The relationship between marginal and average costs

Consider the following scenario to understand the relationship between marginal and average values. Suppose Jacques is a professional basketball

player, and his game log for free throws can be summarized in the following table.

Fill in the columns with Jacques's free$-$throw percentage for each game and his overall free$-$throw average after each game.

On the following graph, use the orange points $($square symbol$)$ to plot Jacques'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

You can think of the result in any one game as being Jacques's marginal free$-$throw percentage. Based on your previous answer, you can deduce that

when Jacques'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 curv

falling

he marginal cost curve is below the average total

cost curve, the average total cost must be

$.$ Also, when the marginal cost curve

rising

the average total cost curve, the average total

cost must be

$.$ Therefore, the marginal cost curve intersects the average total cusccurve