1. **Problem statement:** We are given a demand schedule with prices and quantities and need to derive the demand curve (a function relating quantity demanded $Q$ to price $P$). 2. **Given data:** Price ($P$): 10, 20, 30, 40, 50, 60, 70, 60 Quantity ($Q$): 100, 90, 80, 70, 60, 50, 40, 30 3. **Step 1: Organize data and check for consistency.** Notice the last price 60 corresponds to quantity 30, which is inconsistent with the earlier 60 price and quantity 50. We will consider the first 7 points for a consistent demand curve. 4. **Step 2: Assume a linear demand curve:** $$Q = a - bP$$ where $a$ and $b$ are constants to be determined. 5. **Step 3: Use two points to find $a$ and $b$:** Using points $(P=10, Q=100)$ and $(P=70, Q=40)$: $$100 = a - b \times 10$$ $$40 = a - b \times 70$$ 6. **Step 4: Solve the system:** Subtract second from first: $$100 - 40 = (a - 10b) - (a - 70b)$$ $$60 = 60b \implies b = 1$$ Substitute $b=1$ into first equation: $$100 = a - 10 \implies a = 110$$ 7. **Step 5: Demand curve equation:** $$Q = 110 - P$$ 8. **Step 6: Compute price elasticity of demand at $P=35$:** Price elasticity of demand $E_d$ is: $$E_d = \frac{dQ}{dP} \times \frac{P}{Q}$$ From the demand curve, $\frac{dQ}{dP} = -1$. Calculate $Q$ at $P=35$: $$Q = 110 - 35 = 75$$ Calculate elasticity: $$E_d = (-1) \times \frac{35}{75} = -\frac{35}{75} = -0.4667$$ 9. **Step 7: Interpretation:** Since $|E_d| = 0.4667 < 1$, demand is inelastic at $P=35$. This means quantity demanded is relatively unresponsive to price changes at this price. **Final answers:** - Demand curve: $$Q = 110 - P$$ - Price elasticity of demand at $P=35$ is approximately $-0.47$, indicating inelastic demand.