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Marginal cost at a point

The marginal cost at a point is the derivative evaluated at that number. You differentiate term by term, insert x and get an amount of money per unit. It is not the same as the unit cost, and not the same as the total cost. The number says roughly what the next unit costs when you are already producing that many. Fixed costs disappear when you differentiate.

C′(x)=2ax+bC'(x) = 2ax + bwhen C(x) = ax^2 + bx + c

Symbols

C′C'marginal costNOK
xxnumber of units

Example

C(x)=0.01x2+20x+5000C(x) = 0.01x^2 + 20x + 5000. C′(x)=0.02x+20C'(x) = 0.02x + 20.

C′(100)=0.02⋅100+20=22C'(100) = 0.02 \cdot 100 + 20 = 22 NOK per unit.

The fixed cost is gone in the derivative.
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← Minimum unit cost

Part of Mathematics S1: Cost, revenue and profit.