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MathGroup Archive 2002

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RE: solving for variables in terms of other variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35741] RE: [mg35719] solving for variables in terms of other variables
  • From: "DrBob" <majort at cox-internet.com>
  • Date: Sun, 28 Jul 2002 03:32:20 -0400 (EDT)
  • Reply-to: <drbob at bigfoot.com>
  • Sender: owner-wri-mathgroup at wolfram.com

Emily,

First of all, you want DSolve, not Solve.  Secondly, if you were using
Solve, its second argument is the list of variables you want to solve
for, and I don't think that's what you've listed below... aren't those
the parameters you want to solve in terms of?

Bobby

-----Original Message-----
From: Emily [mailto:emilyhertzer at hotmail.com] 
To: mathgroup at smc.vnet.net
Subject: [mg35741] [mg35719] solving for variables in terms of other variables

Hello!

I am using Mathematica 4.  I am attempting to solve simultaneously a
set of 6 first order conditions for six unknowns.  I have successfully
used the FindRoot command to solve for actual numerical values for the
six unknowns when all other variables in the six equations are
assigned to numeric values.  However, I would now like to solve for
the same six unknowns, this time solving them for expressions
including the other variables (not solving for numeric values).  I
have been trying to use the Solve command to do this but with no
success.  Mathematica comes to a stop when it reaches this line of the
code and, even after running for several hours, gives no result.  Am I
attempting the impossible?  The six first order conditions are fairly
complicated.
Here is an example:

*******

so1 = Exp[
      a1*v1 - b1*v1^2/2 - c*r1]/(1 + Exp[a1*v1 - b1*v1^2/2 - c*r1] + 
        Exp[a2*v2 - b2*v2^2/2 - c*r2] + Exp[a3*v3 - b3*v3^2/2 - c*r3])
so2 = Exp[
      a2*v1 - b2*v2^2/2 - c*r2]/(1 + Exp[a1*v1 - b1*v1^2/2 - c*r1] + 
        Exp[a2*v2 - b2*v2^2/2 - c*r2] + Exp[a3*v3 - b3*v3^2/2 - c*r3])
so3 = Exp[
      a3*v3 - b3*v3^2/2 - c*r3]/(1 + Exp[a1*v1 - b1*v1^2/2 - c*r1] + 
        Exp[a2*v2 - b2*v2^2/2 - c*r2] + Exp[a3*v3 - b3*v3^2/2 - c*r3])
so0 = 1 - so1 - so2 - so3
x1 = (a1 - b1*v1)/c
x2 = (a2 - b2*v2)/c
x3 = (a3 - b3*v3)/c
t1 = so1*(r1 - f1 - df1 + (v1 - k1 - dm1)*x1)
t2 = so2*(r2 - f2 - df2 + (v2 - k2 - dm2)*x2)
t3 = so3*(r3 - f3 - df3 + (v3 - k3 - dm3)*x3)
foc1v = D[t1, v1]
foc2v = D[t2, v2]
foc3v = D[t3, v3]
foc1r = D[t1, r1]
foc2r = D[t2, r2]
foc3r = D[t3, r3]
Solve[{foc1v == 0, foc2v == 0, foc3v == 0, foc1r == 0, foc2r == 0, 
    foc3r == 0}, {v1,v2,v3,r1,r2,r3}]

*******

Here I am hoping to solve {v1,v2,v3,r1,r2,r3} in terms of the f's and
k's.  Any suggestions?  Is Solve the correct command to use?
Thanks.  Any help would be greatly appreciated.





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