Total Revenue · aiwiki.page

Total revenue is the amount a firm earns from selling goods or services during a specified period, before subtracting production and other costs. In microeconomics, it is usually represented by $TR$ and calculated as selling price multiplied by quantity sold. It measures sales activity rather than profitability: a firm can earn substantial revenue while making a loss if its costs exceed its revenue. Total revenue is central to the analysis of output, pricing, and economic profit. (openstax.org)

Definition and measurement

For one product sold at a uniform price,

TR=P\times Q,

where $P$ is the price per unit and $Q$ is the number of units sold during the relevant period. Price and quantity must refer to compatible units and the same period. For example, a hypothetical seller charging $20 per item and selling 500 items in a month has monthly total revenue of $10,000. This calculation says nothing about the expense of producing those items. (openstax.org)

For multiple products or different selling prices, the same identity extends to

TR=\sum_{i=1}^{n}P_iQ_i.

Here, each term represents a product or separately priced group of sales. This is a mathematical extension of the single-product calculation, not an assumption that every item has the same price. Quantity means sales rather than necessarily production: goods produced but not sold do not enter this elementary sales-revenue calculation. (openstax.org)

Total, average, and marginal revenue

Average revenue is revenue per unit sold:

AR=\frac{TR}{Q},\qquad Q>0.

Under uniform pricing, average revenue equals price. Marginal revenue measures the additional revenue associated with selling additional output:

MR=\frac{\Delta TR}{\Delta Q}.

When revenue is a differentiable function of output, marginal revenue is its derivative, $MR=dTR/dQ$ . Thus, total revenue describes the overall sales value, average revenue describes revenue per unit, and marginal revenue describes the change at the margin. (openstax.org)

Under perfect competition, an individual firm takes the market price as given. Its total-revenue curve is a straight line through the origin, with slope $P$ , and $AR=MR=P$ . A firm with market power, such as a monopoly, instead faces a downward-sloping demand curve. Under uniform pricing, selling more generally requires lowering the price on all units, so marginal revenue is below price. (openstax.org)

Demand elasticity and revenue

The effect of a price change on total revenue depends on price elasticity of demand. Price and quantity move in opposite directions along a downward-sloping demand curve, and elasticity measures their relative responsiveness. Holding the demand curve fixed:

With elastic demand, a price increase reduces total revenue, while a decrease raises it.
With inelastic demand, a price increase raises total revenue, while a decrease reduces it.
At unit elasticity, the effects offset locally, so total revenue has no first-order change. (openstax.org)

For differentiable demand, define the positive elasticity magnitude as

\varepsilon=-\frac{dQ}{dP}\frac{P}{Q}.

Differentiating $TR(P)=PQ(P)$ gives

\frac{dTR}{dP}=Q(1-\varepsilon).

This derivation expresses the elasticity–revenue relationship mathematically. An interior revenue maximum therefore requires unit elasticity, together with appropriate conditions ensuring a maximum. The relationship concerns movement along a given demand curve; shifts in supply and demand can change both observed prices and sales, complicating interpretation. (openstax.org)

Revenue maximization and profit maximization

Revenue maximization and profit maximization are different objectives. If total cost is $TC(Q)$ , profit is

\pi(Q)=TR(Q)-TC(Q).

An interior profit optimum normally requires marginal revenue to equal marginal cost, with further conditions ensuring a maximum. Revenue maximization instead requires $MR=0$ at a differentiable interior maximum. With positive marginal costs and the usual demand and cost conditions, profit-maximizing output is lower than revenue-maximizing output. (openstax.org)

For illustration, suppose inverse demand is $P=100-2Q$ . Then $TR=100Q-2Q^2$ and $MR=100-4Q$ . Revenue reaches its maximum at $Q=25$ , where price is $50 and revenue is $1,250. If marginal cost is constantly $20, the profit-maximizing quantity is instead $Q=20$ , provided producing is preferable to not producing. These values are derived from the hypothetical model. (openstax.org)

Economic profit also deducts opportunity costs, including implicit costs of resources owned by the firm. Revenue alone therefore cannot establish whether resources are earning more than their alternative uses. (openstax.org)

Accounting recognition and cash receipts

In financial reporting, revenue recognition determines when sales enter reported revenue. Under IFRS 15, revenue from customer contracts reflects the transfer of promised goods or services and the consideration to which the entity expects to be entitled. Recognition can occur at a point in time or over time as contractual performance obligations are satisfied. (ifrs.org)

Consequently, recognized revenue need not equal cash collected during the same period. A customer may pay before delivery, creating a contract liability, or pay after goods or services have been transferred, leaving a receivable or contract asset. The elementary $P\times Q$ model describes sales value; accounting rules determine the timing and measurement of reported revenue. (ifrs.org)