Sell the same ride three ways: per ride, a flat pass, and a two-part tariff.
Per-ride pricing charges like a monopolist and cuts use. A flat pass makes extra rides free, so guests overuse them. A two-part tariff splits the bill into an entry fee and a per-ride price. Price rides at cost and collect the leftover gain at the gate, and the waste vanishes. The payment formula is below.
For example, running one ride costs the park 500 won. At 3,000 won a ride, 🧑 kids ride only twice. A 5,000-won entry fee plus 500 won a ride makes five rides feel fine. The park pockets its gain in the entry fee.
Rides at an amusement park face demand q=14−P and cost 2 per ride. With a two-part tariff that sets the per-ride price equal to cost, p=2, and charges only an entry fee, how many rides does a guest take, and what is the most the park can charge at the gate?
With the per-ride price equal to cost, the guest rides until one more ride is worth exactly 2: q=14−2=12 rides.
Over those 12 rides the guest holds surplus of the triangle 2(14−2)×12​=72. Set the entry fee to exactly 72 and the guest still (just barely) walks in, while the park's profit is 72 — with zero waste.
By comparison, per-ride pricing alone gives the monopoly price p=8, only 6 rides, profit 36, and deadweight loss 18. The two-part tariff bakes the whole cake — and takes it all.
The same guest (q=14−P, cost 2 per plate) goes to a buffet.
A flat 98 makes every extra plate free.
How many plates do they eat, and how much is wasted for society as a whole?
Flat rate 98 — usage sails past the efficient 12 all the way to 14.Show proof
With a marginal price of 0, the guest eats until a plate is worth nothing: q=14−0=14 plates.
But plates beyond 12 are worth less than their cost of 2.
The waste is the small triangle over that stretch, 22×2​=2.
Total welfare is 98−2×14=70 — exactly 2 short of the efficient 72.
Charging just 2 per plate would have stopped the guest at 12 and erased the waste. The buffet's convenience is bought with those last plates.