Re: Simultaneous equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg25320] Re: Simultaneous equations*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Sat, 23 Sep 2000 03:35:45 -0400 (EDT)*Organization*: Universitaet Leipzig*References*: <8q75t1$sq4@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, I would be greatful if you would give the correct, original equations and not a pice of code without any comments. Before a difference equation can be solved a stability analysis should be done. Every book that deal with the numerical treatment of differential/difference equation has a chapter about the stability analysis *and* you should try to understand your equation *before* you use a computer. Mathematica can help you to solve the equations and make the stability analysis. I will pick only one of your equations, simplify it and show you that the equation is unstable > k[t]=y[t-1]+(1+r[t-1])*k[t-1]-c[t-1], To get a idea I simplify it to > k[t]=(1+r)*k[t-1] with constant r. The solution is k[t]=(1+r)^t k[0] since your r[0] >0 k[t]= (1+r)^t will quickly arrive a huge numerical value. This has *nothing* to do with Mathematica. If your "equations" come from a system of differential equations you have probably choosen a false (unstable) scheme to trun it into d difference equation. You should use NDSolve[] instead. BTW: Your For[] loop syntax is wrong. For[] has only 4 arguments and the last argument is the loop body. You have to write > 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] > ]; where does the last "}" come from ??? Mathematica can't handle invalid user input . Hope that helps Jens "N.Tsotros" wrote: > > 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