Q: Given ATC=3Q2-2Q+4/Q, find FC and VC.
A: There are several different ways to solve this problem, since we know
several different relations among the cost curves:
TC=VC+FC, FC=TC(when Q=0), ATC=TC/Q, AVC=VC/Q, AFC=FC/Q, ATC=AFC+AVC, and MC=dTC/dQ=dVC/dQ.
The easiest way to proceed is to first calculate TC and then use the the fact that FC=TC(when Q=0) and finally solve for VC=TC-FC
To find TC: ATC=TC/Q so TC=ATC*Q. TC = (3Q2-2Q+4/Q)*Q = 3Q3-2Q2+4
To find FC: FC=TC(when Q=0). FC = 3(0)3-2(0)2+4 = 0-0+4 = 4
To find VC: VC=TC-FC. So VC = 3Q3-2Q2+4-4 = 3Q3-2Q2