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A firm faces the following Average Cost function
AC=1500Q^-1 + 300-27Q+1.5Q^2

Calculate the output level that minimizes:

a) Marginal Cost
b)Average Variable cost

I need some help on this question. Thanks.

If the average cost is

AC=1500Q^-1 + 300-27Q+1.5Q^2 ,
then that is the TOTAL cost of selling Q items, divided by Q.
The total cost is then
TC = 1500 + 300 Q -27 Q^2 + 1.5 Q^3
The marginal cost is the derivative of that, d(TC)/dQ
= 300 - 54 Q +4.5 Q^2

Set the derivative of that equal to zero to get the Q value (Quantity) for minimum marginal cost.

To get the minimum average cost, differentiate
1500Q^-1 + 300-27Q+1.5Q^2
directly and set that equal to zero, and solve for Q.

b) askes for average variable cost, does that implie that the average cost function also include a fixed portion? If so, would you do part b differently from what you did?


I am not sure what they meant by "average variable cost". I assumed is is the same as average cost.

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