⚖️ Finding Equilibrium
Equilibrium condition: At equilibrium, quantity demanded equals quantity supplied: $$Q_d = Q_s$$ $$a - bP = c + dP$$ Solve for the equilibrium price: $$P^ = \frac{a - c}{b + d}$$ Then substitute back to find $Q^$.
Worked example: Demand: $Q_d = 100 - 5P$ \n Supply: $Q_s = -20 + 4P$ \n Set equal: $100 - 5P = -20 + 4P$ \n $120 = 9P$ \n $P^ = \frac{120}{9} ≈ $13.33$ \n $Q^ = 100 - 5(13.33) ≈ 33.3$ units
Always check your answer by substituting P into BOTH equations — you should get the same Q.
🔄 Comparative Statics
Comparative statics = comparing the old equilibrium to the new equilibrium after a change in one of the parameters.
- Increase in demand (a rises): $P^$ increases, $Q^$ increases.
- Decrease in demand (a falls): $P^$ decreases, $Q^$ decreases.
- Increase in supply (c rises): $P^$ decreases, $Q^$ increases.
- Decrease in supply (c falls): $P^$ increases, $Q^$ decreases.
Calculating the change: If demand rises from $Q_d = 100 - 5P$ to $Q_d = 120 - 5P$ (a increases by 20), new equilibrium: \n $120 - 5P = -20 + 4P$ → $140 = 9P$ → $P^ = $15.56$ \n $Q^ = 120 - 5(15.56) = 42.2$ \n Price rose from $13.33 to $15.56; quantity rose from 33.3 to 42.2.
From the formula $P^ = \frac{a-c}{b+d}$: increasing a or decreasing c raises P. Increasing b or d (flatter curves = more elastic) reduces the impact on P*.