A cost function represents the cost of producing a certain number of goods or services as a function of the quantity produced. It is typically expressed in algebraic form and used to model economic behavior.
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The cost function can often be written as $C(x) = c_0 + c_1x + c_2x^2 + ... + c_nx^n$, where $c_i$ are constants and $x$ is the quantity produced.
In linear cost functions, the total cost is represented by $C(x) = c_0 + c_1x$, where $c_0$ is the fixed cost and $c_1$ is the variable cost per unit.
Understanding how to derive and interpret the slope and intercept in a linear cost function is crucial for analyzing production costs.
Cost functions can be used to determine break-even points by setting the total revenue equal to the total cost.
Cost functions are integral in solving systems of equations involving production constraints and optimization problems.
Review Questions
How do you represent a linear cost function algebraically?
What do the constants in a quadratic cost function represent?
Explain how you would find the break-even point using a cost function.
Related terms
Fixed Cost: Costs that do not change with the level of output produced, represented by the constant term in a linear cost function.
Variable Cost: Costs that vary directly with the level of output produced, represented by coefficients multiplying $x$ in a linear or nonlinear cost function.
Break-even Point: The production level at which total revenue equals total costs, resulting in neither profit nor loss.