Business Functions — Demand and Supply

Two further functions describe how the quantity of a good bought or sold reacts to its price, and together they let us calculate the market equilibrium.

Demand function, $Q_d = f(P)$, expresses the quantity of a good that buyers are willing to purchase as a function of its price $P$. A typical demand function used in this syllabus is linear and decreasing — as price rises, quantity demanded falls — for instance $Q_d = a - bP$, with $a,b>0$.

Supply function, $Q_s = g(P)$, expresses the quantity that sellers are willing to offer as a function of price $P$. A typical supply function is linear and increasing — as price rises, sellers offer more — for instance $Q_s = -c + dP$, with $c,d>0$.

Market equilibrium is the price $P_e$ and quantity $Q_e$ at which the quantity demanded exactly equals the quantity supplied, i.e. $Q_d = Q_s$ at $P=P_e$. Solving the demand and supply equations simultaneously — setting $f(P)=g(P)$ and solving for $P$, then substituting back into either function to get $Q_e$ — gives the equilibrium price and quantity together. Below $P_e$, quantity demanded exceeds quantity supplied (a shortage, pushing price up); above $P_e$, quantity supplied exceeds quantity demanded (a surplus, pushing price down) — which is exactly why $P_e$ is the price the market tends toward.

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