Consider the model of Section 3.2 with < 1. (a) On the balanced growth path, A = g A A(t), where g

Consider the model of Section 3.2 with θ < 1.

(a) On the balanced growth path, A = g ∗

A A(t), where g ∗

A is the balanced-growthpath value of gA. Use this fact and equation (3.6) to derive an expression for A(t) on the balanced growth path in terms of B, aL , γ , θ, and L(t).

(b) Use your answer to part

(a) and the production function, (3.5), to obtain an expression for Y(t) on the balanced growth path. Find the value of aL that maximizes output on the balanced growth path.