Calculating consumer and producer surplus
Consumer surplus is what buyers save compared with their willingness to pay; producer surplus is what sellers get above their minimum price. With linear curves both are triangles.
Formulas and rules
- CS = ½ × (choke price − p*) × q*
- PS = ½ × (p* − lowest supply price) × q*
- Choke price: demand = 0; lowest supply price: supply = 0
- Total welfare = CS + PS, largest at equilibrium
Your turn
Three problems on this topic. Type numbers like 12.5 or 1,250 and elasticities with their sign.
Task
In a market: demand Q_d = 120 − 4p, supply Q_s = 2p (p in €). Work out consumer surplus, producer surplus and total welfare at equilibrium.
Consumer surplus in €
Producer surplus in €
Total welfare in €
Numbers like 12.5 or 1,250; elasticities with their sign (−0.75); percentages as a number (12.5). Round to 2 decimal places.
Worked example
In a market: demand Q_d = 136 − 4p, supply Q_s = 3p − 18 (p in €). Work out consumer surplus, producer surplus and total welfare at equilibrium.
Worked solution
- 1.Equilibrium: 154 = 7p → p* = 22, q* = 48
- 2.Choke price (demand = 0): p = 136 / 4 = 34; lowest supply price (supply = 0): p = 18 / 3 = 6
- 3.CS = ½ × (34 − 22) × 48 = €288.00
- 4.PS = ½ × (22 − 6) × 48 = €384.00
- 5.Welfare = CS + PS = €672.00
Typical mistake: Forgetting the ½ for the triangle, or measuring to the wrong axis. Consumer surplus is the triangle between demand, the price p* and the price axis.
Common questions
Why is welfare largest at equilibrium?
Every extra unit traded up to q* is worth more to buyers than it costs sellers; beyond q* the opposite holds. Interventions such as taxes or price ceilings therefore shrink the total.