Market equilibrium

The price at which demand and supply balance out is the equilibrium point: it is found by solving a $2\times 2$ linear system.

Definition — Market equilibrium

The equilibrium point is the pair $(p^*;\,q^*)$ at which demand and supply meet: $D(p^*) = S(p^*) = q^*.$ It is the solution of a $2\times 2$ linear system. At that price the market “clears”: all the product supplied is sold, and no customer is left unsatisfied.

Example — Computing the equilibrium

For the previous anti-anxiety drug, with supply curve $S(p) = 500\,p - 2\,500$ (producers start selling when $p\ge 5$ € and offer $500$ more boxes for each euro of price rise), the equilibrium solves $10\,000\Bigl(1-\frac{p}{28}\Bigr) = 500\,p - 2\,500.$ Multiplying by $28$: $280\,000 - 10\,000\,p = 14\,000\,p - 70\,000$, whence $24\,000\,p = 350\,000$, $p^* = 350\,000/24\,000 \approx 14{,}58$ €. Equilibrium quantity $q^* = D(14{,}58) \approx 4\,793$ boxes/month.

The demand $D(p)$ (decreasing) and the supply $S(p)$ (increasing, valid for $p\ge 5$ €) meet at the equilibrium point $E^*\approx(14{,}58;\,4\,793)$.

At prices $p<p^*$ demand exceeds supply (shortage of product, upward pressure); at $p>p^*$ supply exceeds demand (stockpiles, downward pressure). $p^*$ is the price that “matches” willingness to pay with the cost of production.

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Topics: Functions and properties
Concepts: Demand curve · Supply curve · Market equilibrium
Functions: Line
Methods: Market equilibrium
Skills: Modelling · Solving systems