Practice
Market equilibrium and surplus
Equilibrium price and quantity from linear supply and demand, consumer and producer surplus, and the shortage or surplus at another price.
The skill
Equilibrium is the price at which quantity demanded equals quantity supplied. With equations, set them equal, solve for P, and substitute back into either one for Q. At any other price compare the two quantities: below equilibrium there is a shortage, above it a surplus. Consumer surplus is the triangle below demand and above the price, and producer surplus is the triangle above supply and below the price. A common slip is finding the triangle's height from the wrong curve's intercept.
A worked example
In a competitive market for concert tickets, demand is Qd = 54 − 2P and supply is Qs = −30 + 5P, where P is the price in dollars and Q is the number of tickets per week.
What is the equilibrium quantity, in tickets?
Solution
- Set Qd = Qs: 54 − 2P = −30 + 5P, so 7P = 84 and P = 12.
- Q = 54 − 2 × 12 = 30 tickets.
- At this price buyers want to buy exactly the quantity sellers want to sell, so there is no shortage or surplus.
Answer: 30