1. **Problem Statement:** Find the market equilibrium price and quantity given demand and supply functions, analyze market conditions at a specific price, and calculate price elasticity of demand at equilibrium. 2. **Market Equilibrium:** Set quantity demanded equal to quantity supplied: $$Q_d = Q_s$$ Given: $$Q_d = 50 - P$$ $$Q_s = P - 5$$ Set equal: $$50 - P = P - 5$$ 3. **Solve for price $P$:** Add $P$ to both sides and add 5 to both sides: $$50 + 5 = P + P$$ $$55 = 2P$$ Divide both sides by 2: $$\cancel{\frac{55}{2}} = \cancel{\frac{2P}{2}}$$ $$P = 27.5$$ 4. **Find equilibrium quantity $Q$:** Substitute $P=27.5$ into demand function: $$Q = 50 - 27.5 = 22.5$$ 5. **Interpretation:** Equilibrium price is 27.5 birr and equilibrium quantity is 22.5 units. 6. **Market at price 25 birr:** Calculate quantity demanded: $$Q_d = 50 - 25 = 25$$ Calculate quantity supplied: $$Q_s = 25 - 5 = 20$$ Since $Q_d > Q_s$, there is a shortage of 5 units (demand exceeds supply). 7. **Price Elasticity of Demand at Equilibrium:** Formula: $$E_d = \frac{dQ_d}{dP} \times \frac{P}{Q_d}$$ Given: $$\frac{dQ_d}{dP} = -1$$ Calculate: $$E_d = (-1) \times \frac{27.5}{22.5} \approx -1.22$$ 8. **Interpretation:** Since $|E_d| > 1$, demand is elastic, meaning a small increase in price causes a larger percentage decrease in quantity demanded.