Profit maximisation: MC = MR

Profit is π = TR − TC. Profit is at a maximum where the gap between TR and TC is widest — which is exactly where the extra revenue from the last unit equals its extra cost.

The marginal logic is the whole of A-level microeconomics in two lines:

• If MR > MC, the next unit adds more to revenue than to cost — profit rises if you produce it. So expand.
• If MR < MC, the last unit added more to cost than revenue — profit rises if you stop making it. So contract.
• Profit can therefore only be at a maximum where MR = MC.

Exam craft: "profit maximisation" is a rule about the margin, not about charging the highest possible price. A profit-maximising monopolist that raised price further would sell so much less that profit would fall.

The three objectives on one diagram

With a downward-sloping AR (demand) curve, MR falls twice as steeply. That single fact generates all three output levels:

Learn the ordering: the profit-maximising output is always the smallest and carries the highest price; sales maximisation gives the largest output and the lowest price. That is the key evaluation point for consumers.

Should the firm expand?

Worked example — the firm we will use

A firm faces the demand curve P = 20 − Q (P in £, Q in thousands of units). Its marginal cost is constant at £4 and its fixed costs are £20 (thousand).

Skill to bank: for any linear demand curve P = a − bQ, MR = a − 2bQ. Examiners use this constantly.

Your turn — profit-maximising output

Your turn — the profit

Revenue maximisation: MR = 0

Total revenue is at a maximum when the last unit adds nothing to revenue — i.e. where MR = 0. Beyond that, MR is negative and TR falls.

This links straight back to PED (Theme 1):

• Where demand is price elastic (PED > 1 in absolute value), MR is positive — cutting price raises TR.
• Where PED = 1 (unit elastic), MR = 0 — TR is at its maximum.
• Where demand is price inelastic, MR is negative — cutting price lowers TR.

Why would a firm do it? Managers' bonuses are often tied to turnover; sales staff are on commission; and a bigger revenue base can deter entry and build market presence.

Crucial: a revenue-maximising firm produces more and charges less than a profit maximiser — and makes less profit. Revenue is not profit.

Your turn — revenue-maximising output

Revenue vs profit

Sales maximisation: AR = AC

Sales maximisation means selling the largest possible volume subject to a constraint: the firm must still cover its costs — that is, it must at least make normal profit.

Push output any further and AC would exceed AR: the firm would make a loss and could not survive in the long run. So AR = AC is the break-even boundary.

• Motives: to build market share quickly (penetration pricing), to exploit economies of scale, to deter entry, or because managers' status depends on the size of the firm.
• Consumer view: lowest price and highest output of the three objectives — the most allocatively efficient of them.
• Shareholder view: zero supernormal profit means no dividends beyond the minimum, and no retained profit to fund investment.

Precision matters: "sales maximisation" (largest output subject to normal profit, AR = AC) is not the same as "revenue maximisation" (MR = 0). Sales max gives a larger output and a lower price than revenue max.

Satisficing

Satisficing (Herbert Simon) means aiming for an outcome that is "good enough" rather than maximal — sacrificing some profit to keep all stakeholders sufficiently content.

• Shareholders want an acceptable dividend — not necessarily the maximum.
• Workers want decent pay and conditions; consumers want quality; the community wants low pollution.
• Managers face bounded rationality: they lack the perfect information the maximising model assumes, so they follow rules of thumb.

Satisficing typically arises because of the divorce of ownership from control: managers who are not the owners have no strong incentive to squeeze out the last pound of profit, only enough to keep shareholders from revolting.

Which objective is this?

Tap a statement, then tap the objective it describes.

The divorce of ownership from control

Why would any firm not maximise profit? Because in a large company the people who own it (shareholders — the principals) are not the people who run it (managers — the agents).

Partial solutions: pay managers in share options or performance-related pay to align incentives; the threat of hostile takeover disciplines under-performing boards. But share options can encourage short-termism — pumping this year's share price at the expense of long-run investment.

Name the objective

Find the profit-maximising output from a table

The same answer, two ways

Note also: revenue is still rising at Q = 6 (MR = 78 − 70 = 8 > 0), so a revenue maximiser would produce well beyond Q = 4. Different objective, different output.

Match the objective to its condition

Tap a condition on the left, then the objective on the right.

Does profit maximisation really describe firms?

Short run vs long run

The big ideas to know

You've covered the whole of Edexcel 3.2. Press Finish to see your score.