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MathGroup Archive 2002

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solving for variables in terms of other variables

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35719] solving for variables in terms of other variables
  • From: emilyhertzer at hotmail.com (Emily)
  • Date: Sat, 27 Jul 2002 06:43:25 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

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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