Supply & Demand Equilibrium Calculator
Solve for equilibrium price and equilibrium quantity, test for shortages and surpluses, analyze market shifts, and explore consumer surplus, producer surplus, price controls, taxes, subsidies, and deadweight loss.
Background
In a competitive market, equilibrium occurs where quantity demanded = quantity supplied. Policies like price floors, price ceilings, taxes, and subsidies can move the market away from the original equilibrium and change welfare.
How to use this calculator
- Choose the mode that matches your economics problem.
- Enter demand and supply values, then click Calculate.
- Use the graph, summary, and step-by-step to understand equilibrium, interventions, and welfare effects.
How this calculator works
- Equilibrium: solves where Qd = Qs.
- Consumer surplus: area below demand and above price up to the equilibrium quantity.
- Producer surplus: area above supply and below price up to the equilibrium quantity.
- Price controls: checks whether a floor or ceiling is binding.
- Tax / subsidy: computes the new traded quantity, buyer price, seller price, and deadweight loss.
Formulas & Equations Used
Demand: Qd = a - bP
Supply: Qs = c + dP
Equilibrium price: P* = (a - c)/(b + d)
Equilibrium quantity: Q* = a - bP*
Consumer surplus: triangle area above price and below demand
Producer surplus: triangle area below price and above supply
Deadweight loss: the lost gains from trade from moving away from the competitive quantity
Example Problem & Step-by-Step Solution
Example 1 — equilibrium with surplus measures
Suppose Qd = 100 - 5P and Qs = 20 + 3P.
- Set demand equal to supply: 100 - 5P = 20 + 3P.
- Solve: 80 = 8P, so P = 10.
- Find quantity: Q = 100 - 5(10) = 50.
- Inverse demand price intercept is 20, so consumer surplus is ½ × 50 × (20 - 10) = 250.
- Inverse supply price intercept is about -6.67, so producer surplus is ½ × 50 × (10 - (-6.67)) ≈ 416.67.
Example 2 — Binding price ceiling creates a shortage
Suppose Qd = 100 - 5P and Qs = 20 + 3P, and the government sets a price ceiling at P = 8.
- First find the competitive equilibrium: 100 - 5P = 20 + 3P → 80 = 8P → P* = 10.
- Because the ceiling price 8 is below the equilibrium price 10, the price ceiling is binding.
- Find quantity demanded at the ceiling: Qd = 100 - 5(8) = 60.
- Find quantity supplied at the ceiling: Qs = 20 + 3(8) = 44.
- Since Qd > Qs, there is a shortage.
- Shortage size: 60 - 44 = 16 units.
Example 3 — Per-unit tax reduces quantity and creates deadweight loss
Suppose Qd = 100 - 5P and Qs = 20 + 3P, and a per-unit tax of 4 is imposed.
- Start with the original equilibrium: 100 - 5P = 20 + 3P → 80 = 8P → P* = 10, Q* = 50.
- With a tax, the buyer price is 4 higher than the seller price: P_b = P_s + 4.
- Substitute into demand: Qd = 100 - 5(P_s + 4) = 80 - 5P_s.
- Set taxed demand equal to supply: 80 - 5P_s = 20 + 3P_s → 60 = 8P_s → P_s = 7.5.
- Find the buyer price: P_b = 7.5 + 4 = 11.5.
- Find the new traded quantity: Q = 20 + 3(7.5) = 42.5.
- Tax revenue: 4 × 42.5 = 170.
- Deadweight loss: \(\frac{1}{2}\) × 4 × (50 - 42.5) = 15.
Frequently Asked Questions
Q: What is consumer surplus?
Consumer surplus is the extra benefit buyers receive when they pay less than the maximum they were willing to pay.
Q: What is producer surplus?
Producer surplus is the extra benefit sellers receive when they get a price above the minimum they were willing to accept.
Q: When is a price ceiling binding?
A price ceiling is binding when it is set below the market equilibrium price.
Q: When is a price floor binding?
A price floor is binding when it is set above the market equilibrium price.
Q: What does a per-unit tax do?
A per-unit tax drives a wedge between the buyer price and seller price, reduces quantity traded, and creates deadweight loss.