Posted by **Jack** on Friday, January 12, 2007 at 1:26am.

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?

Thanks.

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

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