Calculating market equilibrium
At equilibrium, buyers want to buy exactly as much as sellers offer. Set supply equal to demand, solve for the price and put it back in to get the quantity.
Formulas and rules
- Demand Q_d = a − b·p, supply Q_s = c + d·p
- Equilibrium: Q_d = Q_s → p* = (a − c) / (b + d)
- Quantity: put p* into either function and check with the other
- Inverse demand p = α − β·Q: set the prices equal and solve for Q
- Choke price: the price at which demand falls to zero
Your turn
Three problems on this topic. Type numbers like 12.5 or 1,250 and elasticities with their sign.
Task
Demand is given as the inverse demand function p = 191 − Q and supply as p = 15 + 3Q (p in €). Find the equilibrium quantity and price and the choke price at which nobody buys.
Equilibrium quantity Q*
Equilibrium price p* in €
Choke price in €
Numbers like 12.5 or 1,250; elasticities with their sign (−0.75); percentages as a number (12.5). Round to 2 decimal places.
Worked example
In a market: demand Q_d = 260 − 6p, supply Q_s = 7 + 5p (p in €). Find the equilibrium price and quantity and the revenue at equilibrium.
Worked solution
- 1.Set equal: 260 − 6p = 7 + 5p
- 2.253 = 11p → p* = 253 / 11 = 23
- 3.Into demand: q* = 260 − 6 × 23 = 122 (check with supply: 7 + 5 × 23 = 122)
- 4.Revenue = p* × q* = €23.00 × 122 = €2,806.00
Typical mistake: Losing the sign of the slope when setting equal, or solving for the quantity instead of the price. Always check with the other function: both must give the same quantity.
Demand is given as the inverse demand function p = 279 − 2.5Q and supply as p = 4 + 3Q (p in €). Find the equilibrium quantity and price and the choke price at which nobody buys.
Worked solution
- 1.Set the prices equal: 279 − 2.5Q = 4 + 3Q → 275 = 5.5Q → Q* = 50
- 2.p* = 4 + 3 × 50 = 154
- 3.Choke price: Q = 0 in demand → p = 279
Typical mistake: Mixing up inverse demand and demand: here p is on the left, so you solve for Q, not p.
Common questions
Which function do I put the equilibrium price into?
Either one: at equilibrium supply and demand give the same quantity. Use both and you have your check.
What is the difference between demand and inverse demand?
Demand gives quantity as a function of price (Q = …), inverse demand gives price as a function of quantity (p = …). It is the same curve, solved for the other variable.