Supply and Demand Equilibrium
Supply and demand equilibrium formulas.
Find equilibrium price and quantity where supply meets demand.
The Formulas
Demand: Q_d = a − bP
Supply: Q_s = c + dP
Equilibrium: Q_d = Q_s → a − bP = c + dP
Equilibrium Price: P* = (a − c) / (b + d)
Equilibrium Quantity: Q* = a − bP*
Supply: Q_s = c + dP
Equilibrium: Q_d = Q_s → a − bP = c + dP
Equilibrium Price: P* = (a − c) / (b + d)
Equilibrium Quantity: Q* = a − bP*
Variables
| Symbol | Meaning |
|---|---|
| Q_d | Quantity demanded |
| Q_s | Quantity supplied |
| P | Price per unit |
| a | Demand intercept (maximum quantity at price 0) |
| b | Demand slope (how much quantity drops per unit price increase) |
| c | Supply intercept (base supply at price 0) |
| d | Supply slope (how much quantity rises per unit price increase) |
| P* | Equilibrium price |
| Q* | Equilibrium quantity |
Example 1 — Finding Equilibrium
Demand: Q_d = 100 − 2P. Supply: Q_s = 20 + 3P. Find equilibrium.
Set Q_d = Q_s: 100 − 2P = 20 + 3P
80 = 5P
P* = 16
Q* = 100 − 2(16) = 100 − 32
Equilibrium: Price = $16, Quantity = 68 units
Example 2 — Effect of a Supply Shift
Original supply: Q_s = 20 + 3P. A new technology shifts supply to Q_s = 40 + 3P. Demand stays Q_d = 100 − 2P.
100 − 2P = 40 + 3P → 60 = 5P
New P* = 12
New Q* = 100 − 2(12) = 76
Price drops from $16 to $12, quantity increases from 68 to 76 units.
When to Use It
- Finding the market-clearing price where there is no shortage or surplus
- Analyzing how shifts in supply or demand affect prices
- Understanding the impact of taxes, subsidies, or regulations on markets
- Predicting price changes when costs or consumer preferences shift