Revenue function

Definition

A revenue function calculates the total revenue generated from selling a certain number of units of a product. It is usually expressed as $R(x) = p \cdot x$, where $p$ is the price per unit and $x$ is the number of units sold.

5 Must Know Facts For Your Next Test

1. The revenue function is linear when the price per unit remains constant.
2. In a system of equations, it can be used to find the breakeven point where revenue equals cost.
3. The slope of the revenue function represents the price per unit.
4. Revenue functions are often analyzed alongside cost functions to determine profitability.
5. Changes in price or quantity sold will directly affect the total revenue calculated by this function.

Review Questions

• What does the slope of a revenue function represent?
• How do you express a revenue function mathematically?
• How can you use a revenue function to find a breakeven point in a system of equations?

Related terms

Cost Function: A mathematical representation that calculates total cost incurred by producing a certain number of units, usually expressed as $C(x) = F + V \cdot x$, where $F$ is fixed costs and $V$ is variable cost per unit.

Profit Function: A function that calculates profit as the difference between total revenue and total cost, usually expressed as $P(x) = R(x) - C(x)$.

Breakeven Point: $x$ value at which total revenue equals total cost, meaning no profit or loss occurs; found by solving $R(x) = C(x)$.