Answer to Question #236989 in Economics for KEBEDE AJEME

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

A) FC function doesn't depend on Q, so FC=50; VC=2/3Q3-10Q2+200Q

B) AVC=2/3Q2-10Q+200; AFC=50/Q; ATC= 2/3Q2-10Q+200+50/Q; MC=TC'=2/3×3Q2-10×2Q+200=2Q2-20Q+200

C) AVC reaches the minimum point when its derivative equals to 0. AVC'=2/3×2Q-10=4/3Q-10=0; Q=10×3/4=7.5 So, quantity equals to 7.5, AVC=2/3×7.5^2-10×7.5+200=162.5