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Question: Constrained optimization

Question:Constrained optimization

pepe1000 4
constants derivative
September 25 2005
0
Hi, I am trying to solve a maximization problem using the following Lagrangean: L:=v*K*a^gamma*k^(1-gamma)-1/2*a^2-1/2*k^2 -1/2*r1*v^2*sigma^2-1/2*r2*(1-v)^2*sigma^2 -mu*(v*K*gamma*a^gamma*k^(1-gamma)/a-a) -lambda*((1-v)*K*(1-gamma)*a^gamma*k^(1-gamma)/k-k) I first computed the partial derivatives for a, k, v, mu and lambda (La:=diff(L,a)=0, Lk:=diff(L,k)=0, ...). (K, gamma, r1, r2 and sigma are constants) Then I applied solve ({La,Lk,...},{a,k,v,lambda,mu}) and did not get any result (or message) back. I already tried to solve this problem by step-by-step calculations, but was not successful in getting solutions for a, k and v (stated in terms of gamma, r and sigma). When I make the problem simpler (by setting r1:=0 and r2:=0) I get a solution. It would be great if someone could help me on this. Many thanks!
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