Profit maximisation
Profit maximisation is the assumption that firms choose output where the gap between revenue and cost is greatest, equating marginal revenue and marginal cost.
Economics usually assumes firms try to make as much profit as they can. Simple as it sounds, the rule it implies is sharper than most firms follow.
Profit maximisation is the assumption that a firm chooses its output and price to make the gap between total revenue and total cost as large as possible. It is the standard model of firm behaviour and the source of the central rule that a firm should produce where marginal revenue equals marginal cost.
The marginal rule
The decisive insight is that profit is maximised not by selling as much as possible nor by charging as much as possible, but at the output where the revenue from the next unit just equals its cost. While an extra unit brings in more than it costs, making it adds to profit; once it costs more than it earns, making it subtracts. So the firm expands output up to the point where marginal revenue meets marginal cost, and no further. Totals and averages mislead; the margin decides.
A benchmark, not a description
Like utility maximisation for consumers, profit maximisation is a model, not a faithful portrait. Real firms pursue growth, market share, the quiet life, or the interests of their managers, and they operate with imperfect information about their own costs and demand. The assumption is a benchmark for analysis, valuable because it yields clear predictions, not because every firm rigorously obeys it.
Where reality complicates it
Several things blur the model. Managers may maximise their own interests rather than shareholders', the principal-agent problem. Firms may satisfice, settling for adequate profit, rather than truly maximise. And over what horizon profit is maximised matters: actions that maximise this year's profit can destroy next decade's. A firm starving investment to flatter current earnings is maximising the wrong thing.
Profit maximisation is the firm-side foundation of microeconomics, and the marginal rule it implies is genuinely useful discipline. But it describes a tendency under competitive pressure rather than a faithful account of motive, and its sharpest lesson, think at the margin, is one many real firms honour mainly in the breach.