1. **Problem a:** Calculate the price elasticity of demand using the midpoint formula and classify the demand. The price elasticity of demand (PED) using the midpoint formula is given by: $$PED = \frac{\frac{Q_2 - Q_1}{(Q_1 + Q_2)/2}}{\frac{P_2 - P_1}{(P_1 + P_2)/2}}$$ Where: - $Q_1 = 900$, $Q_2 = 700$ - $P_1 = 550$, $P_2 = 650$ 2. **Calculate the percentage changes:** $$\frac{Q_2 - Q_1}{(Q_1 + Q_2)/2} = \frac{700 - 900}{\frac{900 + 700}{2}} = \frac{-200}{800} = -0.25$$ $$\frac{P_2 - P_1}{(P_1 + P_2)/2} = \frac{650 - 550}{\frac{550 + 650}{2}} = \frac{100}{600} = 0.1667$$ 3. **Calculate PED:** $$PED = \frac{-0.25}{0.1667} = -1.5$$ The absolute value is $1.5 > 1$, so demand is **elastic**. --- 4. **Problem b (i):** Find equilibrium price and quantity where $Q_d = Q_s$. Given: $$Q_d = 120 - 3P$$ $$Q_s = 30 + 2P$$ Set $Q_d = Q_s$: $$120 - 3P = 30 + 2P$$ $$120 - 30 = 3P + 2P$$ $$90 = 5P$$ $$P = \frac{90}{5} = 18$$ 5. **Calculate equilibrium quantity:** Substitute $P=18$ into $Q_d$: $$Q = 120 - 3(18) = 120 - 54 = 66$$ Equilibrium price is $18$ and quantity is $66$. --- 6. **Problem b (ii):** Demand and supply curves: - Demand: $Q_d = 120 - 3P$ - Supply: $Q_s = 30 + 2P$ At equilibrium, curves intersect at $(P, Q) = (18, 66)$. --- 7. **Problem c:** The equilibrium price is called the market clearing or resting price because at this price, the quantity demanded equals the quantity supplied, so there is no surplus or shortage. The market "clears" all goods, and there is no pressure for price to change. --- 8. **Problem d:** Three reasons governments regulate prices: - To protect consumers from excessively high prices (price ceilings). - To ensure producers receive a fair minimum price (price floors). - To control inflation or stabilize markets.