Marginal Analysis
Turn a cost schedule into marginal and average cost, and find where profit peaks.
The last unit whose revenue still covers its cost
Total revenue − total cost
Quantity where average cost is lowest
| Q | TC | TR | MC | MR | AC | AVC | Profit |
|---|---|---|---|---|---|---|---|
| 0 | 3 | 0 | — | — | — | — | -3 |
| 1 | 5 | 6 | 2 | 6 | 5 | 2 | 1 |
| 2 | 8 | 12 | 3 | 6 | 4 | 2.5 | 4 |
| 3 | 12 | 18 | 4 | 6 | 4 | 3 | 6 |
| 4 | 17 | 24 | 5 | 6 | 4.25 | 3.5 | 7 |
| 5 | 23 | 30 | 6 | 6 | 4.6 | 4 | 7 |
| 6 | 30 | 36 | 7 | 6 | 5 | 4.5 | 6 |
Fixed cost is 3 — the cost of producing nothing. Average variable cost strips it out.
Marginal cost is what one more unit adds to total cost, and marginal revenue is what it adds to revenue. Keep producing while MR is at least MC. With costs of 3, 5, 8, 12, 17, 23, 30 and a price of 6, profit peaks at 5 units.
Totals hide the decision; margins reveal it
A total cost column tells you what production costs but not what to do next. The decision is always about one more unit: does it bring in more than it costs? That is the comparison between marginal revenue and marginal cost, and it is why economists reach for the difference between consecutive rows rather than the rows themselves.
The rule follows immediately. While MR exceeds MC, the extra unit adds to profit, so produce it. Once MC passes MR, the extra unit subtracts, so stop. Profit is highest at the last quantity where MR is still at least MC — which is not where average cost is lowest, and not where revenue is highest.
Why sunk costs drop out
Fixed cost appears in every row of the total column and in none of the marginal column, because it does not change when output does. That is the arithmetic behind the advice to ignore sunk costs: they alter how much you make, never what you should do. The same logic separates average cost from average variable cost — the second omits the fixed charge, and is the one that matters for whether to produce at all.
AC = TC ÷ Q; AVC = (TC − fixed cost) ÷ Q
- 1 Write total cost against quantity. Start at Q = 0 so the fixed cost is visible — here it is 3.
- 2 Take differences for marginal cost. From 3 to 5 is an MC of 2 for the first unit, then 3, 4, 5, 6, 7 as output rises.
- 3 Do the same for revenue. At a constant price of 6, every unit adds 6, so MR = 6 throughout.
- 4 Find the last unit worth making. The fifth unit costs 6 and earns 6, so it just breaks even and is still worth making. The sixth costs 7 and earns 6, so it is not.
- 5 Check against total profit. Profit runs −3, 1, 4, 6, 7, 7, 6 — peaking at 7, exactly where the marginal rule said.
The worked schedule
Fixed cost 3, price 6. The marginal columns are differences between consecutive rows.
| Q | TC | TR | MC | MR | AC | AVC | Profit |
|---|---|---|---|---|---|---|---|
| 0 | 3 | 0 | — | — | — | — | −3 |
| 1 | 5 | 6 | 2 | 6 | 5.00 | 2.00 | 1 |
| 2 | 8 | 12 | 3 | 6 | 4.00 | 2.50 | 4 |
| 3 | 12 | 18 | 4 | 6 | 4.00 | 3.00 | 6 |
| 4 | 17 | 24 | 5 | 6 | 4.25 | 3.50 | 7 |
| 5 | 23 | 30 | 6 | 6 | 4.60 | 4.00 | 7 |
| 6 | 30 | 36 | 7 | 6 | 5.00 | 4.50 | 6 |
Three places the rule gets misread
The first is confusing the efficient scale with the profitable one. Average cost is lowest at 3 units here, but profit is highest at 5. Minimising cost per unit is not the objective unless price is fixed at that minimum — a firm happily accepts a higher average cost if the extra units still earn more than they cost.
The second is forgetting that marginal cost crosses average cost at its minimum. That is not a coincidence but arithmetic: while the next unit costs less than the running average it pulls the average down, and once it costs more it pushes the average up. Any average and marginal pair behaves this way, which is a useful check that a schedule has been computed correctly.
The third is the shape of marginal revenue. For a price taker MR equals the price at every quantity, as in the table above. A firm facing a downward-sloping demand curve has to cut the price on every unit to sell one more, so its MR falls faster than its price and lies below it — that case is worked out on the profit maximisation page rather than here.