Profit function

In economics, profit maximization is the short run or long run process by which a firm determines the price and output level that returns the greatest profit. There are several approaches to this problem. The total revenue–total cost perspective relies on the fact that profit equals revenue minus cost and focuses on maximizing this difference, and the marginal revenue–marginal cost perspective is based on the fact that total profit reaches its maximum point where marginal revenue equals marginal cost.

Any costs incurred by a firm may be classed into two groups: fixed costs and variable costs. Fixed costs, which occur only in the short run, are incurred by the business at any level of output, including zero output. These may include equipment maintenance, rent, wages of employees whose numbers cannot be increased or decreased in the short run, and general upkeep. Variable costs change with the level of output, increasing as more product is generated. Materials consumed during production often have the largest impact on this category, which also includes the wages of employees who can be hired and laid off in the span of time (long run or short run) under consideration. Fixed cost and variable cost, combined, equal total cost.

Revenue is the amount of money that a company receives from its normal business activities, usually from the sale of goods and services (as opposed to monies from security sales such as equity shares or debt issuances).

Marginal cost and revenue, depending on whether the calculus approach is taken or not, are defined as either the change in cost or revenue as each additional unit is produced, or the derivative of cost or revenue with respect to the quantity of output. For instance, taking the first definition, if it costs a firm 400 USD to produce 5 units and 480 USD to produce 6, the marginal cost of the sixth unit is 80 dollars.

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