Q9 Healthy Harry's Juice Bar has the following cost schedules: Quantity: 0 vats of juice, 1, 2, 3, 4, 5, 6 Variable cost: 0, 10, 25, 45, 70, 100, 135 Total cost: 30, 40, 55, 75, 100, 130, 165 a) Calculate average variable cost, average total cost and marginal cost for each quantity. b) Graph all three curves.What is the relationship between the marginal-cost curve and the average-total-cost curve? Between the marginal-cost curve and the average- variable-cost curve? Explain.
Question
Q9
Healthy Harry's Juice Bar has the following cost schedules:
Quantity: 0 vats of juice, 1, 2, 3, 4, 5, 6
Variable cost: 0, 10, 25, 45, 70, 100, 135
Total cost: 30, 40, 55, 75, 100, 130, 165
a) Calculate average variable cost, average total cost and marginal cost for each quantity. b) Graph all three curves.What is the relationship between the marginal-cost curve and the average-total-cost curve? Between the marginal-cost curve and the average- variable-cost curve? Explain.
Solution
a)
Average variable cost (AVC) is calculated by dividing the variable cost by the quantity.
Average total cost (ATC) is calculated by dividing the total cost by the quantity.
Marginal cost (MC) is calculated by finding the change in total cost when the quantity changes by one unit.
Quantity: 0, 1, 2, 3, 4, 5, 6 Variable cost: 0, 10, 25, 45, 70, 100, 135 Total cost: 30, 40, 55, 75, 100, 130, 165 Average variable cost: -, 10, 12.5, 15, 17.5, 20, 22.5 Average total cost: -, 40, 27.5, 25, 25, 26, 27.5 Marginal cost: -, 10, 15, 20, 25, 30, 35
b)
When graphing these three curves, you will notice that the MC curve intersects the AVC and ATC curves at their lowest points. This is because when MC is less than AVC or ATC, it pulls the average down, and when MC is greater than AVC or ATC, it pulls the average up.
The MC curve is typically U-shaped, reflecting the law of diminishing marginal returns. Initially, adding more units of a variable input (like labor) increases output by a large amount, but eventually, adding more units of the variable input results in smaller increases in output.
The AVC and ATC curves are also typically U-shaped for the same reason. However, because ATC includes fixed costs, it starts off higher than AVC but decreases more slowly. As output increases, the fixed costs are spread over more units, reducing ATC.
In summary, the MC curve intersects the AVC and ATC curves at their lowest points, and all three curves are typically U-shaped due to the law of diminishing marginal returns.
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