April 10th, 2014, 08:49 AM  #1 
Newbie Joined: Apr 2014 From: Nottingham Posts: 1 Thanks: 0  KuhnTucker Conditions
I am using Matlab to solve a maximisation problem subject the the restriction that xi<=delta*TR(x1,x2). There are two lagrangians associated with my problem: L1=U1(x1,x2)+lambda1*(delta*TR(x1,x2)x1) L2=U2(x1,x2)+lambda2*(delta*TR(x1,x2)x2) I need to solve for the vector (x1,x2) I am investigating two cases: Case 1: The restriction is binding in both lagrangians i.e. xi=delta*TR(x1,x2) for i=1,2. The KuhnTucker conditions for this require that lambda1>0 and lambda2>0. Thus, I have four FOCS's: (i) dL1/dx1 (ii) dL1/dlambda1 (iii) dL2/dx2 (iv) dL2/dlambda2 Case (ii) The restriction xi<=delta*TR(x1,x2) is only binding in the first lagrangian (L1). The KuhnTucker conditions for this require that lambda1>0 and lambda2=0. My question is: How do I incorporate lambda1>0 and lambda2=0 into my system of equations? Do i need to drop one of the first order conditions? Or do I need to drop the lambda2(delta*TR(x1,x2)x2) term in the second lagrangian. 

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conditions, kuhntucker 
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