system of equations

• To: mathgroup at smc.vnet.net
• Subject: [mg73340] system of equations
• From: Lena Calahorrano <lena.calahorrano at rwth-aachen.de>
• Date: Tue, 13 Feb 2007 06:55:24 -0500 (EST)

```Maybe someone can help me solving a system of equations:

I have two equations each of which depends on the the two variables =E2=80
=9Ckheute=E2=80=9D and =E2=80=9CMheute=E2=80=9D and I am interested in the
value of these two variables.

The equations look like this, where all parameters are known:

kheute=C5=A0l*(1/(1+n)*((1-a)*A*Part[f[t],1]^a*(b^2/f+b/f)-(1-a)*A*kheute^a
/(1+a*A*kheute^(a-1)-d))+1/(1+n)^2*b^2/f*((1-a)*A*Part[f[t],1]^a+(1+a*A*Part[f[t],1]^(a-1)-d)*(1-a)*A*Part[f[t-1],1]))/((2+n)/(1+n)+Mheute/bev)

kheute====l*(1/(1+An)*((1-a)*A*Part[Af[t],1]^a*(b^2/f+b/f)-(1-a)*A*kheute^a/(1+a*A*kheute^(a-1)-d))+1/(1+An)^2*b^2/f*((1-a)*A*Part[Af[t],1]^a+(1+a*A*Part[Af[t],1]^(a-1)-d)*(1-a)*A*Part[Af[t-1],1]))/((2+An)/(1+An)-Mheute/bevA)

I can express =E2=80=9Ckheute=E2=80=9D as a function of =E2=80=9CMheute=E2=80=9D, I can plot the two functions and see where they intersect:

solInland==Solve[Simplify[kheute=C5=A0l*(1/(1+n)*((1-a)*A*Part[f[t],1]^a*(b^2/f+b/f)-(1-a)*A*kheute^a/(1+a*A*kheute^(a-1)-d))+1/(1+n)^2*b^2/f*((1-a)*A*Part[f[t],1]^a+(1+a*A*Part[f[t],1]^(a-1)-d)*(1-a)*A*Part[f[t-1],1]))/((2+n)/(1+n)+Mheute/bev)],Mheute]

mInland==Part[Mheute/.solInland,1]

f[kheute_]:==mInland

grafikInland==Plot[f[kheute],{kheute,0.04,0.14},PlotStyle=C2=AE{RGBColor[1,0, 0.501961]}];

solAusland==Solve[Simplify[kheute====l*(1/(1+An)*((1-a)*A*Part[Af[t],1]^a*(b^2/f+b/f)-(1-a)*A*kheute^a/(1+a*A*kheute^(a-1)-d))+1/(1+An)^2*b^2/f*((1-a)*A*Part[Af[t],1]^a+(1+a*A*Part[Af[t],1]^(a-1)-d)*(1-a)*A*Part[Af[t-1],1]))/((2+An)/(1+An)-Mheute/bevA)],Mheute]

mAusland==Part[Mheute/.solAusland,1]

g[kheute_]:==mAusland

grafikAusland==Plot[g[kheute],{kheute,0.04,0.14}];

vergl==Show[grafikInland,grafikAusland];

But when I try to solve for =E2=80=9Ckheute=E2=80=9D, Mathematica runs forever. This is a problem because I eventually want to compute about 50 more steps.

Solve[Simplify[mInland=C5=A0mAusland],kheute]

Is there a better way to do this kind of computation?

Best regards,

Lena Calahorrano

Lena Calahorrano

Lehr- und Forschungsgebiet

Internationale Wirtschaftsbeziehungen

RWTH Aachen

Templergraben 64

52056 Aachen

0241-80-93934

lena.calahorrano at rwth-aachen.de
http://www.iw.rwth-aachen.de

```

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