Equilibrium with linear demand and supply

Statement

Demand $D(p)=200-4p$, supply $S(p)=2p-10$. Find the equilibrium price and quantity.

Solution

At equilibrium $D(p)=S(p)$: $200-4p = 2p-10 \iff 210 = 6p \iff p^*=35.$ Equilibrium quantity: $q^* = S(35)=2\cdot 35-10 = 60$ (check against demand: $D(35)=200-140=60$ ✓).

Equilibrium: $\boxed{(p^*;\,q^*)=(35;\,60)}$.

Links

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