# Marginal cost

In economics, marginal cost is the change in the opportunity cost that arises when the quantity produced is incremented by one unit, that is, it is the cost of producing one more unit of a good. Intuitively, marginal cost at each level of production includes the cost of any additional inputs required to produce the next unit. At each level of production and time period being considered, marginal costs include all costs that vary with the level of production, whereas other costs that do not vary with production are considered fixed. For example, the marginal cost of producing an automobile will generally include the costs of labor and parts needed for the additional automobile and not the fixed costs of the factory that have already been incurred. In practice, marginal analysis is segregated into short and long-run cases, so that, over the long run, all costs (including fixed costs) become marginal.

If the cost function ${\displaystyle C}$ is differentiable, the marginal cost ${\displaystyle MC}$ is the first derivative of the cost function with respect to the quantity ${\displaystyle Q}$.

The marginal cost can be a function of quantity if the cost function is non-linear. If the cost function is not differentiable, the marginal cost can be expressed as follows.

where ${\displaystyle \Delta }$ denotes an incremental change of one unit.

In the simplest case, the total cost function and its derivative are expressed as follows, where Q represents the production quantity, VC represents variable costs, FC represents fixed costs and TC represents total costs.

Since (by definition) fixed costs do not vary with production quantity, it drops out of the equation when it is differentiated. The important conclusion is that marginal cost is not related to fixed costs. This can be compared with average total cost or ATC, which is the total cost divided by the number of units produced and does include fixed costs.

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