Consumer and Producer Surplus Calculator

The formulas

Worked example

Demand: $P=100-Q$. Supply: $P=20+Q$.

FAQ

What is consumer surplus?

Consumer surplus is the difference between what consumers are willing to pay for a good and what they actually pay at the market price, summed across all units purchased. On a standard demand-supply diagram it is the triangular area between the demand curve and the horizontal line at the equilibrium price, bounded on the right by the equilibrium quantity.

What is producer surplus?

Producer surplus is the difference between the market price and the minimum price producers would have accepted, summed across all units sold. It is the triangular area between the horizontal line at the equilibrium price and the supply curve, bounded on the right by the equilibrium quantity.

What is the formula for consumer surplus with linear demand?

If demand is $P=a-bQ$ and the equilibrium price is $P^{\ast }$, then $CS=\frac{1}{2}\times Q^{\ast }\times (a-P^{\ast })$. The height of the triangle is the vertical distance from the equilibrium price up to the choke price ($a$), and the base is the equilibrium quantity $Q^{\ast }$.

What is the formula for producer surplus with linear supply?

If supply is $P=c+dQ$ and the equilibrium price is $P^{\ast }$, then $PS=\frac{1}{2}\times Q^{\ast }\times (P^{\ast }-c)$. The height is the vertical distance from the supply intercept $c$ up to the equilibrium price, and the base is the equilibrium quantity $Q^{\ast }$.

How do I find the equilibrium price and quantity?

Set quantity demanded equal to quantity supplied. With linear curves $P=a-bQ$ and $P=c+dQ$, equate the two to get $Q^{\ast }=\frac{a-c}{b+d}$, then substitute back to get $P^{\ast }=a-b\cdot Q^{\ast }$ (equivalently $P^{\ast }=c+d\cdot Q^{\ast }$). Total surplus is just $CS+PS$.

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