Build surplus from a schedule before using a triangle

Discrete values make the idea visible.

Imagine three buyers value a museum pass at $30, $24, and $15, while three passes cost sellers $8, $18, and $22 to provide. Match the highest remaining benefit with the lowest remaining cost. The first trade creates $22 of surplus, and the second creates $6. A third trade would destroy $7 because its $15 benefit is below its $22 cost. The efficient quantity is therefore two passes, and maximum total surplus is $28.

Sort buyers from highest to lowest willingness to pay and sellers from lowest to highest cost. This produces discrete demand and supply schedules. Compare the first buyer with the first seller, then the second with the second. Continue while benefit covers cost. The ordering ensures scarce units reach their highest-valued uses and are supplied by the lowest-cost sellers.

Any price between $18 and $24 can support those two trades in this simplified schedule. A $20 price gives consumers $14 in total surplus and producers $14. A different price redistributes the $28 without changing the efficient quantity, provided the same two trades occur. This is the discrete version of the area between demand and supply up to equilibrium. It also shows why efficiency is determined by marginal benefit versus marginal cost, not by whether buyers or sellers receive the larger share.

At a $20 price, the first buyer gets $10 of surplus and the second gets $4. The first seller gets $12 and the second gets $2. These amounts total $28. A price of $23 would shift surplus toward sellers but still support two trades: consumer surplus would be $8 and producer surplus $20. Use per-unit differences before summing.

If the price is set above the second buyer’s $24 value, only one buyer may participate even though a second beneficial trade exists. If it is set below the second seller’s $18 cost, only one seller may participate. The missing second trade creates a $6 deadweight loss. A controlled price can therefore prevent the efficient quantity from being exchanged.

Do not total all willingness to pay

Four buyers value a permit at $50, $42, $31, and $18. Four seller costs are $12, $27, $35, and $47. The first two trades create $38 and $15. The third would lose $4, so efficient quantity is two and maximum surplus is $53. Adding all buyer values and subtracting all costs would include inefficient units that should not be produced.

The schedule method prepares you to read shaded graph regions. Each discrete unit is a thin vertical strip between demand and supply. A smooth triangle approximates the sum of many such strips. If the schedule logic is clear, triangle formulas become measurements of an idea rather than memorized geometry.

When a question supplies identical values or costs, more than one individual may fill a position without changing total surplus. The efficient quantity can still be unique even if the identities of traders are not. Distinguish allocation among equal-valued participants from the number of beneficial trades.

Separate a transfer from a loss

Money paid as tax becomes government revenue. A higher price paid by buyers may become seller revenue. Deadweight loss is the value of trades or benefits that no participant receives.