How to calculate long run average total cost?
Understand the Problem
The question is asking for a method or formula to calculate the long-run average total cost in economics. This typically involves understanding how total costs behave over time as production levels change and economies of scale are realized.
Answer
LRATC = \frac{VC}{Q}
Answer for screen readers
The long-run average total cost (LRATC) is calculated by dividing the total variable cost (VC) by the quantity (Q) of output produced: $$LRATC = \frac{VC}{Q}$$
Steps to Solve
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Understand Long Run Average Total Cost (LRATC)
Long Run Average Total Cost (LRATC) is the cost per unit of output incurred when all factors of production are variable over the long term.
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Formula for Total Cost (TC)
The total cost function includes fixed costs (FC) and variable costs (VC):
$$ TC = FC + VC $$
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Eliminate Fixed Costs in the Long Run
In the long run, all costs are variable, so the total cost (TC) is purely the sum of variable costs (VC). Thus:
$$ TC = VC $$
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Calculate Average Cost (AC)
Average Cost (or Average Total Cost) is calculated by dividing the total cost (TC) by the quantity (Q) of output produced:
$$ AC = \frac{TC}{Q} $$
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Long Run Average Total Cost (LRATC)
Since all costs are variable in the long run:
$$ LRATC = \frac{VC}{Q} $$
The long-run average total cost is derived from the long-run total cost function by dividing by the quantity and minimizing the cost for each level of output.
The long-run average total cost (LRATC) is calculated by dividing the total variable cost (VC) by the quantity (Q) of output produced: $$LRATC = \frac{VC}{Q}$$
More Information
The LRATC curve typically exhibits U-shaped characteristics due to economies and diseconomies of scale. Understanding this helps businesses determine the most efficient level of production.
Tips
A common mistake is to include fixed costs when calculating LRATC, but in the long run, all costs are variable.
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