Ramsey Cass Koopmans model.

$($a$)$ Consider the Ramsey Cass Koopmans model where $\mathrm{????}$ at time $0($which as always

the model takes as given$)$ is at the golden$-$rule level: $\mathrm{????}(0)=\mathrm{????}\mathrm{????}\mathrm{????}$

Sketch the paths of $\mathrm{????}$ and $\mathrm{????}.$

$($b$)$ Consider the same initial situation as in part $($a$),$ but in the version of the model

that includes government purchases. Assume that $\mathrm{????}$ is constant and equal $\frac{\text{b}\text{a}\text{r}}{}(\mathrm{????}).$

Crucially, $\frac{\text{b}\text{a}\text{r}}{}(\mathrm{????})\mathrm{????}$ is strictly less than $\mathrm{????}(\mathrm{????}\mathrm{????}\mathrm{????})-(\mathrm{????}+\mathrm{????})\mathrm{????}\mathrm{????}\mathrm{????}$ and strictly greater than $\mathrm{????}({\mathrm{????}}_{**})$

$(\mathrm{????}+\mathrm{????})\mathrm{????}**($where $\mathrm{????}**$ is the level of $\mathrm{????}$ on the balanced growth path the economy

would have if G were constant and equal to $0).$ Sketch the paths of $\mathrm{????}$ and $\mathrm{????}.$

I have repeated khis question. The last one I sent was not attended to$.$ Again, I am particularly

interested in the sketches. Can somebody walk me through?