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Cost functions and relationship to average cost

In the most simple case, the total cost function and its derivative are expressed as follows, where f(Q) is a cost function relating cost to production volume and FC represents fixed costs:

$TC=FC+f(Q)$

$MC={\frac {dTC}{dQ}}={\frac {d(FC+f(Q))}{dQ}}={\frac {df(Q)}{dQ}}$

Since (by definition) the fixed costs do not vary with production volume, the marginal cost is not related to fixed costs; the term drops out of the differentiated equation. This can be compared with average cost or AC, which is the total cost divided by the number of units produced and does include fixed costs.

$AC={\frac {FC+f(Q)}{Q}}$

This result has important implications, since it indicates that the producer who has already incurred the fixed costs should choose to produce (sell) even if the market price is less than average cost, because the marginal revenue (the income received from selling the marginal unit) is greater than or equal to marginal cost. For example, an electric powerplant should produce and sell electricity when it is paid $20 per megawatt if its marginal cost is $15, despite the fact that its average cost (including the cost of building the plant, salaries, etc) is $25 per megawatt. Although the plant is "losing money", it has lost $5 less than if it had not sold the last marginal unit.

In simple Marginal Cost can be calculated as the change in Variable Cost, for every unit produced. So the Variable Cost can be 3200 with one unit of production and 5600 with the second unit of production. Therefore the Marginal Cost at 2 units of production would be 2400.(5600-3200=2400)=Marginal Cost

Cost functions and relationship to average cost

In the most simple case, the total cost function and its derivative are expressed as follows, where ,$f(Q)\,\!$ is a cost function relating cost to production volume and FC represents fixed costs:

$TC=FC+f(Q)\,\!$

$MC={\frac {dTC}{dQ}}={\frac {d(FC+f(Q))}{dQ}}={\frac {df(Q)}{dQ}}$

Since (by definition) the fixed costs do not vary with production volume, the marginal cost is not related to fixed costs; the term drops out of the differentiated equation. This can be compared with average cost or AC, which is the total cost divided by the number of units produced and does include fixed costs.

$AC={\frac {FC+f(Q)}{Q}}$

This result has important implications, since it indicates that the producer who has already incurred the fixed costs should choose to produce (sell) even if the market price is less than average cost, because the marginal revenue (the income received from selling the marginal unit) is greater than or equal to marginal cost. For example, an electric powerplant should produce and sell electricity when it is paid $20 per megawatt if its marginal cost is $15, despite the fact that its average cost (including the cost of building the plant, salaries, etc) is $25 per megawatt. Although the plant is "losing money", it has lost $5 less than if it had not sold the last marginal unit.

In simple Marginal Cost can be calculated as the change in Variable Cost, for every unit produced. So the Variable Cost can be 3200 with one unit of production and 5600 with the second unit of production. Therefore the Marginal Cost at 2 units of production would be 2400.(5600-3200=2400)=Marginal Cost