Supply and Demand Equilibrium
Reference for supply and demand equilibrium formulas.
Solve for price and quantity from linear functions with worked examples and elasticity calculations.
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
Key Notes
- Equilibrium: where supply meets demand: The market-clearing price P* and quantity Q* occur where the supply curve (upward-sloping) intersects the demand curve (downward-sloping). At any other price, either a surplus (price too high) or shortage (price too low) drives the market back toward equilibrium.
- Shifts vs movements along curves: A price change causes a movement along a curve. A change in any other variable (income, input costs, technology, preferences, prices of related goods) shifts the entire curve. Confusing these two is the most common error in supply-demand analysis.
- Demand shifters: Income (normal vs inferior goods), prices of substitutes and complements, consumer preferences, expected future prices, and number of buyers. Supply shifters: input costs, technology, number of sellers, government taxes/subsidies, and expected future prices.
- Elasticity determines the outcome of shifts: When supply increases, whether price or quantity changes more depends on demand elasticity. Inelastic demand → mostly lower price; elastic demand → mostly higher quantity. The more inelastic side bears more of a tax burden.
- Applications: Supply and demand analysis is used in price prediction, agricultural policy (price floors and ceilings), tax incidence analysis, minimum wage effects, rent control analysis, and understanding any market where prices and quantities are determined by voluntary exchange.