posted by Jack on .
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.