Subjects economics

Area Under Curve 993124

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1. **Problem Statement:** Calculate the total area under the price-quantity curve for Customer A, which consists of an upper triangle, a rectangle, and a lower triangle, representing the total value or expenditure. 2. **Formula and Explanation:** The total area under the curve is the sum of the areas of the upper triangle, rectangle, and lower triangle. - Area of a rectangle: $$\text{Area} = \text{width} \times \text{height}$$ - Area of a triangle: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. **Given Data for Customer A at price 20:** - Quantity consumed = 0 days - Rectangle area = 0 - Upper triangle area = 200 - Lower triangle area = 0 4. **Calculate total area at price 20:** $$\text{Total area} = 0 + 200 + 0 = 200$$ 5. **Calculate total area at price 0:** - Quantity consumed = 20 days - Rectangle area = 0 - Upper triangle area = 0 - Lower triangle area = 200 $$\text{Total area} = 0 + 0 + 200 = 200$$ 6. **Calculate total area at price 10:** - Quantity consumed = 10 days - Rectangle area = 100 - Upper triangle area = 50 - Lower triangle area = 50 $$\text{Total area} = 100 + 50 + 50 = 200$$ 7. **Interpretation:** The total area under the curve remains constant at 200 for Customer A, representing the total expenditure or value across different prices and quantities. **Final answer:** $$\boxed{200}$$