Supply & Demand: How a Market Finds Its Own Price

Two curves, one price

The demand curve slopes downward: as price rises, the quantity buyers are willing to purchase falls. The supply curve slopes upward: as price rises, the quantity sellers are willing to offer increases. Where the two curves cross is the market equilibrium — the price P* and quantity Q* at which the amount buyers want to buy exactly equals the amount sellers want to sell, with nothing left over and nothing unmet.

The linear model

With linear demand and supply functions, the equilibrium is just the solution of two simultaneous equations:

Q_d = a - b*P        (demand: falls as P rises)
Q_s = c + d*P        (supply: rises as P rises)

set Q_d = Q_s:   a - b*P* = c + d*P*
                 P* = (a - c) / (b + d)
                 Q* = a - b*P*

Consumer and producer surplus

Consumer surplus is the value buyers get above what they actually paid: the area between the demand curve and the horizontal line at P*, from zero up to Q*. Producer surplus is the mirror image — the area between the price line and the supply curve. For linear curves both are simple triangles, so total surplus, the standard economic measure of how much value a competitive market creates, is easy to compute directly from the diagram:

consumer surplus = 0.5 * Q* * (demand price at Q=0  -  P*)
producer surplus = 0.5 * Q* * (P*  -  supply price at Q=0)

Shifting the curves

A change in price moves you along a fixed curve. A change in anything else — income, the price of a substitute good, consumer tastes for demand; input costs, technology, the number of sellers for supply — shifts the entire curve to a new position, which moves the equilibrium point along the other curve. A rise in demand (the curve shifts right) raises both P* and Q*; a rise in supply (the curve shifts right) lowers P* but still raises Q*, since more is now offered at every price.

Price floors, price ceilings and deadweight loss

A price ceiling set below P* makes it illegal to charge the equilibrium price, so quantity demanded exceeds quantity supplied at the capped price — a shortage, which then has to be rationed by queues, waiting lists or luck instead of price. A price floor set above P* has the mirror effect: quantity supplied exceeds quantity demanded — a surplus of unsold goods or, in a labour market, unemployment. In both cases some trades that would have made both a buyer and a seller better off never happen, and the surplus that disappears entirely (captured by neither side) is the deadweight loss triangle, the standard measure of how costly it is to stop a market from clearing at its own equilibrium.

Frequently asked questions

Try it live

Everything above runs in your browser — open Supply & Demand and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.