Market Equilibrium

Definition

Given a linear demand function P = f(Q) (downward sloping) and a linear supply function P = g(Q) (upward sloping), the equilibrium price and quantity are the coordinates of the point where the two lines intersect — the unique price at which the quantity producers wish to supply exactly equals the quantity consumers wish to buy. Away from that point, the market is out of balance: if the market price sits above equilibrium, supply exceeds demand and unsold stock pushes price back down; if it sits below, demand exceeds supply and the resulting shortage pushes price back up.

In the Book

Section 1.5 builds the demand function from the "black box" idea of a function generally (f(x) = 2x + 3), then specialises to Q = f(P) and its inverse P = g(Q), and works a full example with P_D = −2Q + 50 and P_S = ½Q + 25, sketching both curves to find their intersection at (10, 30) — equilibrium quantity 10, equilibrium price 30. The book then extends the same worked example to a government-imposed fixed tax of $5 per good, shifting the supply curve upward and finding the new equilibrium at quantity 8, price 34 — demonstrating that a policy intervention is analysed as a shift in one of the two curves, and the market simply re-settles at the new intersection point. Section 1.5 also generalises the analysis to a two-commodity (multicommodity) market, where equilibrium requires solving a system of simultaneous linear equations rather than reading a single graphical intersection, since each good's demand can depend on the other good's price.

Why It Matters

Market equilibrium is the economic instance of a much more general idea: wherever two opposing forces are each modeled as functions of the same variable, the system settles at their point of balance, and displacement from that point triggers forces that restore it — the same structure as a thermostat, a predator-prey population balance, or a negotiated price in any two-sided market. Framing a system this way — as two curves and their crossing point, rather than a single function to be solved — is what makes it possible to predict how an external shock (a tax, a supply shortage, a shift in preferences) moves the whole system to a new resting point rather than just changing one side of it.