Consumer and producer surplus measure the extra benefit created when buyers and sellers trade at a market price. On a supply and demand graph, these values appear as areas near the equilibrium point. Calculus is useful because demand and supply curves are often nonlinear, so exact areas require definite integrals.
Surplus helps economists estimate how much value a market creates beyond the price actually paid or received.
Consumer surplus is the area between the demand curve and the equilibrium price from 0 to the equilibrium quantity. Producer surplus is the area between the equilibrium price and the supply curve over the same interval. The equilibrium quantity and price come from solving D(Q) = S(Q).
Once the equilibrium is known, definite integrals turn the shaded regions on the graph into numerical measures of economic benefit.
Key Facts
- Equilibrium occurs where D(Q*) = S(Q*) and the equilibrium price is P* = D(Q*) = S(Q*).
- Consumer surplus is CS = integral from 0 to Q* of [D(Q) - P*] dQ.
- Producer surplus is PS = integral from 0 to Q* of [P* - S(Q)] dQ.
- Total surplus is TS = CS + PS = integral from 0 to Q* of [D(Q) - S(Q)] dQ.
- Demand curves usually slope downward because buyers are willing to buy more at lower prices.
- Supply curves usually slope upward because sellers are willing to produce more at higher prices.
Vocabulary
- Consumer surplus
- Consumer surplus is the total difference between what buyers are willing to pay and what they actually pay.
- Producer surplus
- Producer surplus is the total difference between the market price sellers receive and the minimum price they would accept.
- Demand curve
- A demand curve gives the price buyers are willing to pay for each quantity of a good.
- Supply curve
- A supply curve gives the price sellers require to provide each quantity of a good.
- Equilibrium
- Equilibrium is the price and quantity where the demand curve and supply curve intersect.
Common Mistakes to Avoid
- Using the wrong equilibrium quantity, which is wrong because the integral limits for both surplus calculations must run from 0 to Q* where demand equals supply.
- Integrating price alone instead of the difference between curves, which is wrong because surplus is an area between a willingness curve and the market price or supply curve.
- Reversing the subtraction order, which is wrong because consumer surplus uses D(Q) - P* and producer surplus uses P* - S(Q) to keep the shaded areas positive.
- Forgetting units, which is wrong because the integral multiplies price by quantity, so surplus is measured in money such as dollars.
Practice Questions
- 1 Demand is D(Q) = 50 - 2Q and supply is S(Q) = 10 + 2Q. Find Q*, P*, consumer surplus, and producer surplus.
- 2 Demand is D(Q) = 100 - Q^2 and supply is S(Q) = 20 + 3Q. If the equilibrium quantity is Q* = 8 and the equilibrium price is P* = 36, compute the consumer surplus and producer surplus.
- 3 If a tax raises the price buyers pay and lowers the price sellers receive, explain how the consumer surplus and producer surplus areas on a supply and demand graph change.