Consumer surplus is the extra benefit that buyers receive when they pay a price that is lower than the maximum price they were willing to pay.
Mathematically, it is the area between the demand curve and the price line up to the quantity bought.
In LaTeX: \$CS = \int{0}^{Q^*} (Pd(q) - P^*)\,dq\$.
Consumer surplus measures the welfare that consumers gain from market transactions.
A higher CS means consumers feel they are getting more value for their money, which encourages spending and supports a healthy economy.
In exams, you’ll often be asked to explain how CS reflects consumer welfare and how it changes when prices or demand shift.
Imagine a fruit stand where the price of an apple is set at £1.
If you’re willing to pay up to £3 for an apple, the difference (£3 – £1 = £2) is your consumer surplus.
The more apples you buy at £1, the more surplus you accumulate, until you reach the point where the price equals your maximum willingness to pay.
This simple picture helps you visualise the “area under the demand curve” concept.
Suppose the demand equation is \$Q = 10 - 2P\$ and the market price is £2.
First find the quantity demanded:
\$Q^* = 10 - 2(2) = 6\$
The demand curve can be rearranged to \$P_d(Q) = 5 - 0.5Q\$.
Consumer surplus is the area of the triangle below the demand curve and above the price line:
\$CS = \frac{1}{2} \times (Q^*) \times (P_{\text{max}} - P^*) = \frac{1}{2} \times 6 \times (5 - 2) = 9\$
So, the consumer surplus is £9.
Tip 1: Always sketch the demand curve and the price line before calculating CS. The area you need is the triangle or trapezoid between them.
Tip 2: Remember that CS is a positive value; if the price rises above the willingness to pay, CS becomes zero.
Tip 3: In multiple-choice questions, look for the correct formula: \$CS = \int (Demand - Price) dq\$.
| Concept | Definition |
|---|---|
| Consumer Surplus | Area between the demand curve and the price line up to the quantity bought. |
| Producer Surplus | Area between the price line and the supply curve up to the quantity sold. |