### 3. The Relationship Between Marginal and Average CostsConsider the following scenario to understand the relationship between marginal and average values. Suppose Caroline is a professional basketball player, and her game log for free throws can be summarized in the following table.**Instructions:** Fill in the columns with Caroline's free-throw percentage for each game and her 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 | | |### ExplanationThis table is designed to help illustrate the concept by comparing Caroline's individual performances (marginal values) against her cumulative performance (average values). Each column needs to be filled out to reflect the marginal free-throw percentage for each game and then the average free-throw percentage after each game.**Column Details:**- **Game Result:** The number of successful free-throws out of the total attempts for that game.- **Total:** The cumulative successful free-throws out of the cumulative total attempts by that game.- **Game Free-Throw Percentage:** The percentage of successful free-throws in that specific game.- **Average Free-Throw Percentage:** The overall percentage of successful free-throws up to and including that game.By completing this table, the relationship between Caroline's game-by-game performance and her overall average can be clearly seen, emphasizing how individual performances impact the overall average. On the following graph, use the orange points (square symbol) to plot Caroline’s free-throw percentage for each game individually, and use the green points (triangle symbol) to plot her 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.*Graph Details:*- **Title:** (None provided, likely something related to Free-Throw Percentages)- **Y-Axis:** Free-Throw Percentage (0% to 100%)- **X-Axis:** Game (0 to 5)*Legend:*- **Orange Square Points:** Game Free-Throw Percentage- **Green Triangle Points:** Average Free-Throw Percentage**Instructions for Analysis:**You can think of the result in any one game as being Caroline’s marginal free-throw percentage. Based on your previous answer, you can deduce that when Caroline’s marginal free-throw percentage is below the average, the average must be **(blank space to be filled in)**.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 **(drop-down selection)**. Also, when the marginal cost curve is above the average total cost curve, the average total cost must be **(drop-down selection)**. Therefore, the marginal cost curve intersects the average total cost curve **(drop-down selection)**.

The marginal cost of production and marginal revenue can be used to maximise product output and…

On the following graph, use the orange points (square symbol) to plot Caroline's free-throw percentage for each game individually, and use the green points (triangle symbol) to plot her 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. 100 0- 90 Game Free-Throw Percentage 80 70 60 Average Free-Throw Percentage 50 40 30 20 10 0 0 5 GAME You can think of the result in any one game as being Caroline's marginal free-throw percentage. Based on your previous answer, you can deduce that when Caroline'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 FREE-THROW PERCENTAGE 2 3

On the following graph, use the orange points (square symbol) to plot Caroline's free-throw percentage for each game individually, and use the green points (triangle symbol) to plot her 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. 100 0- 90 Game Free-Throw Percentage 80 70 60 Average Free-Throw Percentage 50 40 30 20 10 0 0 5 GAME You can think of the result in any one game as being Caroline's marginal free-throw percentage. Based on your previous answer, you can deduce that when Caroline'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 FREE-THROW PERCENTAGE 2 3

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the following scenario to understand the relationship between marginal and average values. Suppose Sam is a professional basketball player, and his game log for free throws can be summarized in the following table. Fill in the columns with Sam's free-throw percentage for each game and his overall free-throw average after each game. Game Result Total Game Free-Throw Percentage Average Free-Throw Percentage Game 1 8/10 80 12/20 14/28 16/32 22/40 2 3 4 5 8/10 4/10 2/8 2/4 6/8 80 On the following graph, use the orange points (square symbol) to plot Sam'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.
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