Examples
Marginal cost from a total cost function
Total cost differentiated term by term, marginal cost found at ten units, and why the fixed cost drops out.
- 0:51
- Economics problems
- Narrated by Erinome
- English
Made from a prompt
Total cost is TC = 100 + 5Q + Q². Find the marginal cost at Q = 10.
Video transcript
In this video, we find marginal cost from a total cost function.
Consider question one. Total cost is T C equals one hundred plus five Q plus Q squared. Find the marginal cost at Q equals ten.
Marginal cost is the derivative of total cost with respect to output.
The constant contributes zero, five Q contributes five, and Q squared contributes two Q. So marginal cost equals five plus two Q.
At Q equals ten, marginal cost equals five plus two times ten, giving twenty-five.
Notice that fixed cost does not affect marginal cost. Hence, marginal cost at ten units of output is twenty-five cost units per additional unit of output.
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