Q.From the cost schedule in Worked Example 3, identify the output at which Average Variable Cost is minimum, and verify the relationship between Marginal Cost and Average Variable Cost at that output.

Average variable cost is lowest where the cost of the next unit stops dragging it down and starts pushing it up; at that output marginal cost equals average variable cost. …

Given: the AVC and MC columns from Worked Example 3: AVC = $30, 25, 22, 22, 23.6, 26.33$ and MC = $30, 20, 16, 22, 30, 40$ for $Q=1\ldots6$.

Step 1 — Locate minimum AVC: the AVC values fall to $22$ at $Q=3$ and $Q=4$, then rise to $23.6$ and $26.33$. The minimum of AVC (22) is reached at $Q=4$, the last output before AVC begins to rise.

Step 2 — Read MC at that output: at $Q=4$, $MC=22$, which equals $AVC=22$.

Step 3 — Check the relationship on both sides:

• At $Q=3$: $MC=16$, $AVC=22$, so $MC<AVC$ — and AVC was still falling (25 → 22).
• At $Q=4$: $MC=AVC=22$ — AVC at its minimum.
• At $Q=5$: $MC=30$, $AVC=23.6$, so $MC>AVC$ — and AVC is now rising (22 → 23.6).

So MC cuts AVC from below, exactly at AVC's minimum, precisely as the theory predicts. …

Confusing the minimum of AVC with the minimum of MC — MC reaches its own minimum earlier (16 at Q=3), whereas M …