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Solve and parametric nonlinear equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93771] Solve and parametric nonlinear equations
  • From: "alessandro tavoni" <atavoni at Princeton.EDU>
  • Date: Tue, 25 Nov 2008 07:18:28 -0500 (EST)

Hello, I am newbie to Mathematica 6, and I am having some difficulties with
Solve.



I have a two algebraic equations in two variables and two parameters and I
need to numerically solve the system over an interval of values for the
parameters.



When using Solve, I get the message: Solve::tdep: The equations appear to
involve the variables to be solved for in an essentially non-algebraic way.



I tried several alternative approaches, but no one worked. Findroot works
fine, but I need the symbolic solution since I am interested in the values
of the solutions when the parameters alfa and beta change. To simplify
matters, I assign a numerical value to lambda, but that's not enough to make
it analytically solvable apparently. Here's the code:  



\[Lambda] = .43

\!\(\*OverscriptBox["U1",

RowBox[{"\[IndentingNewLine]", "DifR"}]]\) = 14 - 6 \[Beta]



\!\(\*OverscriptBox["U1", "UifR"]\) = 4 - 18 \[Alpha]



\!\(\*OverscriptBox["U1", "UifL"]\) = 10 - 2 \[Alpha]



\!\(\*OverscriptBox["U1", "DifL"]\) = 9



\!\(\*OverscriptBox["U2", "LifD"]\) = 9



\!\(\*OverscriptBox["U2", "RifD"]\) = 8 - 6 \[Alpha]



\!\(\*OverscriptBox["U2", "RifU"]\) = 22 - 18 \[Beta]



\!\(\*OverscriptBox["U2", "LifU"]\) = 12 - 2 \[Beta]



eq1 = Pu == \[ExponentialE]^(\[Lambda] (

\!\(\*OverscriptBox["U1", "UifL"]\) Ql +

\!\(\*OverscriptBox["U1",

        "UifR"]\) (1 - Ql)))/(\[ExponentialE]^(\[Lambda] (

\!\(\*OverscriptBox["U1", "UifL"]\) Ql +

\!\(\*OverscriptBox["U1",

          "UifR"]\) (1 - Ql))) + \[ExponentialE]^(\[Lambda] (

\!\(\*OverscriptBox["U1", "DifL"]\) Ql +

\!\(\*OverscriptBox["U1", "DifR"]\) (1 - Ql))))

eq2 = Ql == \[ExponentialE]^(\[Lambda] (

\!\(\*OverscriptBox["U2", "LifU"]\) Pu +

\!\(\*OverscriptBox["U2",

        "LifD"]\) (1 - Pu)))/(\[ExponentialE]^(\[Lambda] (

\!\(\*OverscriptBox["U2", "LifU"]\) Pu +

\!\(\*OverscriptBox["U2",

          "LifD"]\) (1 - Pu))) + \[ExponentialE]^(\[Lambda] (

\!\(\*OverscriptBox["U2", "RifU"]\) Pu +

\!\(\*OverscriptBox["U2", "RifD"]\) (1 - Pu))))

Solve[{eq1, eq2}, {Pu, Ql}]



Any suggestions would be much appreciated,



Alessandro



--

Alessandro Tavoni

Ph.D. candidate

Advanced School of Economics, University of Venice "C=E0 Foscari"

 <http://venus.unive.it/alessandro.tavoni>
http://venus.unive.it/alessandro.tavoni

LevinLab member <http://www.eeb.princeton.edu/~slevin/Labdirectory.html> 
 at
Princeton University





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