Practice
Equilibrium and disequilibrium
Equilibrium price and quantity from linear supply and demand, and the shortage or surplus at another price.
The skill
Equilibrium is the price where quantity demanded equals quantity supplied. Set the demand and supply equations equal, solve for P, then substitute it into either equation for Q. At a price above equilibrium sellers offer more than buyers want, a surplus that pushes the price down; below it there is a shortage that pushes the price up. Students often get the direction backward, so check which quantity is larger before naming it a shortage or a surplus.
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 price, in dollars?
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: 12