Monopoly Schedule: Find Output, Price and Profit

The rule is to compare additions, not totals.

Check Four Output Decisions

The schedule cases below use listed feasible quantities with marginal net gains that cross from positive to negative once. The falling-cost case assumes a stable, continuous interior solution with downward-sloping MR. In a discrete schedule, a cost fall can leave the selected row unchanged if no comparison reverses.

Compare Changes with Common Units

Compute total revenue from price times quantity, then marginal revenue from changes in total revenue. Compare MR and MC for the same unit or output block. Stopping before the first negative marginal contribution works when later contributions cannot turn positive again. With an irregular schedule, compare total profit across every feasible row, including shutdown when relevant.

Follow Five Calculation Steps

Use a fixed order:

Distinguish Demand Price from MR

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.

Read Price and Then Calculate Profit

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.

Make the Revenue and Price Entries Agree

At quantities 1 through 4, MR is $28, $20, $12, and $4. MC is $8, $11, $15, and $22. The best listed quantity is two units because the third has MC>MR and the fourth also reduces profit. With zero sales giving zero revenue, the first two MR entries total $48, so the demand price at two must be $24. Given total cost of $24, profit is 2(24)-24=$24. The second unit’s $20 MR is not the selling price. The completed table below makes each total consistent.

Convert Block Changes to Per-Unit Values

When output rises by ten units, a $100 increase in revenue means $10 MR per unit; a $120 increase means $12 per unit. Divide the cost change by the same quantity change before comparing per-unit MR and MC. These are averages over the listed block, not information about each unobserved unit within it.

Compare Revenue and Profit Peaks

To maximize revenue among listed choices, find the largest TR entry. With a single-crossing MR pattern, a change from positive to negative MR identifies the peak; zero MR can give a tie. Profit instead includes cost. Positive marginal costs can place its maximizing row earlier, but compare the actual entries rather than assuming the two rows must differ in every discrete table.

Cross-Check the Profit Calculation

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.

Include the Short-Run Shutdown Choice

For a short-run loss, first identify the best operating choice. If fixed cost is unavoidable during the shutdown period, compare its revenue with variable cost: covering variable cost can make operation better than shutdown even when total economic profit is negative. Price and AVC at that operating output give the same comparison for positive quantity. Market power does not remove this cost test.

Respect Listed Outputs and Ties

Keep the feasible choices visible. A five-unit block might be profitable on average even though the table says nothing about the best intermediate integer quantity. Do not interpolate an unlisted output unless the question supplies a rule allowing it.

If a marginal contribution is zero and all other relevant choices are less profitable, adjacent output rows can tie for maximum profit. Report the tie when asked for every maximizing output. A rule that includes the zero-contribution unit finds one maximizer; it does not prove uniqueness.

Read the Output and Cost Rules

OpenStax’s monopoly lesson explains why MR selects quantity while demand supplies price. Its output-decision lesson shows total-profit comparisons and short-run shutdown logic; its price-taking revenue curve differs from a monopolist’s. The completed schedule and additional examples below were independently calculated, not copied source questions.

Check the Completed Four-Unit Schedule

Complete the earlier $28, $20, $12, $4 MR schedule by starting TR at zero. The given $24 total cost at two units, together with the first two marginal costs of $8 and $11, implies a $5 cost at zero output. The two-unit row therefore has a $24 price and $24 profit; its totals reconcile with the marginal changes.

The largest listed profit is $24 at Q = 2, even though total revenue keeps rising through Q = 4. At two units, ATC is $24/2 = $12: ($24 − $12) × 2 confirms the $24 profit. Read the $24 demand price rather than substituting the $20 MR entry.

Test Block Changes and an Irregular Schedule

In a separate five-unit-block example, TR at Q = 0, 5, 10, 15 is $0, $90, $160, $200, while TC is $20, $60, $115, $175. Which listed output is best? Then consider an independent one-unit example with TR of $0, $14, $24, $30, $32 and TC of $10, $16, $29, $30, $40 for Q = 0 through 4. Does stopping at the first negative addition still find the global best row?

Try Three Schedule Questions

Connect Tables and Monopoly Decisions

Compare output, profit and deadweight loss, review the short-run output and cost comparison, or continue in the CLEP Microeconomics learning hub.