# Step-by-Step Solution ## 1. **Understanding the Problem** - The Salmond family pays a flat fee for water (not metered). - They **consume 10,000 gallons/month** at this flat fee. - If the **price per 1,000 gallons = £50**, they would **consume 0 gallons**. - We are to **draw the monthly demand curve**, assume it is a straight line. ## 2. **Setting up the Variables** Let: - \( Q \) = gallons of water consumed per month. - \( P \) = price per 1,000 gallons. Given points: - When \( Q = 10,000 \), \( P = 0 \) (flat fee, so marginal price is zero). - When \( Q = 0 \), \( P = 50 \) (at £50/1,000 gallons, they buy none). ## 3. **Writing the Demand Equation** The demand curve is a straight line, so in point-slope form: \[ \frac{P - P_1}{Q - Q_1} = \frac{P_2 - P_1}{Q_2 - Q_1} \] Plugging in: - \( (Q_1, P_1) = (10,000, 0) \) - \( (Q_2, P_2) = (0, 50) \) \[ \frac{P - 0}{Q - 10,000} = \frac{50 - 0}{0 - 10,000} = \frac{50}{-10,000} = -0.005 \] \[ P = -0.005(Q - 10,000) \] \[ P = -0.005Q + 50 \] Or, rearranged: \[ P = 50 - 0.005 Q \] ## 4. **Interpretation** - **Intercept:** At \( Q = 0 \), \( P = 50 \). - **Slope:** For every 1,000 gallon increase, price falls by £5. ## 5. **Graphical Representation** The demand curve is a straight line from (0, £50) to (10,000, £0): ```plaintext Price (£/1,000 gal) | |\ | \ | \ | \ | \ | \ |______\___________ 10,000 Quantity (gallons/month) ``` *Alt text: A straight downward-sloping line from (0, £50) to (10,000, £0)* ## 6. **Final Answer** **The Salmond family’s monthly demand curve for water is:** \[ P = 50 - 0.005Q \] where: - \( P \) is the price per 1,000 gallons (in £) - \( Q \) is the quantity of water consumed per month (in gallons) This straight-line demand curve passes through (0, £50) and (10,000, £0).