Expert: Paul Klarreich - 6/26/2006

Question
I am lost when it comes to this problem in my homework -
please help!

Let C(q)=q^3-18q^2+750q be the cost function for a certain
company. Find the average cost C(q) and the marginal cost MC
(q) . For what values of q are C(q) and MC(q) minimized? Explain
(briefly) the economic interpretation of these minima, stressing
the difference.  And as a follow up, Let p=200 - q/15 be the
demand function for another company.  Compute the elasticity
of demand and use this to find the maximum revenue.  

Answer
Hi, Todd,

Subject:  Cost functions...
Question:  I am lost when it comes to this problem in my homework -
please help!

Let C(q)=q^3-18q^2+750q be the cost function for a certain
company. Find the average cost C(q) and the marginal cost MC(q) . For what values of q are C(q) and MC(q) minimized? Explain (briefly) the economic interpretation of these minima, stressing the difference.  And as a follow up, Let p=200 - q/15 be the demand function for another company.  Compute the elasticity of demand and use this to find the maximum revenue.  

-------------------------------------
Sorry, now you have loaded things up with so much business jargon that this is out of my league.  Now I suspect you can do a lot of this by using the graph sketching process we went through in the last example.

Of course, your C(q) is a polynomial, so there won't be any asymptotes to worry about, but you will be able to find critical and inflection points and categorize them as max and min, etc, just as we did then.  I suspect (but you have the proof) that your MC is nothing other than C'(q), and in that case it is minimized at one of the inflection points.  

But as to the rest, you have to make sure you have definitions for all the terms you are using -- average cost, marginal cost, demand function, etc.