Formula

Equilibrium Price and Quantity Formulas for a Linear Market Model

In the general linear market model with demand QD=abPQ^D = a - bP and supply QS=c+dPQ^S = c + dP, the market equilibrium occurs where quantity demanded equals quantity supplied (QD=QSQ^D = Q^S). Equating the two functions yields abP=c+dPa - bP = c + dP. Solving for price gives the equilibrium price: P=acb+dP^* = \frac{a - c}{b + d}. Substituting PP^* back into either the demand or supply function yields the equilibrium quantity: Q=ad+bcb+dQ^* = \frac{ad + bc}{b + d}. Because a>ca > c and all parameters are positive, both PP^* and QQ^* are strictly positive.

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Updated 2026-06-29

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