Use a schedule when curves are replaced by numbers

The rule is to compare additions, not totals.

Compute total revenue from price times quantity, then marginal revenue from adjacent changes in total revenue. Compare each MR with the corresponding MC. Produce an additional unit while MR is at least MC. Stop before the first unit whose MC exceeds MR. If output changes in blocks, calculate both marginal values per unit of change.

Use a fixed order:

Suppose price is $24 at two units, $21 at three, and $18 at four. TR is $48, $63, and $72, so MR of the third is $15 and of the fourth is $9. The demand prices $21 and $18 are not those marginal revenues because selling more required price cuts on earlier units.

After choosing quantity, return to the demand schedule for price. This is essential because the MR entry used to choose the last unit is not the price charged. Then subtract total cost from total revenue, or use (P-ATC)Q. A schedule distractor often reports MR as price, chooses the quantity where demand price equals MC, or finds the largest total revenue without considering cost.

Schedule decision from additions

At quantities 1 through 4, MR is $28, $20, $12, and $4. MC is $8, $11, $15, and $22. Produce two units because the third has MC>MR. If demand price at two is $26 and total cost is $24, profit is 2(26)-24=$28. The $20 MR of the second unit is not the price.

If output rises in increments of ten, both marginal values must be divided by ten. A $100 increase in TR over ten units is MR of $10 per unit, not $100. Compare values with common units.

The quantity that maximizes total revenue occurs where MR changes sign near zero. Profit maximum occurs where MR meets MC. With positive MC, profit-maximizing output is generally smaller than revenue-maximizing output. A table option that selects the largest TR ignores cost.

Check profit using both methods when possible. TR-TC should equal (P-ATC)Q. If they differ, ATC was read at the wrong quantity or an arithmetic error occurred. This cross-check is especially helpful when several rows are close.

For a loss, the monopolist also compares price with AVC at the chosen output. Market power does not eliminate shutdown logic. It only changes how MR and price are found.

When quantity increments exceed one, divide both changes by the increment. A $120 revenue increase over ten units is MR of $12 per unit, not $120. MC must be expressed over the same units before comparison.

Use two profit checks when possible: TR-TC and (P-ATC)Q. They should match. If not, price or ATC was read from the wrong row. A schedule often places a tempting MR value beside the correct demand price. The cross-check exposes that error.