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I try to simulate a growth model with two state (capital $K$ and resource stock $S$) and two control variables. (consumption $C$ and resource extraction $R$ )

When I try to find steady state from which I could find after the initial conditions for $K_{0}$, $S_{0}$ and $R_{0}$ , $C_{0}$.

For $S_{0}=1$ I find a negative value for $K_{0}$ and all other initial conditions are positive.

Is that possible ? I think mathematically, a negative initial condition can be fine but economically I have doubts. I have found nothing about this issue on literature.

optimal control
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    I am having a difficult time interpreting this sentence: "When I try to find steady state from which I could find after the initial conditions for $K_{0}$, $S_{0}$ and $R_{0}$ , $C_{0}$." There seem to be some superfluous words but I also don't understand what steady states and initial conditions have to do with each other, except that you converge to one specific steady state from specific initial conditions. – Giskard Aug 14 '15 at 18:21
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    @denesp I first find numerical values for variables at steady state. After I multiply them by (1-10^-5) in order to have an approximate initial conditions. As my model is locally stable, I must find some specific initial values which will not be so far from steady state. This multiplication by (1-10^-5) could be a little bit sloppy at first but it has been also made by some other researchers in their numerical analysis. So, I think I am safe at this point.

    reference : http://www.cer.ethz.ch/resec/people/tsteger/econ_growth_math_ramsey.pdf

     – optimal control Aug 14 '15 at 22:33
  • I see. Could you please also give the equations defining the dynamics of your two variable model? – Giskard Aug 14 '15 at 22:46
  • By your second comment it appears that you are performing $$K_0 = K_{ss}\times(1-10^{-5})$$. If $K_{ss}>0$ how can the multiplication lead to negative values? If I misunderstood, please add content (equations, that is) in the question, they will provide more clear guidance than comments. – Alecos Papadopoulos Aug 15 '15 at 02:32
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    Sorry for my late response. Hopefully, I found initial conditions. I will edit my post with all details very soon in order to share the method with the stack exchange community. – optimal control Aug 21 '15 at 18:46

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