The equilibrium price

The market finds its resting point when the quantity demanded equals the quantity supplied: mathematically, it is the solution of the system formed by the two curves.

Definition — Market equilibrium

The equilibrium price $p^\ast$ and the equilibrium quantity $Q^\ast$ are found by imposing $Q_d = Q_s$: $a - b\,p = -c + d\,p \implies p^\ast = \frac{a+c}{b+d}, \qquad Q^\ast = a - b\,p^\ast.$ Geometrically it is the intersection of the two lines in the $(p,Q)$ plane.

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Topics: Linear systems
Concepts: Supply and demand · Equilibrium price
Skills: Model · Solve systems