Siteadmin, Bureaucrats, Check users, nsAm_Govt_101RO, nsAm_Govt_101RW, nsAm_Govt_101_ta, nsJudgesRO, nsJudgesRW, nsJudges_talkRO, nsJudges_talkRW, nsTeam2RO, nsTeam2RW, nsTeam2_talkRO, nsTeam2_talkRW, oversight, Administrators
125,797
edits
Changes
Jump to navigation
Jump to search
Line 62:
Line 62: − + − −
Economics Homework Seven - Model (view source)
Revision as of 06:56, November 1, 2009
, 06:56, November 1, 2009almost done, last proof not quite there
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).
:
:No student attempted this! Perhaps I made it too scary. Using the hint, I define MC in terms of AVC: MC for the "Q+1" unit is: MC(Q+1)=TC(Q+1)-TC(Q). Next I can write TC in terms of AVC: TC=AVC*Q. Thus MC(Q+1)=AVC(Q+1)*(Q+1) - AVC(Q)*Q. Thus MC(Q+1)=AVC(Q+1)*Q + AVC(Q+1) - AVC(Q)*Q. Now regroup as the hint suggests: MC(Q+1)=Q*(AVC(Q+1)-AVC(Q)) + AVC(Q+1) <in progress>
: