6. The relationship between marginal and average costs Consider the following scenario to understand the relationship between marginal and average values. Suppose Brian is a professional basketball player, and his game log for free throws (an be summarized in the following table. Fill in the columns wlth Brian's freethrow percentage for each game and hls overall free throw average after each game. Game Game Result Total Game FreeThrow Percentage Average FreeThrow Percentage 1 5,18 6l8 as 75 2 zle 8l16 |:| |:| 3 2l4 10,120 E E 4 Elm 18l30 E E 5 8/10 26MB E E On the followlng graph, use the orange oolnts (square symbol) to plot Brlan's freethrow percentage for each game lhdlw'dually, and use the green .oolhts 1' trlahgle symbol) to plot his overall average freethrowr 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. mo -I- so so Game FreeTh row Percentage 70 A 30 . Average Free-Throw Peroentage FREE-THROW PERCENTAGE 8 40 SCI 20 10 El |. El 1 2 El 4 5 GAME You can think of the result in any one game as being Brian's marginal freethrow percentage. Based on your previous answer, you can deduce that when Brian's marginal freethrow percentage is belowI the averager the average must be V . You can now apply this analysis to production costs. For a Ushaped average total cost curver when the marginal cost curve is below the average total cost curve, the average total cost must be V . Also, when the marginal cost curve is above the average total cost curve, the average total cost must be V . Therefore, the marginal cost curve intersects the average total cost curve V . Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically. 100 -I- so so Game FreeThrow Percentage 70 A 50 . Average Free-Throw Peroentage FREE-THROW PERCENTAGE 53 40 so 20 10 u |. u 1 2 3 4 5 GAME You can think of the result in any one game as being Brian's marginal freethrow percentage. Based on your previous answer, you can deduce that I.vhen Brian's marginal freethrow percentage is belovi.I the average, the average must be V . falling You can now apply this analysis to production costs. For a Ushaped average total cost c n the marginal cost curve is below the average total cost curver the average total cost must be V . Also, I.vhen the marginal cost cu IVE the average total cost curve, the average total cost must be V . Thereforer the marginal cost curve intersects the average tot. ve V . On the following graph, use the orange points (square symbol) to plot Brian'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. 100 -0- Game Free-Throw Percentage 70 30 Average Free-Throw Percentage FREE-THROW PERCENTAGE 50 40 30 20 10 0 2 3 GAME You can think of the result in any one game as being Brian's marginal free-throw percentage. Based on your previous answer, you can deduce that when Brian's marginal free-throw percenta falling ow the average, the average must be rising You can now apply this analysis to producti For a U-shaped average total cost 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 curveOn the followlng graph, use the orange points {square symbol) to plot Brian's freethrow percentage for each game lhdlvldually, and use the green points {triangle symbol) to plot his overall average free throw percentage after each game. Note: Plot your points in the orderin which you would like them connected. Line segments will connect the points automatically. (2) 100 -I- so 9.0 Game FreeThrow Percentage 70 A 50 . Average Free-Throw Peroentage FREE-THROW PERCENTAGE 8 40 so 20 10 u |. u 1 2 a 4 5 GAME You can think of the result in any one game as being Brian's marginal freethrow percentage. Based on your previous answer, you can deduce that I.vhen Brian's n. ' freethrow percentage is below the average, the average must be V . . analysis to production costs. For a Ushaped average total cost curver when the marginal cost curve is below the average total - total cost must be V . Also, when the marginal cost curve is above the average total cost curve, the average total cost must be V . Therefore, the marginal cost curve intersects the average total cost curve V . On the following graph, use the orange points (square symbol) to plot Brian'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. (?) 100 -0- 90 Game Free-Throw Percentage 30 70 A 80 Average Free-Throw Percentage 50 FREE-THROW PERCENTAGE 40 30 20 10 0 2 GAME You can think of the result in any one game as being Brian's marginal free-throw percentage. Based off nice that when the average total cost is at 0 when Brian's marginal free-throw percentage is below the average, the average must be at its maximum You can now apply this analysis to production costs. For a U-shaped average total cost curve, when th erage total at its minimum 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