How to Calculate a Two-Part Tariff
A two-part tariff charges an access fee plus a per-unit price. With identical buyers the firm sets the per-unit price at marginal cost and the fee at each buyer's consumer surplus.
The Two-Part Tariff formula
Calculator
Enter a buyer's demand line, marginal cost and the number of buyers to get the access fee and per-unit price.
The price at which this buyer stops buying altogether.
Where the same demand line meets the quantity axis. It fixes the slope.
Constant cost of supplying one more unit.
How many customers face this same demand curve.
The surplus triangle under demand and above the price line is worth $128, so that is the most the fixed fee can charge before the buyer walks away.
- Per-unit price to charge
- $4
- Units each buyer takes
- 16
- Total charge per buyer
- $192
- Profit from all buyers
- $6,400
Setting the per-unit price at $4, the marginal cost, keeps the buyer at the efficient quantity so the surplus to collect is as big as it gets.
At a price equal to marginal cost the demand line puts each buyer at 16 units.
Each buyer pays $192 in total, the access fee plus the per-unit charges on the units taken.
Per-unit revenue only covers marginal cost, so the whole $6,400 above cost comes from the access fees.
How to calculate Two-Part Tariff, step by step
- 1Set the per-unit price at marginal cost. Pricing each unit at MC leaves the buyer taking the efficient quantity, which makes the surplus available to capture as large as it can be.
- 2Find the quantity each buyer takes at that price. Read it off the demand curve at P = MC. For a straight-line demand, quantity = (choke price − MC) ÷ slope, where the slope is the choke price divided by the quantity demanded at a price of zero.
- 3Measure the consumer surplus that is left. Consumer surplus is the triangle under demand and above the price line: ½ × (choke price − MC) × quantity bought.
- 4Charge that surplus as the access fee. Set A equal to the surplus, which leaves the buyer indifferent between paying and walking away while the firm keeps the whole gain from trade.
- 5Add the two parts for the total bill. Total charge = A + (MC × quantity). Profit per buyer equals A, because the per-unit revenue only covers the marginal cost of the units sold.
Worked example: Two-Part Tariff
Each buyer's demand runs from a choke price of $20 down to 20 units at a price of zero, so demand is P = 20 − Q, and marginal cost is a constant $4. Setting the per-unit price at $4 means each buyer takes 20 − 4 = 16 units. The consumer surplus left over is ½ × (20 − 4) × 16 = $128, so the access fee is $128. The total charge per buyer = 128 + (4 × 16) = $192, and with 50 identical buyers the firm collects 50 × 128 = $6,400 above its marginal cost.
Two-Part Tariff questions
Why is the per-unit price set at marginal cost?
Any price above MC would shrink the quantity bought and shrink the surplus triangle with it. Charging MC keeps output at the efficient level, which leaves the largest possible surplus for the access fee to collect.
What changes when buyers are not identical?
One fee can no longer equal everyone's surplus. A fee large enough to capture the heavy user's surplus drives the light user out of the market, so the firm usually settles for a smaller fee and a per-unit price above marginal cost.
Is a two-part tariff allocatively efficient?
With identical buyers, yes on quantity: output matches the competitive level where P = MC, so there is no deadweight loss. The distribution changes instead, since the whole surplus ends up with the firm rather than with buyers.
Where do two-part tariffs show up in practice?
Amusement parks charging admission plus a price per ride, warehouse clubs charging membership plus shelf prices, and phone plans charging a line fee plus usage are the standard examples.
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