<p>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 $R$ )</p>

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

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

<p>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. </p>

CC BY-SA 3.0
2015-08-14T18:21:10.973Z
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
CC BY-SA 3.0
2015-08-14T22:33:29.877Z
@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
CC BY-SA 3.0
2015-08-14T22:46:29.480Z
I see. Could you please also give the equations defining the dynamics of your two variable model?
Giskard
CC BY-SA 3.0
2015-08-15T02:32:09.597Z
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
CC BY-SA 3.0
2015-08-21T18:46:43.843Z
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
<simulations>
negative initial conditions in a growth model
optimal control
# negative initial conditions in a growth model

(Asked by: username_0 on 2015-08-14)

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.

**Tags:** simulations
> **Comments:**
> **username_1**: 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.  
> **username_0**: @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  
> **username_1**: I see. Could you please also give the equations defining the dynamics of your two variable model?  
> **username_2**: 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.  
> **username_0**: 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.  

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## 0 answers

