Choose the feasible output with the greatest total profit.
The firm compares the additional revenue and cost of changing output. In the standard smooth diagram, the profit-maximising condition is MR = MC where MC is rising, with profit increasing before and decreasing after the relevant crossing. The equality is not sufficient by itself if there are other feasible candidates or boundaries. For discrete quantities, compare feasible total profits: exact equality need not occur. After identifying output, read its selling price from demand/AR, not from MR. Maximum profit is the largest difference TR-TC, not necessarily the largest revenue or lowest average cost.
- Objective
- Feasible choices are outputs the firm can actually select. Compare total revenue minus total cost across them, including zero output where available, to find the greatest total profit.
- Smooth condition
- A smooth or continuous model allows output to vary gradually, rather than only in whole batches. The standard candidate is MR = MC with MC rising; check that profit increases before it and decreases after it.
- Discrete condition
- Discrete choices are separate options, such as zero, one or two whole batches. Compare their total profits: no available choice has to give exact MR = MC.
Apply the distinction
Check the crossing
Before the relevant crossing, MR exceeds MC, so more output adds more revenue than cost and raises profit. After it, MC exceeds MR and extra output lowers profit. Also compare the lowest and highest permitted outputs, or other crossings, when relevant.
Read price
Find quantity from the marginal comparison, then price on AR/demand.
Profit area
AR-AC is profit per unit. Multiply that height by the number of units Q to get total profit: (AR-AC) x Q. In a diagram this is a rectangle, not just the distance between the two curves.
Losses and operation
A maximum among output choices can be negative. Whether to operate or exit requires relevant avoidable costs and alternatives, taught in firm strategies.
| Q | TR | TC | Profit | MR of added batch | MC of added batch |
|---|---|---|---|---|---|
| 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: Compare all six workshop choices
The workshop may choose zero to five batches. Its TR values are [0,30,56,78,96,110] and TC values [18,28,42,60,84,114], all dollars per week.
- Subtract TC from TR: profits are [-18,2,14,18,12,-4]. Three batches give the highest feasible profit, $18.
- The third batch adds MR $22 and MC $18, increasing profit by $4. The fourth adds MR $18 and MC $24, reducing profit by $6.
- No increment has MR exactly equal to MC. The discrete optimum is still clear from the feasible profit comparison.
- In a separate smooth model, AR=40-2Q, MR=40-4Q and MC=4+2Q. Set 40-4Q=4+2Q: this gives 36=6Q, so Q=6 at the relevant rising-MC crossing. Price is 40-2(6)=$28 on AR, not the $16 on MR. This model is separate from the workshop table.
Watch out for this
Any point where MR = MC must be the best feasible choice.
Check the qualifying crossing, alternatives and boundaries. With discrete choices, compare total profits rather than forcing an equality.
Check your understanding
In the workshop table, which output gives the greatest feasible profit?
- Five, because revenue is highest.
- Three, because TR - TC is 18 and exceeds every other listed option.
- There is no answer because MR never exactly equals MC.