How to Calculate Equilibrium Price and Quantity
Equilibrium price is the price where Qd = Qs; set the demand and supply equations equal, solve for P, then substitute P back in to find Q.
The Market Equilibrium formula
Calculator
Enter demand as Qd = a − bP and supply as Qs = c + dP; this solves Qd = Qs for equilibrium price and quantity.
The a in Qd = a − bP: quantity demanded if the good were free.
Enter b as a positive number. Each $1 of price cuts quantity demanded by b units.
The c in Qs = c + dP. It is zero when supply runs straight through the origin.
Each $1 of price pulls d more units onto the market.
Setting 100 − 4P equal to 20 + 6P clears the market at $8.
- Equilibrium quantity (Q*)
- 68
- Quantity supplied at P* (check)
- 68
- Equilibrium check
- Valid equilibrium
At $8 buyers want 68 units, which is exactly what sellers bring to market.
Substituting P* into the supply equation should return the same quantity, which checks your algebra.
How to calculate Market Equilibrium, step by step
- 1Write both equations the same way. Express demand and supply with quantity on the left, such as Qd = a − bP and Qs = c + dP.
- 2Set quantity demanded equal to quantity supplied. At equilibrium the market clears, so the amount buyers want equals the amount sellers offer.
- 3Solve for the equilibrium price. Collect the P terms on one side and the constants on the other, then divide to isolate P.
- 4Substitute to find the equilibrium quantity. Plug the equilibrium price into either equation; both should give the same quantity, which doubles as a check on your algebra.
Worked example: Market Equilibrium
If Qd = 100 − 4P and Qs = 20 + 6P, set 100 − 4P = 20 + 6P, which gives 80 = 10P and P = $8. Substituting back: Qd = 100 − 4(8) = 68 and Qs = 20 + 6(8) = 68, so equilibrium quantity is 68 units.
Market Equilibrium questions
What happens if the price is above equilibrium?
A surplus appears, because quantity supplied exceeds quantity demanded at that price. Sellers cut the price until it falls back to equilibrium.
Do demand and supply have to be linear?
No, but exam problems almost always use linear equations, since setting Qd = Qs then gives one price you can solve by hand.
How do you find equilibrium from inverse equations?
If you are given P = a − bQ and P = c + dQ, set the two prices equal and solve for Q first, then substitute back to get P.
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