Profit function

Definition

A profit function, often denoted as $P(x)$, represents the difference between total revenue and total costs for a given number of units sold or produced, $x$. It is a key concept in economic analysis and optimization.

5 Must Know Facts For Your Next Test

1. The profit function can be expressed as $P(x) = R(x) - C(x)$, where $R(x)$ is the revenue function and $C(x)$ is the cost function.
2. To find the break-even points, set the profit function equal to zero and solve for $x$.
3. If the revenue and cost functions are linear, then the profit function will also be linear.
4. The slope of a linear profit function indicates the rate of change of profit per unit increase in sales or production.
5. In systems of equations, solving for where two different profit functions intersect can provide insights into competitive market outcomes.

Review Questions

• How do you express a profit function using revenue and cost functions?
• What does it mean to find a break-even point in terms of a profit function?
• Explain how you would determine if two companies have identical profits using their respective profit functions.

Related terms

Revenue Function: A mathematical representation that calculates total revenue based on the number of units sold. Typically denoted as $R(x) = p \cdot x$, where $p$ is the price per unit.

Cost Function: Represents the total cost incurred in producing a certain number of units. Commonly expressed as $C(x) = FC + VC \cdot x$, where $FC$ is fixed costs and $VC$ is variable cost per unit.

Break-Even Point: The level of output at which total revenue equals total costs, resulting in zero profit. It is found by solving $R(x) = C(x)$.