
Economics Economics Forum  Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance 
 LinkBack  Thread Tools  Display Modes 
October 19th, 2013, 05:59 AM  #1 
Newbie Joined: Sep 2013 Posts: 4 Thanks: 0  is this function concave?
is (x1^2+x2^2)^1/2 a concave function? In the lecture today we were going through the lagrangian multiplier and the condition was that the utility function has to be concave. But when I check this function on a 3D graph the function seems convex? Am I missing something? 
October 28th, 2013, 08:57 AM  #2 
Newbie Joined: Oct 2013 Posts: 2 Thanks: 0  Re: is this function concave?
If I remember correctly: Concavity requires: Both second derivative negative and hessian determinant negative First derivatives x1*(x1^2+x2^2)^1/2 x2*(x1^2+x2^2)^1/2 Second derivatives (x1^2+x2^2)^1/2  x1^2(x1^2+x2^2)^3/2 (x1^2+x2^2)^1/2  x2^2(x1^2+x2^2)^3/2 Positive assuming Assuming x1,x2>0 which is a very natural. Then the second derivatives are positive and they thus don't qualify for a concave function. 

Tags 
concave, function 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Is this function concave?  AEcon  Algebra  1  October 20th, 2013 11:29 AM 
The Midpoint of a Concave Function  loveinla  Calculus  0  May 15th, 2013 06:56 AM 
Find Interval Where Function Concave Up  henoshaile  Calculus  4  October 29th, 2012 12:32 PM 
Concave Function of a Convex Function  swagatopablo  Algebra  0  October 10th, 2012 10:49 PM 
strict concave function  jefferson_lc  Calculus  1  June 12th, 2009 04:04 PM 