Quiz 6

Q: If TC= 4q2+8q+100 and P=88, find the maximum profit for a perfectly competitive firm and determine the shutdown price.

A:  Profit maximization is where MR=MC.  The competitive assumption is that P=MR, so MR=88.  MC=dTC/dq=8q+8.
Thus the optimal quantity is where 88=8q+8 or q=10.  Profits would be 88*10-4(10)2-8(10)-100=300.

The shut down price is where AVC=MC.  VC= 4q2+8q, so AVC = 4q+8.  Setting MC=AVC gives 8q+8=4q+8 or q=0.  The value of AVC when q=0 is 8.  (Technically we do not have an AVC when q=0 as it would have required us to divide VC by 0.  But for and price above 8 the firm would operate and for any price below 8 the firm would prefer to shutdown.)