Consumer and Producer Surplus Calculator: Equilibrium, Taxes, Price Controls and Deadweight Loss
Find consumer and producer surplus from linear demand and supply curves, a graph’s intercepts or one purchase. Covers market equilibrium, per-unit taxes, price ceilings and floors, and deadweight loss.
How it works
Demand P = a − bQ, supply P = c + dQ · equilibrium Q* = (a − c) ÷ (b + d), P* = a − bQ* · consumer surplus CS = ½ × Q* × (a − P*) · producer surplus PS = ½ × Q* × (P* − c) · with a per-unit tax t: Qt = (a − c − t) ÷ (b + d), tax revenue = t × Qt, deadweight loss = ½ × t × (Q* − Qt) · one purchase: CS = (willingness to pay − price) × units
Consumer surplus is the gap between what buyers would have been willing to pay and what they actually pay. Producer surplus is the gap between the price sellers receive and the lowest price they would have accepted. On a supply-and-demand graph they are the two triangles above and below the market price. Their sum, total surplus, measures the gains from trade. There are three ways to enter a problem. With demand and supply equations (P = a − bQ and P = c + dQ), the calculator solves for the equilibrium and the surplus areas. It can also add a per-unit tax, a price ceiling or a price floor and show the tax revenue, the shortage or excess supply, who bears the tax and the deadweight loss, compared side by side with the free market. With graph points, enter the two intercepts and the equilibrium price and quantity, as in most textbook diagrams. With one purchase, enter what the buyer would pay, the price and, if you like, the seller’s minimum. The curves are straight lines, and under a ceiling the scarce units go to the buyers who value them most, so real-world losses can be larger. The Price Elasticity calculator measures how quantity responds to price. This calculator measures welfare: the dollar value buyers and sellers gain, and what taxes and price controls cost.
Worked example
Demand is P = 100 − 2Q and supply is P = 10 + Q. Setting them equal gives 100 − 2Q = 10 + Q, so Q* = 90 ÷ 3 = 30 units and P* = 100 − 2 × 30 = $40. Consumer surplus = ½ × 30 × (100 − 40) = $900. Producer surplus = ½ × 30 × (40 − 10) = $450, so total surplus is $1,350. A $15 per-unit tax would cut the quantity to 25. Buyers would pay $50 and sellers keep $35. Consumer surplus falls to $625, producer surplus to $312.50, the government collects $375 and $37.50 is lost as deadweight loss.
Sources: Penn State EBF 200: Market equilibrium example (P = 100 − 2Q, P = 10 + Q) · Business Calculus with Excel (U. Lethbridge), 7.8 Consumer and producer surplus · Omni Calculator: Consumer surplus (willing price minus actual price)
Frequently asked questions
How do you calculate consumer surplus?
For one purchase, subtract the price from the most you were willing to pay: paying $80 for something worth $100 to you gives $20. For a market with a straight demand curve, it is the triangle ½ × quantity × (demand intercept − price).
How do you calculate producer surplus?
It is the price minus the lowest price sellers would accept, summed over all units sold. With a straight supply curve it is ½ × quantity × (price − supply intercept). For P = 10 + Q and an equilibrium of $40 at 30 units, that is ½ × 30 × 30 = $450.
What is deadweight loss?
The total surplus lost when trade falls below the efficient quantity, for example because of a tax, price ceiling or price floor. For a per-unit tax it is the triangle ½ × tax × (drop in quantity).
How does a price ceiling affect consumer surplus?
Buyers who still get the good pay less, but fewer units are sold, so some buyers lose out completely. Consumer surplus can rise or fall. Producer surplus always falls, and the units no longer traded become deadweight loss.
Who pays a tax, buyers or sellers?
It depends on the slopes, not on who sends the money to the government. The side whose curve is steeper (less elastic) bears more. With demand P = 100 − 2Q and supply P = 10 + Q, buyers bear two thirds of the tax.
What is total surplus?
Consumer surplus plus producer surplus plus any tax revenue. In a competitive market without interventions it is at its maximum at the equilibrium quantity.
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This calculator is for educational purposes. Double-check important results before acting on them.