1. **Problem Statement:** Given Average Cost (AC) = 30 and Average Variable Cost (AVC) = 20 at output level $S$, calculate Total Fixed Cost (TFC). Also, explain why the short-run average cost curve is U-shaped. 2. **Formula and Explanation:** - Average Cost (AC) is defined as total cost per unit of output: $$AC = \frac{TC}{Q}$$ - Average Variable Cost (AVC) is variable cost per unit of output: $$AVC = \frac{TVC}{Q}$$ - Total Fixed Cost (TFC) is the part of total cost that does not change with output. - Relationship between AC, AVC, and AFC (Average Fixed Cost): $$AC = AVC + AFC$$ - Since $$AFC = \frac{TFC}{Q}$$, we can find TFC by rearranging. 3. **Calculation of TFC:** Given: $$AC = 30, \quad AVC = 20, \quad Q = S$$ Calculate AFC: $$AFC = AC - AVC = 30 - 20 = 10$$ Calculate TFC: $$TFC = AFC \times Q = 10 \times S = 10S$$ 4. **Explanation of U-shaped Short-run Average Cost Curve:** - Initially, as output increases, average cost decreases due to increasing returns to the variable factor and better utilization of fixed resources. - After a certain point, diminishing returns set in, causing average cost to rise. - This combination of decreasing then increasing costs results in a U-shaped curve. - The fixed costs spread over more units initially reduce average cost, but variable costs eventually dominate and increase it. **Final Answer:** $$TFC = 10S$$ The short-run average cost curve is U-shaped because of initially increasing returns and later diminishing returns to the variable factor, combined with the spreading effect of fixed costs.