# Consider the following scenario to understand the relationship between marginal and average…

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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 . 