Market equilibrium calculator with workings
Enter demand Q_d = a − b·p and supply Q_s = c + d·p. You get the equilibrium price and quantity, consumer and producer surplus, the choke price and the price elasticities at equilibrium.
Result
- Equilibrium price p*
- 30
- Equilibrium quantity Q*
- 60
- Consumer surplus
- 900
- Producer surplus
- 600
- Choke price (demand = 0)
- 60
- Price elasticity of demand at p*
- −1
- Price elasticity of supply at p*
- 1.5
At equilibrium demand is unit elastic (|ε| = 1).
Workings
- 1Set equal: 120 − 2p = −30 + 3p
- 2120 − (−30) = (2 + 3) · p → p* = 150 / 5 = 30
- 3Into demand: Q* = 120 − 2 × 30 = 60 (check with supply: −30 + 3 × 30 = 60)
- 4Choke price: Q_d = 0 → p = 120 / 2 = 60; consumer surplus = ½ × (60 − 30) × 60 = 900
- 5Lowest supply price: Q_s = 0 → p = 30 / 3 = 10; producer surplus = ½ × (30 − 10) × 60 = 600
- 6Demand elasticity: ε = dQ/dp × p/Q = −2 × 30 / 60 = −1; supply: 3 × 30 / 60 = 1.5
How it works
Q_d = Q_s → a − b·p = c + d·p → p* = (a − c) / (b + d)
- Equilibrium quantity: put p* into demand (or supply).
- Consumer surplus: ½ × (choke price − p*) × Q*.
- Point price elasticity of demand: ε = dQ/dp × p/Q = −b × p*/Q*.
If demand is given as inverse demand p = α − β·Q, rearrange first: Q = α/β − (1/β)·p, so a = α/β and b = 1/β.
Frequently asked questions
Why is the elasticity negative?+
Because demand falls when the price rises. Often only the absolute value is used: above 1 is elastic, below 1 inelastic.