Two differential equations -- Need to find steady state values

[beaf123]

Homework Statement

I have found the two equations describing the system. They are.

ċ(t) = 1/θ [ f`(k(t)) -(n + δ + β)]c(t)
k̇(t) =f(k(t) - (n +d)k(t) - c(t)
Plugging in the numbers:
ċ(t) = 2 [ 0,25k^(-0,25) -(0,10)]c(t)
k̇(t) =k^0,25 - (0,6)k(t) - c(t)
Since ċ(t) and k̇(t) =0 in steady state ⇒
2 [ 0,25k^(-0,25) -(0,10)]c(t)=0
k̇(t) =k^0,25 - (0,6)k(t) - c(t)=0
So have do I solve this for K* and C*?
I have tried some algebra, but can`t get it to work.

Homework Equations

The Attempt at a Solution

 

[Asim Riaz]

To solve for the steady state values, we need to solve the two equations simultaneously.From the first equation, we can see that c(t) must be 0 in order for the equation to be satisfied.Plugging this into the second equation, we get:k̇(t) = k^0,25 - (0,6)k(t) = 0Solving this equation for k(t), we get:k* = 5^4Plugging this back into the first equation, we get:ċ(t) = 2 [ 0,25(5^4)^(-0,25) - (0,10)]c(t) = 0Solving this equation for c(t), we get:c* = 0Therefore, the steady state values are k* = 5^4 and c* = 0.