The balanced growth path of the model of Section 5.3.

Consider the model of Section 5.3 without any shocks. Let y∗, k∗, c∗, and G∗ denote the values of Y/(AL), K/(AL), C/(AL), and G/(AL) on the balanced growth path; w∗ the value of w/A; ∗ the value of L/N; and r∗ the value of r.

(a) Use equations (5.1) (5.4), (5.23), and (5.26) and the fact that y∗, k∗, c∗, w∗,

∗, and r∗ are constant on the balanced growth path to find six equations in these six variables. (Hint: The fact that c in [5.23] is consumption per person, C/N, and c∗ is the balanced-growth-path value of consumption per unit of effective labor, C/(AL), implies that c = c∗∗A on the balanced growth path.)

(b) Consider the parameter values assumed in Section 5.7.

What are the implied shares of consumption and investment in output on the balanced growth path? What is the implied ratio of capital to annual output on the balanced growth path?