8. The relationship between marginal and average costs Consider the following scenario to understand the relationship between marginal and average values. Suppose Sean is a professional basketball player, and his game log for free throws can be summarized in the following table. Fill in the columns with Sean's free-throw percentage for each game and his overall free-throw average after each game. Game Game Result Average Free-Throw Percentage 6/8 75 2/8 2/4 8/10 Total Game Free-Throw Percentage 6/8 75 8/16 10/20 18/30 26/40 8/10 On the following graph, use the orange points (square symbol) to plot Sean's free-throw percentage for each game individually, and use the green points (triangle symbol) to plot his overall average free-throw percentage after each game. Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. Game Free-Throw Percentage Average Free-Throw Percentage FREE-THROW PERCENTAGE GAME You can think of the result in any one game as being Sean's marginal free-throw percentage. Based on your previous answer, you can deduce that when Sean's marginal free-throw percentage is above the average, the average must be You can now apply this analysis to production costs. For a U-shaped average total cost cu amin cost a falling "In the marginal cost curve is below the average total them cost curve, the average total cost must be Also, when the marginal cost cu rising pve the average total cost curve, the average total cost must be . Therefore, the marginal cost curve intersects the average total cost curve You can think of the result in any one game as being Sean's marginal free-throw percentage. Based uce that when Sean's marginal free-throw percentage is above the average, the average must be at its minimum at its maximum You can now apply this analysis to production costs. For a U-shaped average total cost curve, when til erage total when the average total cost is at 0 cost curve, the average total cost must be . Also, when the marginal cost curve is above age total cost must be . Therefore, the marginal cost curve intersects the average total cost curve