The cost curves from Short-Run Costs fit together in a pattern. Once you see why, you can sketch them from memory.
Key idea
When marginal cost is below an average, the average falls; when it is above, the average rises. So MC crosses AVC and ATC at their lowest points. AFC falls the whole way, so the gap between ATC and AVC (which equals AFC) narrows as output grows.
Why it works
Think of a running grade average. If your average is 80 and you score 70 on the next test, your average falls; score 90, and it rises. The next test is the "marginal" score. Costs work the same way: each new unit's cost (MC) pulls the average cost toward it. The average stops falling and starts rising exactly when MC moves from below it to above it, which is the bottom of the average curve.
Worked example: Grades as a model
A student's average over four tests is 80. The fifth test scores 70. What happens to the average? What if it scores 95?
- Total so far: $4 \times 80 = 320$.
- With 70: $(320 + 70) \div 5 = 78$, down. With 95: $(320 + 95) \div 5 = 83$, up.
- A marginal value below the average pulls it down; above it pulls it up.
Answer: 78 (down) or 83 (up).
Worked example: Find the bottom of ATC
In the table from the last lesson, ATC is \$50, \$31, \$24, \$21, \$22, \$24 for 1 to 6 units, and MC is \$20, \$12, \$10, \$12, \$26, \$34. Where is ATC lowest, and how does MC explain it?
- ATC is lowest at 4 units (\$21).
- The 4th unit's MC (\$12) is below the average before it (\$24), so ATC falls to \$21.
- The 5th unit's MC (\$26) is above \$21, so ATC rises to \$22. MC crosses ATC between 4 and 5 units, at the bottom.
Answer: At 4 units; MC passes from below ATC to above it there.
Common mistake
Thinking marginal cost is at its lowest where it crosses average total cost. The crossing is at the lowest point of the average; MC's own minimum comes earlier, at a smaller quantity. Check on the picture: MC is already rising where it meets ATC.