everyone one price: a single-price monopolist. Price discrimination means charging different buyers different prices for the same good. It takes market power: a perfectly competitive price taker sells nothing above the market price. So it happens under monopoly, oligopoly and monopolistic competition only.

Why two prices? Tourists who flew in for the week will pay a lot. Locals have options: the beach, the pool, another day.

Quick refresher from Unit 2: price elasticity of demand is the percent change in quantity demanded divided by the percent change in price. Ignore the minus sign: above 1 is elastic; below 1, inelastic.

If a 10% price rise cuts local visits by 30%, that's 30 ÷ 10 = 3: elastic. If it cuts tourist visits by 5%, that's 0.5: inelastic.

The rule: the less elastic group pays the higher price. Tourists pay $50; locals get $25 to keep them coming. Each visitor costs the park $20. So every $25 local ticket still adds $5 of profit, while tourists keep paying $50. The park needs market power and a way to stop resale, or locals would resell cheap tickets to tourists. So the $25 ticket needs an ID with a local address.

So what just happened? One: tourists, less elastic, pay $50. Two: locals, more elastic, pay $25, still above the $20 cost. Three: an ID check stops resale.

Now push it all the way. Perfect price discrimination charges every buyer their willingness to pay: the most they would pay. Six visitors walk up. Their top prices: $80, $70, $60, $40, $30 and $10. The park's only cost is $20 per visitor, its marginal cost. With one price for everyone, $60 earns the most: three visitors pay. Revenue: 3 × $60 = $180. Cost: 3 × $20 = $60. Profit: $180 − $60 = $120. Cutting to $40 adds a fourth visitor's $40, but the first three each pay $20 less: revenue falls from $180 to $160.

Quick refresher from Module 4.2: a single-price monopolist cuts the price on every unit to sell one more, so marginal revenue is below price. Here it's $160 − $180 = −$20, below the $20 marginal cost. So the park stops at three.

Quick refresher from Unit 2: consumer surplus is willingness to pay minus price. At $60, that's $20 + $10 + $0 = $30.

Quick refresher from Module 4.2: deadweight loss is surplus from trades worth making that never happen. The $40 and $30 visitors are shut out: ($40 − $20) + ($30 − $20) = $30.

Now the gate reads minds and charges each visitor their top price. The $40 ticket lowers no one else's price, so the park sells to everyone whose top price beats $20: five visitors, not the $10 one. Revenue: $80 + $70 + $60 + $40 + $30 = $280. Cost: 5 × $20 = $100. Profit: $280 − $100 = $180, up from $120. With no fixed cost, that's also producer surplus. Consumer surplus is now $0: everyone paid their maximum. Deadweight loss is $0: every visit worth its cost happens. That's the efficient version.

The extra $60 of profit is the old consumer surplus plus the old deadweight loss.

So what just happened? One: one price of $60 earned $120, leaving $30 of consumer surplus and $30 of deadweight loss. Two: a separate price for each visitor let five in. Three: profit hit $180; consumer surplus and deadweight loss hit $0.

Now the AP graph, starting with a single-price monopoly.

Quick refresher: find QM where MR crosses MC, go straight up to the demand curve, then across: that's the price, PM.

Consumer surplus is the triangle below demand and above PM, out to QM. Deadweight loss is the triangle from QM out to where MC crosses demand, between D and MC. With perfect price discrimination, prices step down demand like a staircase, one buyer at a time. It sells until a buyer's top price falls to marginal cost, where demand crosses MC. Label it Q2: the quantity a competitive market would produce.

Quick refresher: allocative efficiency means price equals marginal cost, so every unit buyers value at least as much as its cost gets made. In our table, the $30 visitor got in and the $10 visitor didn't, since a visit costs $20.

The lowest price, P2, is right there: from where D crosses MC, go straight across to the price axis. Exam trap: P2 is not where MR = MC, not where ATC meets demand, and not where MC meets ATC. On a recent AP exam, about four in ten students got this right. Both triangles, consumer surplus and deadweight loss, become the firm's surplus, all the way out to Q2. Exam trap two: more people buy, so students say consumer surplus rises. It falls to zero, and you must say why: each consumer is charged the maximum price they're willing to pay.

So what just happened on the graph? One: one price stops at QM. Two: the discriminator goes on to Q2 and P2, where D crosses MC. Three: consumer surplus and deadweight loss go to zero.

Exam moment: two questions the way the AP exam asks them, then one free-response part.

A single-price monopolist switches to perfect price discrimination. What happens to its output, consumer surplus and deadweight loss, in that order? A) Falls, falls to zero, grows B) Unchanged, falls to zero, unchanged C) Rises, rises, disappears D) Rises, falls to zero, disappears E) Rises, falls to zero, grows

The answer is D. Output rises to where demand crosses MC. Each buyer pays their maximum, so consumer surplus is zero. With no worthwhile trade left out, deadweight loss disappears. C is the classic slip: consumer surplus can't rise when everyone pays their maximum. B keeps output where MR = MC. A: output and deadweight loss reversed. E counts captured surplus as lost.

The only seller of a design app sells licenses to students and to businesses. A 10% price rise would cut business purchases by 4% and student purchases by 15%. If it price discriminates, who pays more? A) Businesses: more elastic demand B) Businesses: less elastic demand C) Students: more elastic demand D) Students: less elastic demand E) Neither: same license, same price

The answer is B. Elasticity is percent change in quantity over percent change in price. Businesses: 4 ÷ 10 = 0.4, inelastic. Students: 15 ÷ 10 = 1.5, elastic. Less elastic pays more. C reverses the rule. D flips the division, 10 ÷ 15 and 10 ÷ 4. A: right group, wrong reason. E forgets one good can carry two prices.

Free response. Harbor Line, the only ferry to an island, earns positive economic profit. Suppose it now engages in perfect price discrimination. What would happen to consumer surplus? Explain.

To earn the point: the assertion, consumer surplus decreases to zero, and the reason, Harbor Line charges each consumer the maximum price that consumer is willing to pay. The costly mistake: saying it increases, or giving no reason. On a recent AP exam, fewer than one student in three earned this point.

So what just happened on the free response? One: we stated that consumer surplus falls to zero. Two: we gave the reason: each rider is charged the most they are willing to pay. Three: no reason, no point.

Recap: different buyers, different prices, and the less elastic group pays more. A perfect price discriminator produces where demand crosses marginal cost, leaving zero consumer surplus and zero deadweight loss. Next: Module 4.4, Monopolistic Competition.