Question

Given the Tc function Tc=10000 +100q-10q²+(1/3)q³ a. Find the MC function b. Find the slope of the MC function c. Find the output at which MC is equal to AVC

Answer 1

a.

$$MC=100-20q+q^2$$

b.

$$MC'=-20+2q$$

c.

$$AVC=100-10q+\frac{1}{3}q^2$$

$$100-20q+q^2=100-10q+\frac{1}{3}q^2$$

$$\frac{2}{3}q=10$$

$$q=15$$