Problem with Solve
- To: mathgroup at smc.vnet.net
- Subject: [mg45071] Problem with Solve
- From: Andreas Reinstaller <Andreas.Reinstaller at wu-wien.ac.at>
- Date: Mon, 15 Dec 2003 07:48:15 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
I have a bizarre Problem. In trying to run this standard economics
maximization problem Mathematica runs ad infinitum. Same if instead of
Solve I use NSolve. Same if I split up the problem in doing first the
partial derivatives etc. It is definitely a Solve/NSolve problem, but I
can't believe that it is not able to do this numerical stories on such a
standard problem with so well-behaved functions.
Foc[f_,x_]:=Map[(D[f,#]==0)&,x]
Parameters:
L=80; K=80; \alpha1= 3/4; \alpha2 = 1- \alpha1; \beta1 = 1/3; \beta2=1 -
\beta2;
Q1 = L1^\alpha1 K1^\alpha2
Q2 = (L-L1)^\beta1 (K-K1)^\beta2
R = pQ1 + Q2
Out = Flatten[Solve[FOC,[R,{L1,K1}],{K1,L1}]]
Curiously it works for \alpha1 = 2/3 but for \alpha1 = 3/4 as above, or any
other value such as \alpha1 = 0.7 \alpha2 = 0.3
I should be grateful if anybody could give me a hint on the sources of this
problem, and on how to be able to use any type of exponents.
Thanks,
Andreas
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