When the quantity of output (Q) is treated as a continuous variable, the marginal cost (MC) is precisely defined as the first derivative of the total cost function, C(Q), with respect to quantity. The formula is: $MC = \frac{dC(Q)}{dQ}$. This calculates the instantaneous rate of change in total cost for an infinitesimal increase in output. [2, 4, 8]

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Marginal cost (MC) represents the additional cost a firm incurs to produce more output. It can be viewed in two ways: for discrete changes, it is the cost of producing one additional unit. More generally, when quantity (Q) is treated as a continuous variable, the marginal cost is the derivative of the total cost function, C(Q), with respect to Q. This represents the instantaneous rate of change in total cost and corresponds to the slope of the total cost function. [1, 2]

Marginal Cost

To cite the ebook, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/.

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CORE Econ - The Economy 2.0: Microeconomics

The marginal cost (MC) can be estimated by calculating the ratio of the change in total cost ($ΔC$) to the change in the quantity of output ($ΔQ$). The formula is expressed as: $MC \approx \frac{ΔC}{ΔQ}$.

Estimating Marginal Cost

In the short run, a firm's marginal cost often increases as output rises because some inputs are fixed. To increase production, a firm might need to intensify its operations, such as by running extra shifts or reallocating resources from other product lines, leading to higher marginal costs. These factors can include equipment strain, worker fatigue, overtime wages, and higher energy consumption. For example, a bakery might incur higher costs for each additional loaf by operating overnight or shifting production away from other baked goods.

Increasing Marginal Cost in the Short Run

In certain scenarios, a firm's marginal cost (MC) may decrease as its production output (Q) increases. This can happen if expanding the scale of production enables the firm to utilize its inputs more effectively, thereby reducing the cost of each extra unit produced. The graphical methods employed to depict cost curves for firms with rising marginal costs can be similarly adapted to illustrate the cost structures of firms experiencing decreasing marginal costs.

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