Question

Consider the following total cost function: TC = 2/3Q3 – 10Q2 + 200Q + 50 A) Identify the FC and VC function? B) Calculate AVC, AFC, ATC, and MC functions C) Determine the level of output at which AVC reaches minimum point and the minimum AVC at that level of output? 

Answer 1

$$TC=\frac{2}{3}Q^3-10Q^2+200Q+50$$

A)

$$FC=50$$

$$VC=\frac{2}{3}Q^3-10Q^2+200Q$$

B)

$$AVC=\frac{2}{3}Q^2-10Q+200$$

$$AFC=\frac{50}{Q}$$

$$ATC=\frac{2}{3}Q^2-10Q+200+\frac{50}{Q}$$

$$MC=2Q^2-20Q+200$$

C)

$$\frac{\varDelta AVC}{\varDelta Q}=\frac{4}{3}Q-10$$

$$Q=7.5$$