Phase Diagram

The phase diagram plots actual investment $s f(\tilde{k})$ and break-even investment $(n + g + \delta)\tilde{k}$ against $\tilde{k}$. They intersect at the steady state $\tilde{k}^*$.

Actual investment $sf(k)$ is the fraction of output saved and invested. Break-even investment $(n+g+\delta)k$ is what must be invested to keep $k$ constant as capital depreciates and effective labour grows.

When $sf(k) > (n+g+\delta)k$: $\dot{k} > 0$, capital per worker rises. When $sf(k) < (n+g+\delta)k$: $\dot{k} < 0$, capital per worker falls. When equal: steady state $\dot{k} = 0$.