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