Changes

11.  (Challenging, with extra credit)  Prove mathematically that MC>MR for all Q>0 in the honors discussion above.  (Hint:  define MC in terms of the change in AVC, and then regroup the terms and draw conclusions about them to show MC>MR).

11.  (Challenging, with extra credit)  Prove mathematically that MC>MR for all Q>0 in the honors discussion above.  (Hint:  define MC in terms of the change in AVC, and then regroup the terms and draw conclusions about them to show MC>MR).

:AVC = TVC/Q

:MR=P, and in perfect competition, AVC=MC.  Here, when Q>0, AVC>MR, which is why the firm shuts down.  But if AVC>MR, then AVC>P because P=MR. Because AVC=MC, then MC>P and MC>MR, as the question asked.

 

:MC is the cost to make the Q+1 good.  What is this cost in terms of AVC?

 

:AVC_Q+1 = TVC_Q+1/(Q+1)

 

:(this answer not complete yet, but is still being written)