[其他] 函數問題 請大家幫忙

看板Math作者 (小黑)時間14年前 (2011/10/05 22:22), 編輯推噓3(3010)
留言13則, 4人參與, 最新討論串1/1
第一大題 1. Is the following function concave or convex? why? F(x,y) = (x-1)^a(y-2)^b , a,b > 0 2. Is the above function quasi-concave? 3. If we maximize the above function subject to the constraint p1X + p2Y = 100 where p1 & p2 are parameters. Find the effects of a & p1 on the maximal values of F(x,y) , respectivly. 第二大題 F(x,y,z) = (x-a)^p(y-2)^q(z-3)^r a,p,q,r > 0 1. Is the above function concave? 2. Soppose that you want to maximize the above function subject to the constraint x + 2y +3z = 100 Is the objective function quasi-concave? 3. How the maximum value of F(x,y,z) changes as the parameter a changes 請大家幫助我 我需要中文詳解~~~~ -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 111.248.168.174

10/05 23:52, , 1F
好像經濟的題目...
10/05 23:52, 1F

10/06 01:04, , 2F
二階Hessian矩陣是負定的就concave,concave就一定
10/06 01:04, 2F

10/06 01:06, , 3F
是Quasi-concave。其他單純效用極大化,再把解值代回
10/06 01:06, 3F

10/06 01:06, , 4F
目標函數求出Value function,再做比較靜態
10/06 01:06, 4F

10/06 01:08, , 5F
J大大說的是第幾題是concave??
10/06 01:08, 5F

10/06 01:09, , 6F
我沒說是concave,我只說你去做出二階Hessian矩陣
10/06 01:09, 6F

10/06 01:09, , 7F
如果是負定的就是concave
10/06 01:09, 7F

10/06 01:18, , 8F
懇請解出第1.2大題是否concove或convex第一小題就好
10/06 01:18, 8F

10/06 01:32, , 9F
這題做二階Hessian還是看不出正負定,條件a和b太少了
10/06 01:32, 9F

10/06 01:37, , 10F
還有也沒有說在哪點上代值是正負,完全無法看出正負定
10/06 01:37, 10F

10/07 01:49, , 11F
若是把這題看成真的是在解經濟學的話
10/07 01:49, 11F

10/07 01:51, , 12F
通常這種Stone-Geary效用函數會假設0<p, q, r<1
10/07 01:51, 12F

10/07 01:52, , 13F
所以要請原PO去看看題目有沒有多做這假設或者p+q+r=1
10/07 01:52, 13F
文章代碼(AID): #1EZ6WlKJ (Math)