Question

If TC =1000Q – 30Q2 + Q3, then the quantity at which ATC is minimized is

If TC =1000Q – 30Q2 + Q3, then the quantity at which ATC is minimized is

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Answer #1

Given,

First determine ATC by dividing TC by Q

The average total cost will be minimized when the first derivative is set equal to zero and the second derivative is a positive number.

Differentiating ATC wrt to Q we get

Now equating the first derivative to zero we get

Solving, for Q we get

Q = 30/2 = 15

Again differentiating ATC wrt Q we get

Second derivative is positive number. Thus, ATC will be minimized at Q = 15 units.

Answer Q = 15 units

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