solving simple first order condition

• To: mathgroup at smc.vnet.net
• Subject: [mg54050] solving simple first order condition
• From: juejung <juejung at indiana.edu>
• Date: Wed, 9 Feb 2005 09:27:22 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi all,

I have the following problem with a simple First Order Condition (FOC) out
of an OLG model in Economics.

u[c_] := c^(1 - sigma)/(1 - sigma);
Ts[x_] := theta*x;
maxFun[se_] := u[(1 - tau)*w - s] + beta*u[R*s + Ts[R*s]];
der = FullSimplify[D[maxFun[s], s]]
sol = Solve[{der == 0}, {s}]

Why can't Mathematica solve this simple FOC when I can do it so easily by
hand.

If I use the FOC and replace the (1+theta) by Theta (capital theta) and do
the same Solve command, then it works (as shown in sol1 below) and I can
get a closed form solution.

sol1 = Solve[{(beta*R*Theta)/(R*s*Theta)^sigma -
(-s + w - tau*w)^(-sigma) == 0}, {s}]

I find it annoying that I apparently have to replace all (1+something)
expressions by a single variable (easy here, but cumbersome in more
involved models). Is there an easy simplify command hidden somewhere??

Best
Juergen
------------------
Juergen Jung
Indiana University
Bloomington, US

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```

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