⚖️ Finding Equilibrium
Equilibrium condition: At equilibrium, quantity demanded equals quantity supplied: $$Qd = Qs$$ $$a - bP = c + dP$$ Solve for the equilibrium price: $$P^ = \frac{a - c}{b + d}$$ Then substitute back to find $Q^$.
Worked example: Demand: \n Supply: \n Set equal: \n \n $P^ = \frac{120}{9} ≈ \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.
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🔄 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): increases, increases.
- Decrease in demand (a falls): decreases, decreases.
- Increase in supply (c rises): decreases, increases.
- Decrease in supply (c falls): increases, decreases.
Calculating the change: If demand rises from to (a increases by 20), new equilibrium: \n → → $P^ = \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 : increasing a or decreasing c raises P. Increasing b or d (flatter curves = more elastic) reduces the impact on P.