What this lesson teaches
I can explain profit as total revenue minus total cost and find the profit-maximising output where MR equals MC with MC rising.
Syllabus 9570, 2.2.1(a). Objectives of Firms: Firms aim to maximise profits; Profit as the difference between total revenue and total cost; Profit-maximising output occurs at the point when marginal revenue (MR) equals marginal cost (MC) and where MC is rising
Make a guess
A firm makes 100 units. Making the 101st would add $12 to revenue and $9 to cost. What should it do?
- Make it, and keep going until MR = MC.
- Make fewer, because its total cost would rise by $9.
- Stop now, because profit is already positive.
Show the answer
Make it, and keep going until MR = MC.
The 101st unit adds $3 to profit. Each extra unit whose MR is above MC raises profit, so the firm should expand.
A firm maximises profit by producing where MR = MC, then charging the price on its demand curve.
If the next unit adds more to revenue than to cost (MR > MC), producing it raises profit. If it adds more to cost (MR < MC), producing it lowers profit.
So the firm keeps expanding until MR = MC, with MC rising. That output, Q*, maximises profit.
The price is read from the AR (demand) curve at Q*, not from where MR meets MC.
Profit per unit is AR - AC at Q*. Total supernormal profit is the rectangle (AR - AC) x Q*.
- Rule
- Produce where MR = MC, with MC rising.
- Price
- Read from AR at that output.
- Profit
- (AR - AC) x Q.
| Batches | TR | TC | Profit | MR | MC |
|---|---|---|---|---|---|
| 0 | $0 | $18 | -$18 | - | - |
| 1 | $30 | $28 | $2 | $30 | $10 |
| 2 | $56 | $42 | $14 | $26 | $14 |
| 3 | $78 | $60 | $18 | $22 | $18 |
| 4 | $96 | $84 | $12 | $18 | $24 |
| 5 | $110 | $114 | -$4 | $14 | $30 |
Worked example: The workshop's best output
The workshop can make 0 to 5 batches. Its total revenues are $0, $30, $56, $78, $96, $110 and total costs $18, $28, $42, $60, $84, $114.
- Profits: -$18, $2, $14, $18, $12, -$4.
- The 3rd batch adds $22 of revenue and $18 of cost (MR > MC), so it raises profit by $4.
- The 4th batch adds $18 of revenue and $24 of cost (MR < MC), so it lowers profit by $6.
- Best output: 3 batches, with profit of $18. With whole batches, MR never exactly equals MC; stop where the next unit would cost more than it earns.
Watch out for this
The firm charges the price where MR meets MC.
MR = MC gives the output. The price comes from the AR curve at that output, which is higher.
Check your understanding
The 4th, 5th and 6th items a workshop turns out bring in MR of $9, $8 and $7, and MC of $6, $7 and $11. Where does its profit peak?
- At 6 items, because MR is still positive at the 6th.
- At 4 items, because that is where MR is furthest above MC.
- At 5 items, because the 6th would cut profit by $4.
Show the answer
At 5 items, because the 6th would cut profit by $4.
Right. The 5th item adds $8 - $7 = $1 to profit. The 6th brings in $7 but costs $11.