# How to derive and draw phase diagrams: Ramsey-Cass Koopmans model

I am confused by how to construct phase diagrams. For instance, I have been given the following two equations from the Ramsey model:

\begin{align*} \frac{\dot C}{C}=&\frac{1}{\gamma} (F_K(K) - \delta -\theta)\\ \\ \dot K =& F(K)= C- \delta K \end{align*}

But I do not get how to get from those equations to the standard phase diagram of the Ramsey model, with a C-K axis, and what looks like a downwards facing parabola for the equation of motion for k. I've looked through various online lecture notes for the model, and I'm usually okay with the algebraic manipulations. I can just never understand how it relates to the phase diagram picture. An intuitive explanation, or an perhaps reference to an introduction to phase diagrams which would explain it would be very much appreciated!

• Have you tried Wolfram Alpha? – Rodrigo de Azevedo Apr 8 at 20:44