Supply and Demand Equilibrium
Calculate equilibrium price and quantity from linear supply and demand functions.
Covers consumer surplus, producer surplus, and price floors and ceilings.
The Formula
At equilibrium: Q_d = Q_s (set demand equal to supply and solve)
Market equilibrium occurs where the quantity demanded equals the quantity supplied. At this point, there is no shortage or surplus — the market clears naturally.
Variables
| Symbol | Meaning |
|---|---|
| Q_d | Quantity demanded (typically: Q_d = a - bP) |
| Q_s | Quantity supplied (typically: Q_s = c + dP) |
| P | Price per unit |
| a, b, c, d | Constants specific to the market |
Example 1
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) = 68
Equilibrium: Price = $16, Quantity = 68 units
Example 2
Demand: Q_d = 50 - P. Supply: Q_s = -10 + 2P. Find equilibrium.
50 - P = -10 + 2P
60 = 3P → P = 20
Q = 50 - 20 = 30
Equilibrium: Price = $20, Quantity = 30 units
When to Use It
Use the equilibrium formula when:
- Finding the natural market price for a product
- Analyzing the effect of taxes or subsidies on markets
- Predicting how supply or demand shifts affect prices
- Understanding market clearing in competitive markets
Key Notes
- Equilibrium price clears the market: At the equilibrium price, quantity supplied equals quantity demanded — there is no surplus and no shortage. The market "clears."
- Surplus drives price down: If price is above equilibrium, supply exceeds demand (surplus). Sellers lower prices to clear inventory, pushing the price back toward equilibrium.
- Shortage drives price up: If price is below equilibrium, demand exceeds supply (shortage). Buyers bid up the price, pushing it back toward equilibrium.
- Shifts vs movements along the curve: A change in price causes movement along a curve. Changes in income, preferences, input costs, or technology shift the entire curve, changing the equilibrium point.
- Real markets are imperfect: The model assumes perfect competition, rational actors, and immediate price adjustment. Real markets have friction, information asymmetry, and monopoly power that cause persistent deviations from equilibrium.