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.