Difficulty: Intermediate | Prerequisites: Consumer surplus, demand curves, marginal cost, basic profit maximisation.
When a seller controls access to two complementary goods (here, movie tickets and popcorn), the pricing of one good affects how much surplus the seller can extract from the other. This is the domain of two-part tariffs and tied-goods pricing. The problem asks you to think like a monopolist who can set both a fixed fee (the ticket price) and a per-unit price (popcorn), and who must consider that customers know both prices before deciding whether to show up at all. You should already be comfortable computing consumer surplus as the area under a demand curve and above the price line.
Harry maximises profit by pricing popcorn at marginal cost ($1/quart) and setting the ticket price equal to $5 (the reservation price) plus the entire consumer surplus from popcorn at that price ($4.50). This extracts every dollar of value from each identical customer. Any other combination leaves money on the table or drives customers away.
Two-part tariff
A pricing scheme with a fixed fee (paid for access) and a per-unit charge (paid for usage). Think of it as "pay to enter, then pay per item." Gym memberships with per-class fees, amusement-park entry plus ride tickets, and Costco memberships are all examples.
Reservation price
The maximum amount a consumer would pay for a good rather than go without it entirely. In simple terms, it is the ceiling above which the customer walks away.
Consumer surplus
The difference between what a consumer is willing to pay and what they actually pay, summed over all units purchased. Graphically, it is the triangle (or area) between the demand curve and the price line.
Marginal cost (MC)
The cost of producing one additional unit. Here, MC of a movie seat is $0 (zero) and MC of popcorn is $1/quart.
Tied goods (complementary goods in pricing)
Goods that are sold together or whose consumption is linked, so that the price of one affects the demand for the other. In simple terms, the ticket and the popcorn are a package in the customer's mind.
Surplus extraction
The seller's ability to capture consumer surplus as profit, typically through price discrimination or multi-part pricing. Think of it as converting the customer's willingness to pay into the seller's revenue.
Harry owns a movie theatre. All customers are identical.
Each customer's reservation price for the movie is $5.
Each customer's demand for popcorn is Pc = 4 – Qc, where Pc is the price in dollars and Qc is quantity in quarts.
Marginal cost of a movie seat: $0.
Marginal cost of popcorn: $1/quart.
Harry advertises his prices in advance, so customers know both the ticket price and the popcorn price before deciding whether to attend.
A customer attends if and only if their total surplus from the visit is non-negative.
Total surplus = (reservation price for movie – ticket price) + (consumer surplus from popcorn at the posted price).
If this sum is negative, the customer stays home. Harry gets nothing.
Scheme 1: Monopoly-price popcorn, low ticket price
If Harry sets popcorn at the monopoly price, he maximises popcorn profit per customer but leaves less surplus for the customer to give up via the ticket.
Monopoly pricing for popcorn: MR = MC. Demand is Pc = 4 – Qc, so MR = 4 – 2Qc. Set MR = 1: Qc = 1.5 quarts, Pc = $2.50.
Popcorn profit per customer: (2.50 – 1) × 1.5 = $2.25.
Consumer surplus from popcorn: 0.5 × (4 – 2.50) × 1.5 = $1.125.
Customer's total willingness to attend: $5 (movie) + $1.125 (popcorn CS) = $6.125.
Maximum ticket price: $6.125 – cost already paid for popcorn above MC… Actually, let us think about this differently.
The customer pays the ticket price up front and then buys popcorn at $2.50/quart. Their net surplus from the visit is: ($5 – ticket) + $1.125.
Harry can charge up to ticket = $5 + $1.125 = $6.125 and the customer still attends (just barely).
Total profit per customer: ticket + popcorn profit = $6.125 + $2.25 = $8.375.
Scheme 2: Marginal-cost popcorn, high ticket price
Set Pc = MC = $1. Then Qc = 4 – 1 = 3 quarts.
Popcorn profit per customer: (1 – 1) × 3 = $0.
Consumer surplus from popcorn: 0.5 × (4 – 1) × 3 = $4.50.
Customer's total willingness: $5 + $4.50 = $9.50.
Maximum ticket price: $9.50.
Total profit per customer: $9.50 + $0 = $9.50.
Scheme 3: Free popcorn (Pc = 0)
Qc = 4 – 0 = 4 quarts. Cost to Harry: $4.
Consumer surplus from popcorn: 0.5 × 4 × 4 = $8. But the customer pays nothing, so their surplus is $8.
Customer's total willingness: $5 + $8 = $13.
Maximum ticket price: $13.
Total profit: $13 – $4 (popcorn cost) = $9.
Worse than Scheme 2 because Harry is subsidising popcorn below cost.
Set popcorn price equal to marginal cost ($1) and set the ticket price equal to $9.50.
Profit per customer: $9.50. This is the maximum achievable.
The logic: by pricing popcorn at MC, Harry maximises the total surplus generated by the popcorn transaction. He then captures all of that surplus (plus the movie reservation price) through the ticket price. Any popcorn price above MC creates a deadweight loss that shrinks the total pie Harry can extract.
This is the classic two-part tariff result: set the per-unit price at marginal cost to maximise total surplus, then use the fixed fee (ticket) to extract that surplus.
All customers are identical, so one price scheme fits everyone.
Customers have full information about both prices before deciding to attend.
The ticket price functions as the "entry fee" in the two-part tariff, and popcorn is the "usage" component.
At Pc = $1 (MC), the efficient quantity of popcorn is consumed (3 quarts), and the consumer surplus is as large as it can be ($4.50), giving Harry the largest possible base from which to extract profit via the ticket.
Popcorn demand curve: Pc = 4 – Qc
Marginal revenue (popcorn): MR = 4 – 2Qc
Optimal popcorn price (two-part tariff): Pc = MC = $1
Optimal popcorn quantity: Qc = 4 – 1 = 3 quarts
Consumer surplus from popcorn at Pc = $1: CS = 0.5 × (4 – 1) × 3 = $4.50
Optimal ticket price: Ticket = Reservation price + CS from popcorn = $5 + $4.50 = $9.50
Profit per customer: π = $9.50 + ($1 – $1) × 3 = $9.50
Graphical sketch: Draw the popcorn demand curve (downward-sloping line from Pc = 4 at Qc = 0 to Pc = 0 at Qc = 4). Draw a horizontal line at Pc = $1 (marginal cost). The consumer surplus is the triangle above Pc = $1 and below the demand curve, with base 3 and height 3, area = $4.50. This triangle plus the $5 movie reservation price gives the total value Harry captures through the ticket.
This is the pricing logic behind amusement parks (high entry fee, rides priced near cost), inkjet printers (cheap printer, expensive cartridges), and razor-and-blade models. Costco charges a membership fee (fixed) and sells goods near wholesale cost (per-unit near MC). The movie-theatre version is slightly unusual because in practice theatres do the opposite: cheap tickets, expensive popcorn. That works when customers underestimate their popcorn spending or when customers differ in their popcorn demand, but the uniform-customer, full-information setup in this problem reverses the logic.
Students often assume Harry should charge the monopoly price for popcorn. He should not, because a higher popcorn price creates deadweight loss that shrinks the total surplus he can extract via the ticket.
A common mistake is forgetting that the customer's attendance decision depends on both prices. If the ticket is too high, the customer stays home regardless of how cheap the popcorn is.
Students sometimes forget to add the reservation price for the movie ($5) to the consumer surplus from popcorn when calculating the maximum ticket price.
Some students treat the two goods as independent pricing problems. They are not. The whole point is that the ticket price and the popcorn price interact through the customer's participation constraint.
⚠️ The hint in the assignment tells you to list out different pricing schemes and compare. Do this explicitly: at least two or three schemes with the arithmetic shown, then state why the MC-pricing scheme dominates.
⚠️ The graphical answer must show the demand curve, the MC line, the consumer surplus triangle, and a clear label indicating that the ticket captures this surplus plus the reservation price.
⚠️ Be ready to explain in words the intuition: pricing popcorn above MC shrinks the total pie (creates deadweight loss), and since Harry captures the whole pie through the ticket, any deadweight loss comes directly out of his profit.
True or false: The profit-maximising popcorn price in this problem is the monopoly price. (False; it is marginal cost.)
Fill in the blank: Consumer surplus from popcorn when Pc = $1 is ______ . ($4.50.)
True or false: If customers did not know the popcorn price in advance, Harry's optimal strategy might change. (True; the full-information assumption is crucial to the two-part tariff logic.)
Fill in the blank: Harry's profit per customer under the optimal scheme is ______ . ($9.50.)
True or false: Giving away popcorn for free would generate higher profit than pricing it at $1. (False; free popcorn costs Harry $4 per customer in production costs, reducing profit to $9.)
Q: At what price should Harry sell movie tickets and popcorn to maximise profit, given that all customers are identical, reservation price is $5, popcorn demand is Pc = 4 – Qc, MC of a seat is $0, and MC of popcorn is $1?
A: Set Pc = $1 (marginal cost). At that price, each customer buys 3 quarts and enjoys $4.50 in consumer surplus. Set the ticket price at $5 + $4.50 = $9.50 to extract the full surplus. Profit per customer is $9.50.
Q: Why not charge the monopoly price for popcorn ($2.50) and adjust the ticket price accordingly?
A: At Pc = $2.50, popcorn profit is $2.25 per customer and popcorn consumer surplus is $1.125. The maximum ticket becomes $5 + $1.125 = $6.125. Total profit: $6.125 + $2.25 = $8.375, which is less than $9.50. The monopoly popcorn price creates a deadweight loss of $1.125, and since Harry could have captured that surplus through the ticket, he is worse off.
Q: What if customers were heterogeneous (different reservation prices for the movie)?
A: The clean two-part tariff result breaks down. Harry would face a trade-off between setting a high ticket (extracting more from high-value customers but losing low-value ones) and setting a low ticket with higher popcorn margins. This is closer to the real-world cinema model: moderately priced tickets and high popcorn markups, because the ticket price cannot be tailored to each customer's willingness to pay.
This material connects to monopoly pricing and deadweight loss (the reason monopoly popcorn pricing is suboptimal here), consumer surplus measurement, and price discrimination (the two-part tariff is a form of first-degree price discrimination when all consumers are identical). It also links to the theory of bundling and to industrial organisation topics on tied sales.
Two-part tariff, two-part pricing, tied goods, complementary goods pricing, reservation price, consumer surplus extraction, marginal cost pricing, monopoly pricing, deadweight loss, profit maximisation, movie theatre popcorn problem, entry fee plus usage fee, amusement park pricing, Costco model, first-degree price discrimination, NYU microeconomics