An interesting situation in the Ramsey Cass Koopmans model.

(a) Consider the Ramsey Cass Koopmans model where k at time 0 (which as always the model takes as given) is at the golden-rule level: k(0) = kGR.

Sketch the paths of c and k.

(b) Consider the same initial situation as in part (a), but in the version of the model that includes government purchases. Assume that G is constant and equal G. Crucially, G is strictly less than f (kGR) − (n + g)kGR and strictly greater than f (k∗) − (n + g)k∗ (where k∗ is the level of k on the balanced growth path the economy would have if G were constant and equal to 0).
Sketch the paths of c and k. (Hint: This question is hard but can be answered by thinking things through slowly and carefully.)