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a system of equations and Solve[ ]


I am trying to solve the following problem using Mathematica.  Define:

 utility := X^a*Y^b
 constraint := Income - Px*X - Py*Y
 maxutility := utility + lambda*constraint
 FOC1 := D[maxutility, X]
 FOC2 := D[maxutility, Y]
 FOC3 := D[maxutility, lambda]
 solutionset := Solve[{FOC1==0, FOC2==0, FOC3==0}, {X, Y, lambda}]

 I get a message:
 Solve::"tdep":
     "The equations appear to involve transcendental functions of the \
 variables in an essentially non-algebraic way."

 Can anybody help with advice on how to use Mathematica to solve this
system of three equations?  The system is solvable by hand in about 3-5
minutes.

 Jordan

 jgmilev at amherst.edu
 (please reply by email)



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