Knowing how the curves fit together (How Marginal and Average Costs Relate) lets you predict what a cost change does. The key is whether the change depends on how much the firm makes.
Key idea
A change in fixed cost (rent, a license fee, a lump-sum tax) shifts AFC and ATC only. MC and AVC don't move, so the quantity that maximizes profit doesn't change. A change in variable cost (wages, materials, a per-unit tax) shifts MC, AVC and ATC.
Why it works
Marginal cost is the change in total cost from one more unit. A \$500 license fee is paid whether the firm makes 10 units or 100, so it adds nothing to the cost of the next unit: MC is unchanged, and so is AVC, which only counts variable cost. Spread over the units, though, the fee raises the average total cost, by \$500 ÷ q. A \$2 per-unit tax, by contrast, adds \$2 to the cost of every unit, so MC, AVC and ATC all rise by \$2.
Worked example: A license fee
A food truck's city license rises from \$600 to \$1,000 a year. It sells 2,000 meals a year. What happens to its MC, AVC and ATC at 2,000 meals?
- The fee is a fixed cost: MC and AVC don't change.
- ATC rises by $\$400 \div 2{,}000 = \$0.20$ per meal.
- Since MC didn't move, the best quantity doesn't change in the short run.
Answer: MC and AVC unchanged; ATC up \$0.20.
Worked example: A per-unit tax
A city adds a \$0.50 tax on each meal sold. What happens to MC, AVC and ATC?
- Every meal now costs \$0.50 more to sell, so the tax is a variable cost.
- MC, AVC and ATC each rise by \$0.50 at every quantity.
Answer: All three rise by \$0.50.
Common mistake
Shifting MC when fixed cost changes, and so predicting that a lump-sum fee changes how much a firm produces. Check: ask "does this cost change with the number of units?" If not, it can't change the cost of one more unit.
In the long run a big enough fixed cost can matter: if price no longer covers ATC, some firms leave the industry (Entry, Exit and the Long Run).