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Consider the following scenario to understand the relationship between marginal and average values.

Suppose Raphael is a professional basketball player, and his game log for free throws can be summarized in the following table.

Fill in the columns with Raphael’s free-throw percentage for each game and his overall free-throw average after each game.

Game | Game Result | Total | Game Free-Throw Percentage | Average Free-Throw Percentage |

1 | 8/10 | 8/10 | 80 | 80 |

2 | 6/10 | 14/20 | ||

3 | 1/5 | 15/25 | ||

4 | 3/5 | 18/30 | ||

5 | 8/10 | 26/40 |

On the following graph, use the orange points (square symbol) to plot Raphael’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 0 1 2 3 4 5 100 90 80 70 60 50 40 30 20 10 0

FREE-THROW PERCENTAGE GAME

You can think of the result in any one game as being Raphael’s marginal free-throw percentage. Based on your previous answer, you can deduce that when Raphael’s marginal free-throw percentage is below the average, the average must be . You can now apply this analysis to production costs. For a U-shaped average total cost (ATC) curve, when the marginal cost curve is below the average total cost curve, the average total cost must be . Also, when the marginal cost curve is above the average total cost curve, the average total cost must be . Therefore, the marginal cost curve intersects the average total cost curve .