Re: a system of equations and Solve[ ]

• To: mathgroup at smc.vnet.net
• Subject: [mg13255] Re: [mg13138] a system of equations and Solve[ ]
• From: Jeffrey K Mackie-Mason <jmm at umich.edu>
• Date: Fri, 17 Jul 1998 03:17:49 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```On Mon, 13 Jul 1998, Jordan Milev wrote:

> 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.

You should get _Computational Economics and Finance_, Hal Varian ed.,
Springer-Verlag.  (You can find it from the Wolfram Web site, I
believe.)  There are chapters on using Mathematica for solving a wide
variety of  economic and finance problems.  Hal has a chapter on using
Mathematica to solve  basic micro problems and comparative statics --
he basically has this  problem as an example, as I recall (but probably
using CES, not  Cobb-Douglas utility).  The book includes a disk with
Mathematica programs and  functions to assist in doing this problem as
well as many others more  complex.

---
Prof. Jeff MacKie-Mason     http://www-personal.umich.edu/~jmm/ Dept. of
Economics and School      internet:      jmm at umich.edu
of Information
Univ. of Michigan                     phone:       313-647-4856 Ann
Arbor, MI 48109-1220                fax:       313-764-2475

```

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