Let C(q)=q^3-18q^2+750q the cost function for a certain company.?

a) let C(q)=q^3-18q^2+750q 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? (Be careful here!). Explain (briefly) the economic interpretation of these minima, stressing the difference.





b) let p= 180-q/9 be the demand function for another company. Compute the elasticity of demand and use this to find the maximum revenue.

Let C(q)=q^3-18q^2+750q the cost function for a certain company.?
Average cost = C(q)/q = q^2 - 18q + 750


Marginal cost = C'(q) = 3q^2 - 36q + 750





To fine the minima, we need to differentiate:


(AC)' = 2q - 18


so we have a critical point at q = 9


(AC)'' = 2 %26gt; 0, so the critical point is a minimum


(MC)' = 6q - 36


so we have a critical point at q = 6


(MC)'' = 6 %26gt; 0, so the critical point is a minimum





The average cost is minimized when q = 9, but the marginal cost is minimized when q = 6. The marginal cost refers only to the last item made, whereas the average cost refers to all the items made in the past.