Marginal cost comes from changes in total or variable cost

Fixed cost cancels between adjacent output levels.

MC=Δ TC/Δ Q=Δ VC/Δ Q. If output rises by one and total cost rises from $360 to $380, MC is $20. If output rises by five, divide the cost change by five. Dividing $380 by output instead would produce an average.

Fixed cost cancels because it is the same in neighboring rows: Δ TC=Δ(FC+VC)=Δ FC+Δ VC=0+Δ VC. This is why either total cost or variable cost produces the same marginal cost. If your two calculations differ, the rows or quantity change were used incorrectly.

Always attach MC to the output added. If TC rises from $360 at 20 units to $380 at 21, $20 is the marginal cost of the twenty-first unit. It is not the MC “at 20” in a way that belongs to the twentieth unit. Tables sometimes position marginal values between rows. Wording clarifies the unit.

MC crosses AVC and ATC at their minimum points. When MC is below an average, the next unit lowers that average. When MC is above, it raises the average. MC does not cross AFC because AFC falls continuously and the marginal-average story does not apply in the same way.

For a discrete schedule, the crossing can occur between displayed quantities. If previous ATC is $18 and the next unit’s MC is $20, the new ATC rises. If MC is $15, it falls. Exact equality is not required in a table for the minimum to be identified around the change in direction.

Complete one row

At 20 units, fixed cost is $100 and variable cost is $260. TC is $360, AFC is $5, AVC is $13, and ATC is $18. If TC at 21 units is $380, the twenty-first unit’s MC is $20. Because $20 exceeds the previous ATC of $18, ATC begins to rise.

The average at 21 units would be $380/21≈$18.10, confirming the prediction. You did not need to calculate it to know direction. The marginal-average rule provides a fast conceptual check and a full arithmetic verification when requested.

MC answers whether another unit is worth producing when compared with marginal revenue. ATC measures profit per unit at the chosen output. An answer that chooses output where price equals ATC uses a break-even measure for a marginal decision. Keep the roles separate.

If marginal cost is computed between nonadjacent totals, state the limit of the data. The quotient gives average added cost per unit across the interval, not each missing unit’s separate MC. A single-best-answer item will either ask for that interval value or provide adjacent rows when one unit’s cost is required.

Units expose common errors. Δ TC/Δ Q is dollars per added unit. TC/Q is dollars per unit averaged over all output. TC alone is total dollars. Before choosing a numerical option, write the requested unit. A distractor produced by dividing the final total by the final quantity may be accurate ATC and still be entirely wrong for MC.