RE: Re: Simultaneous equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg25360] RE: [mg25331] Re: [mg25282] Simultaneous equations*From*: "peter lindsay" <pl10 at st-andrews.ac.uk>*Date*: Sun, 24 Sep 2000 03:01:29 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, At the start of the For loop, I think there is a missing { ( opening curly brace ) Peter Lindsay -----Original Message----- From: Richard Finley [mailto:rfinley at medicine.umsmed.edu] To: mathgroup at smc.vnet.net Subject: [mg25360] [mg25331] Re: [mg25282] Simultaneous equations Nick, Your code blows up because k(t) becomes less than zero and then you start getting complex roots for terms such as k(t)^a...that is terms such as (-.2)^.36 ; this then propatates to all your other terms since they mostly depend on k(t). How you handle that would depend on the details of your problem. regards..RF >>> "N.Tsotros" <travis at beackle.fsnet.co.uk> 09/19/00 01:45AM >>> Hi, The following problem may, at first sight, look like a "debugging" problem but, in fact, it is not. I'd therefore be very grateful if you could have a quick look at it. Consider the following simple code: g=0.983; d=0.1; dg=0.1; a=0.36; z=0.2; rtp=0.04; s=g/(1+rtp); prod=1; r[-1]=0.0434463; c[-1]=0.706982; y[-1]=0.604069; w[-1]=12.8993; h[-1]=10.4277; q[-1]=1.34837; k[-1]=2.36875; invgp[-1]=0.0943875; inv[-1]=0.236875; gp[-1]=0.943857; For[t=0, t<=400, t++, tp[t]=0.07, tc[t]=0.23, k[t]=y[t-1]+(1+r[t-1])*k[t-1]-c[t-1], gp[t]=invgp[t-1]+(1-dg)*gp[t-1], r[t]=a*(1-tp[t]-tc[t])*prod*(k[t]^(a-1))*(gp[t]^z)-d, q[t]=prod*(k[t]^a)*(gp[t]^z), y[t]=(1-a)*(1-tp[t]-tc[t])*prod*(k[t]^a)*(gp[t]^z), invgp[t]=tp[t]*q[t], h[t]=((1+r[t-1])*(h[t-1]-y[t-1]))/g, w[t]=h[t]+(1+r[t])*k[t], c[t]=(1-s)*w[t] }]; Print[" "] Print["q k gp "] Print["_________________"] For[t=-1, t<=400, t++, { var[t,1]=N[q[t]/q[-1],4], var[t,2]=N[k[t]/k[-1],4], var[t,3]=N[gp[t]/gp[-1],4], Print[var[t,1]," ",var[t,2]," ",var[t,3]] } ] I want to find how variables like q, k and gp evolve over time (400 periods), from t=0 to t=400. Running the program, however, I find that, after a few periods, the path (FOR loop) "explodes". The right transition path should produce a value of unity for all variables in each period t. Any ideas why is this so? The equations of the program are correct (checked n times, believe me!) so I wonder whether the problem arises simply because Mathematica cannot handle these sort of simultaneous calculations, ie. solving the 9 difference equations in the FOR loop simultaneously. Any help/reply would be greatly appreciated. Nick -----Original Message----- From: Richard Finley [mailto:rfinley at medicine.umsmed.edu] To: mathgroup at smc.vnet.net Subject: [mg25360] [mg25331] Re: [mg25282] Simultaneous equations Nick, Your code blows up because k(t) becomes less than zero and then you start getting complex roots for terms such as k(t)^a...that is terms such as (-.2)^.36 ; this then propatates to all your other terms since they mostly depend on k(t). How you handle that would depend on the details of your problem. regards..RF >>> "N.Tsotros" <travis at beackle.fsnet.co.uk> 09/19/00 01:45AM >>> Hi, The following problem may, at first sight, look like a "debugging" problem but, in fact, it is not. I'd therefore be very grateful if you could have a quick look at it. Consider the following simple code: g=0.983; d=0.1; dg=0.1; a=0.36; z=0.2; rtp=0.04; s=g/(1+rtp); prod=1; r[-1]=0.0434463; c[-1]=0.706982; y[-1]=0.604069; w[-1]=12.8993; h[-1]=10.4277; q[-1]=1.34837; k[-1]=2.36875; invgp[-1]=0.0943875; inv[-1]=0.236875; gp[-1]=0.943857; For[t=0, t<=400, t++, tp[t]=0.07, tc[t]=0.23, k[t]=y[t-1]+(1+r[t-1])*k[t-1]-c[t-1], gp[t]=invgp[t-1]+(1-dg)*gp[t-1], r[t]=a*(1-tp[t]-tc[t])*prod*(k[t]^(a-1))*(gp[t]^z)-d, q[t]=prod*(k[t]^a)*(gp[t]^z), y[t]=(1-a)*(1-tp[t]-tc[t])*prod*(k[t]^a)*(gp[t]^z), invgp[t]=tp[t]*q[t], h[t]=((1+r[t-1])*(h[t-1]-y[t-1]))/g, w[t]=h[t]+(1+r[t])*k[t], c[t]=(1-s)*w[t] }]; Print[" "] Print["q k gp "] Print["_________________"] For[t=-1, t<=400, t++, { var[t,1]=N[q[t]/q[-1],4], var[t,2]=N[k[t]/k[-1],4], var[t,3]=N[gp[t]/gp[-1],4], Print[var[t,1]," ",var[t,2]," ",var[t,3]] } ] I want to find how variables like q, k and gp evolve over time (400 periods), from t=0 to t=400. Running the program, however, I find that, after a few periods, the path (FOR loop) "explodes". The right transition path should produce a value of unity for all variables in each period t. Any ideas why is this so? The equations of the program are correct (checked n times, believe me!) so I wonder whether the problem arises simply because Mathematica cannot handle these sort of simultaneous calculations, ie. solving the 9 difference equations in the FOR loop simultaneously. Any help/reply would be greatly appreciated. Nick