Consumer Surplus

Some buyers would have paid more than the market price. Adding up those savings across every buyer gives the area between the demand curve and the price line.

How it works

Area between curves

In one sentence

Consumer surplus is the area between the demand curve and the price up to the quantity sold: $CS = \int_0^{q^*}\left(D(q) - p^*\right)dq$ .

General formula

{\htmlData{sym=0}{CS}} = \int_0^{{\htmlData{sym=3}{q^*}}}\big({\htmlData{sym=1}{D(q)}} - {\htmlData{sym=2}{p^*}}\big)\,{\htmlData{sym=4}{dq}}

Each buyer would have paid up to $D(q)$ ; paying only $p^*$ saves $D(q) - p^*$ , and adding up the savings is an integral.

What the symbols mean

$CS$
Consumer surplus
Total savings: what buyers were willing to pay minus what they paid.
$D(q)$
Demand curve
The most a buyer will pay for the q-th unit.
$p^*$
Market price
The price everyone actually pays.
$q^*$
Quantity sold
How many units sell at that price.
$dq$
Slice of units
One thin sliver of units. The integral adds up the savings on each.

The demand curve $D(q)$ gives the most anyone would pay for the $q$ -th unit.
At price $p^*$ , buyers purchase $q^*$ units, where $D(q^*) = p^*$ .
The region between $D$ and $p^*$ , from $0$ to $q^*$ , is the total savings.

Learn the math

Area Between CurvesCalc I · Lesson 49, Applications of Integrals