Cost function
A
cost function specifies the cost $C$ as a function of the number of items $x.$ Thus, $C(x)$ is the cost of $x$ items, and has the form
Cost = Variable Cost + Fixed Cost
where the variable cost is a function of $x$ and the fixed cost is a constant. A cost function of the form
$C(x) = mx + b$
is called a
linear cost function; the variable cost is $mx$ and the fixed cost is $b.$ The slope $m$ in a linear cost function is the
marginal cost, and measures the incremental cost per item.
Example
Your long-distance phone service charged you a $\$100$ initiation fee and charges an additional $\$2$ per call. Then the cost of making $x$ long-distance calls is
$C(x) = 2x + 100\qquad$ \t
(which happens to be a linear function) is a sum of two parts: a constant, or
fixed cost, $\$100$, which is the same regardless of the number $x$ of long-distance calls, or "items" being purchased, and a
variable cost, $2x,$ which does depend on the number of items purchased:
Cost = Variable Cost + Fixed Cost
The quantity 2 by itself is the incremental cost per call; we call 2 the
marginal cost. The fixed cost 100 is the $C$
-intercept of the linear cost function.