Reading a Cost Table
- Compute fixed, variable, total, average and marginal cost from partial data
- Explain why marginal cost intersects average total cost at its minimum
- Explain why average fixed cost falls continuously
Seven columns, all derivable from two
Given total fixed cost and total variable cost at each quantity, everything else follows. TC = TFC + TVC. AFC = TFC/Q. AVC = TVC/Q. ATC = TC/Q, which also equals AFC + AVC. MC = the change in TC from one more unit, which equals the change in TVC since fixed cost does not change. Exam tables give you some columns and ask for others, so knowing which definitions connect them is the whole skill.
Why average fixed cost falls forever
TFC is constant, so AFC = TFC/Q must fall as Q rises — always, with no minimum. This is "spreading the overhead", and it is why ATC keeps falling for a while even after AVC has started to rise: the falling AFC outweighs the rising AVC. Once the rise in AVC dominates, ATC turns upward, which gives ATC its U-shape.
Why MC cuts the averages at their minimums
A marginal value pulls an average toward itself. While MC is below ATC, each new unit costs less than the running average, so the average falls. While MC is above ATC, the average rises. So MC must cross ATC exactly at ATC's minimum — and the same argument puts the MC–AVC crossing at AVC's minimum. This is not a coincidence about cost curves; it is arithmetic true of any marginal-and-average pair.
A firm has TFC of $100. At 10 units TVC is $80; at 11 units TVC is $95. Compute ATC at 10 units, MC of the eleventh unit, and ATC at 11 units.
- 1.At 10 units: TC = 100 + 80 = $180, so ATC = 180/10 = $18.00.
- 2.MC of the eleventh unit = ΔTVC = 95 − 80 = $15.00.
- 3.At 11 units: TC = 100 + 95 = $195, so ATC = 195/11 = $17.73.
- 4.MC of $15.00 is below ATC of $18.00, so ATC fell — consistent with the marginal-pulls-average rule.
Marginal cost is a cost per unit of OUTPUT, and it is the difference between consecutive totals — not a total divided by a quantity. Computing MC as TC/Q gives you average total cost and answers a different question.
Total cost is $260 at 20 units and $272 at 21 units. The marginal cost of the twenty-first unit is:
Average total cost is falling. It follows that at this output:
Average fixed cost:
When a cost table has gaps, fill in TC and TVC first, then derive the averages and marginals. Working out of order leads to using an unfilled cell, which propagates through every later answer.
Answer the 3 checkpoints as you read.
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